A Model Comparison for Count Data with a Positively Skewed Distribution with an Application to the Number of University Mathematics Courses Completed

ERIC Educational Resources Information Center

Liou, Pey-Yan

2009-01-01

The current study examines three regression models: OLS (ordinary least square) linear regression, Poisson regression, and negative binomial regression for analyzing count data. Simulation results show that the OLS regression model performed better than the others, since it did not produce more false statistically significant relationships than…

Applying Regression Analysis to Problems in Institutional Research.

ERIC Educational Resources Information Center

Bohannon, Tom R.

1988-01-01

Regression analysis is one of the most frequently used statistical techniques in institutional research. Principles of least squares, model building, residual analysis, influence statistics, and multi-collinearity are described and illustrated. (Author/MSE)

Online Statistical Modeling (Regression Analysis) for Independent Responses

NASA Astrophysics Data System (ADS)

Made Tirta, I.; Anggraeni, Dian; Pandutama, Martinus

2017-06-01

Regression analysis (statistical analmodelling) are among statistical methods which are frequently needed in analyzing quantitative data, especially to model relationship between response and explanatory variables. Nowadays, statistical models have been developed into various directions to model various type and complex relationship of data. Rich varieties of advanced and recent statistical modelling are mostly available on open source software (one of them is R). However, these advanced statistical modelling, are not very friendly to novice R users, since they are based on programming script or command line interface. Our research aims to developed web interface (based on R and shiny), so that most recent and advanced statistical modelling are readily available, accessible and applicable on web. We have previously made interface in the form of e-tutorial for several modern and advanced statistical modelling on R especially for independent responses (including linear models/LM, generalized linier models/GLM, generalized additive model/GAM and generalized additive model for location scale and shape/GAMLSS). In this research we unified them in the form of data analysis, including model using Computer Intensive Statistics (Bootstrap and Markov Chain Monte Carlo/ MCMC). All are readily accessible on our online Virtual Statistics Laboratory. The web (interface) make the statistical modeling becomes easier to apply and easier to compare them in order to find the most appropriate model for the data.

The Development and Demonstration of Multiple Regression Models for Operant Conditioning Questions.

ERIC Educational Resources Information Center

Fanning, Fred; Newman, Isadore

Based on the assumption that inferential statistics can make the operant conditioner more sensitive to possible significant relationships, regressions models were developed to test the statistical significance between slopes and Y intercepts of the experimental and control group subjects. These results were then compared to the traditional operant…

Assistive Technologies for Second-Year Statistics Students Who Are Blind

ERIC Educational Resources Information Center

Erhardt, Robert J.; Shuman, Michael P.

2015-01-01

At Wake Forest University, a student who is blind enrolled in a second course in statistics. The course covered simple and multiple regression, model diagnostics, model selection, data visualization, and elementary logistic regression. These topics required that the student both interpret and produce three sets of materials: mathematical writing,…

Regression Model Term Selection for the Analysis of Strain-Gage Balance Calibration Data

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred; Volden, Thomas R.

2010-01-01

The paper discusses the selection of regression model terms for the analysis of wind tunnel strain-gage balance calibration data. Different function class combinations are presented that may be used to analyze calibration data using either a non-iterative or an iterative method. The role of the intercept term in a regression model of calibration data is reviewed. In addition, useful algorithms and metrics originating from linear algebra and statistics are recommended that will help an analyst (i) to identify and avoid both linear and near-linear dependencies between regression model terms and (ii) to make sure that the selected regression model of the calibration data uses only statistically significant terms. Three different tests are suggested that may be used to objectively assess the predictive capability of the final regression model of the calibration data. These tests use both the original data points and regression model independent confirmation points. Finally, data from a simplified manual calibration of the Ames MK40 balance is used to illustrate the application of some of the metrics and tests to a realistic calibration data set.

New robust statistical procedures for the polytomous logistic regression models.

PubMed

Castilla, Elena; Ghosh, Abhik; Martin, Nirian; Pardo, Leandro

2018-05-17

This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications. © 2018, The International Biometric Society.

Regression Models and Fuzzy Logic Prediction of TBM Penetration Rate

NASA Astrophysics Data System (ADS)

Minh, Vu Trieu; Katushin, Dmitri; Antonov, Maksim; Veinthal, Renno

2017-03-01

This paper presents statistical analyses of rock engineering properties and the measured penetration rate of tunnel boring machine (TBM) based on the data of an actual project. The aim of this study is to analyze the influence of rock engineering properties including uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), rock brittleness index (BI), the distance between planes of weakness (DPW), and the alpha angle (Alpha) between the tunnel axis and the planes of weakness on the TBM rate of penetration (ROP). Four (4) statistical regression models (two linear and two nonlinear) are built to predict the ROP of TBM. Finally a fuzzy logic model is developed as an alternative method and compared to the four statistical regression models. Results show that the fuzzy logic model provides better estimations and can be applied to predict the TBM performance. The R-squared value (R2) of the fuzzy logic model scores the highest value of 0.714 over the second runner-up of 0.667 from the multiple variables nonlinear regression model.

Detection of outliers in the response and explanatory variables of the simple circular regression model

NASA Astrophysics Data System (ADS)

Mahmood, Ehab A.; Rana, Sohel; Hussin, Abdul Ghapor; Midi, Habshah

2016-06-01

The circular regression model may contain one or more data points which appear to be peculiar or inconsistent with the main part of the model. This may be occur due to recording errors, sudden short events, sampling under abnormal conditions etc. The existence of these data points "outliers" in the data set cause lot of problems in the research results and the conclusions. Therefore, we should identify them before applying statistical analysis. In this article, we aim to propose a statistic to identify outliers in the both of the response and explanatory variables of the simple circular regression model. Our proposed statistic is robust circular distance RCDxy and it is justified by the three robust measurements such as proportion of detection outliers, masking and swamping rates.

Predicting recreational water quality advisories: A comparison of statistical methods

USGS Publications Warehouse

Brooks, Wesley R.; Corsi, Steven R.; Fienen, Michael N.; Carvin, Rebecca B.

2016-01-01

Epidemiological studies indicate that fecal indicator bacteria (FIB) in beach water are associated with illnesses among people having contact with the water. In order to mitigate public health impacts, many beaches are posted with an advisory when the concentration of FIB exceeds a beach action value. The most commonly used method of measuring FIB concentration takes 18–24 h before returning a result. In order to avoid the 24 h lag, it has become common to ”nowcast” the FIB concentration using statistical regressions on environmental surrogate variables. Most commonly, nowcast models are estimated using ordinary least squares regression, but other regression methods from the statistical and machine learning literature are sometimes used. This study compares 14 regression methods across 7 Wisconsin beaches to identify which consistently produces the most accurate predictions. A random forest model is identified as the most accurate, followed by multiple regression fit using the adaptive LASSO.

Development of LACIE CCEA-1 weather/wheat yield models. [regression analysis

NASA Technical Reports Server (NTRS)

Strommen, N. D.; Sakamoto, C. M.; Leduc, S. K.; Umberger, D. E. (Principal Investigator)

1979-01-01

The advantages and disadvantages of the casual (phenological, dynamic, physiological), statistical regression, and analog approaches to modeling for grain yield are examined. Given LACIE's primary goal of estimating wheat production for the large areas of eight major wheat-growing regions, the statistical regression approach of correlating historical yield and climate data offered the Center for Climatic and Environmental Assessment the greatest potential return within the constraints of time and data sources. The basic equation for the first generation wheat-yield model is given. Topics discussed include truncation, trend variable, selection of weather variables, episodic events, strata selection, operational data flow, weighting, and model results.

The Equivalence of Regression Models Using Difference Scores and Models Using Separate Scores for Each Informant: Implications for the Study of Informant Discrepancies

ERIC Educational Resources Information Center

Laird, Robert D.; Weems, Carl F.

2011-01-01

Research on informant discrepancies has increasingly utilized difference scores. This article demonstrates the statistical equivalence of regression models using difference scores (raw or standardized) and regression models using separate scores for each informant to show that interpretations should be consistent with both models. First,…

Methods for calculating confidence and credible intervals for the residual between-study variance in random effects meta-regression models

PubMed Central

2014-01-01

Background Meta-regression is becoming increasingly used to model study level covariate effects. However this type of statistical analysis presents many difficulties and challenges. Here two methods for calculating confidence intervals for the magnitude of the residual between-study variance in random effects meta-regression models are developed. A further suggestion for calculating credible intervals using informative prior distributions for the residual between-study variance is presented. Methods Two recently proposed and, under the assumptions of the random effects model, exact methods for constructing confidence intervals for the between-study variance in random effects meta-analyses are extended to the meta-regression setting. The use of Generalised Cochran heterogeneity statistics is extended to the meta-regression setting and a Newton-Raphson procedure is developed to implement the Q profile method for meta-analysis and meta-regression. WinBUGS is used to implement informative priors for the residual between-study variance in the context of Bayesian meta-regressions. Results Results are obtained for two contrasting examples, where the first example involves a binary covariate and the second involves a continuous covariate. Intervals for the residual between-study variance are wide for both examples. Conclusions Statistical methods, and R computer software, are available to compute exact confidence intervals for the residual between-study variance under the random effects model for meta-regression. These frequentist methods are almost as easily implemented as their established counterparts for meta-analysis. Bayesian meta-regressions are also easily performed by analysts who are comfortable using WinBUGS. Estimates of the residual between-study variance in random effects meta-regressions should be routinely reported and accompanied by some measure of their uncertainty. Confidence and/or credible intervals are well-suited to this purpose. PMID:25196829

Newer classification and regression tree techniques: Bagging and Random Forests for ecological prediction

Treesearch

Anantha M. Prasad; Louis R. Iverson; Andy Liaw; Andy Liaw

2006-01-01

We evaluated four statistical models - Regression Tree Analysis (RTA), Bagging Trees (BT), Random Forests (RF), and Multivariate Adaptive Regression Splines (MARS) - for predictive vegetation mapping under current and future climate scenarios according to the Canadian Climate Centre global circulation model.

Hyperparameterization of soil moisture statistical models for North America with Ensemble Learning Models (Elm)

NASA Astrophysics Data System (ADS)

Steinberg, P. D.; Brener, G.; Duffy, D.; Nearing, G. S.; Pelissier, C.

2017-12-01

Hyperparameterization, of statistical models, i.e. automated model scoring and selection, such as evolutionary algorithms, grid searches, and randomized searches, can improve forecast model skill by reducing errors associated with model parameterization, model structure, and statistical properties of training data. Ensemble Learning Models (Elm), and the related Earthio package, provide a flexible interface for automating the selection of parameters and model structure for machine learning models common in climate science and land cover classification, offering convenient tools for loading NetCDF, HDF, Grib, or GeoTiff files, decomposition methods like PCA and manifold learning, and parallel training and prediction with unsupervised and supervised classification, clustering, and regression estimators. Continuum Analytics is using Elm to experiment with statistical soil moisture forecasting based on meteorological forcing data from NASA's North American Land Data Assimilation System (NLDAS). There Elm is using the NSGA-2 multiobjective optimization algorithm for optimizing statistical preprocessing of forcing data to improve goodness-of-fit for statistical models (i.e. feature engineering). This presentation will discuss Elm and its components, including dask (distributed task scheduling), xarray (data structures for n-dimensional arrays), and scikit-learn (statistical preprocessing, clustering, classification, regression), and it will show how NSGA-2 is being used for automate selection of soil moisture forecast statistical models for North America.

Patterns of medicinal plant use: an examination of the Ecuadorian Shuar medicinal flora using contingency table and binomial analyses.

PubMed

Bennett, Bradley C; Husby, Chad E

2008-03-28

Botanical pharmacopoeias are non-random subsets of floras, with some taxonomic groups over- or under-represented. Moerman [Moerman, D.E., 1979. Symbols and selectivity: a statistical analysis of Native American medical ethnobotany, Journal of Ethnopharmacology 1, 111-119] introduced linear regression/residual analysis to examine these patterns. However, regression, the commonly-employed analysis, suffers from several statistical flaws. We use contingency table and binomial analyses to examine patterns of Shuar medicinal plant use (from Amazonian Ecuador). We first analyzed the Shuar data using Moerman's approach, modified to better meet requirements of linear regression analysis. Second, we assessed the exact randomization contingency table test for goodness of fit. Third, we developed a binomial model to test for non-random selection of plants in individual families. Modified regression models (which accommodated assumptions of linear regression) reduced R(2) to from 0.59 to 0.38, but did not eliminate all problems associated with regression analyses. Contingency table analyses revealed that the entire flora departs from the null model of equal proportions of medicinal plants in all families. In the binomial analysis, only 10 angiosperm families (of 115) differed significantly from the null model. These 10 families are largely responsible for patterns seen at higher taxonomic levels. Contingency table and binomial analyses offer an easy and statistically valid alternative to the regression approach.

Numerical and Qualitative Contrasts of Two Statistical Models for Water Quality Change in Tidal Waters

EPA Science Inventory

Two statistical approaches, weighted regression on time, discharge, and season and generalized additive models, have recently been used to evaluate water quality trends in estuaries. Both models have been used in similar contexts despite differences in statistical foundations and...

Regression: The Apple Does Not Fall Far From the Tree.

PubMed

Vetter, Thomas R; Schober, Patrick

2018-05-15

Researchers and clinicians are frequently interested in either: (1) assessing whether there is a relationship or association between 2 or more variables and quantifying this association; or (2) determining whether 1 or more variables can predict another variable. The strength of such an association is mainly described by the correlation. However, regression analysis and regression models can be used not only to identify whether there is a significant relationship or association between variables but also to generate estimations of such a predictive relationship between variables. This basic statistical tutorial discusses the fundamental concepts and techniques related to the most common types of regression analysis and modeling, including simple linear regression, multiple regression, logistic regression, ordinal regression, and Poisson regression, as well as the common yet often underrecognized phenomenon of regression toward the mean. The various types of regression analysis are powerful statistical techniques, which when appropriately applied, can allow for the valid interpretation of complex, multifactorial data. Regression analysis and models can assess whether there is a relationship or association between 2 or more observed variables and estimate the strength of this association, as well as determine whether 1 or more variables can predict another variable. Regression is thus being applied more commonly in anesthesia, perioperative, critical care, and pain research. However, it is crucial to note that regression can identify plausible risk factors; it does not prove causation (a definitive cause and effect relationship). The results of a regression analysis instead identify independent (predictor) variable(s) associated with the dependent (outcome) variable. As with other statistical methods, applying regression requires that certain assumptions be met, which can be tested with specific diagnostics.

Detecting influential observations in nonlinear regression modeling of groundwater flow

USGS Publications Warehouse

Yager, Richard M.

1998-01-01

Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

Methods for estimating the magnitude and frequency of peak streamflows at ungaged sites in and near the Oklahoma Panhandle

USGS Publications Warehouse

Smith, S. Jerrod; Lewis, Jason M.; Graves, Grant M.

2015-09-28

Generalized-least-squares multiple-linear regression analysis was used to formulate regression relations between peak-streamflow frequency statistics and basin characteristics. Contributing drainage area was the only basin characteristic determined to be statistically significant for all percentage of annual exceedance probabilities and was the only basin characteristic used in regional regression equations for estimating peak-streamflow frequency statistics on unregulated streams in and near the Oklahoma Panhandle. The regression model pseudo-coefficient of determination, converted to percent, for the Oklahoma Panhandle regional regression equations ranged from about 38 to 63 percent. The standard errors of prediction and the standard model errors for the Oklahoma Panhandle regional regression equations ranged from about 84 to 148 percent and from about 76 to 138 percent, respectively. These errors were comparable to those reported for regional peak-streamflow frequency regression equations for the High Plains areas of Texas and Colorado. The root mean square errors for the Oklahoma Panhandle regional regression equations (ranging from 3,170 to 92,000 cubic feet per second) were less than the root mean square errors for the Oklahoma statewide regression equations (ranging from 18,900 to 412,000 cubic feet per second); therefore, the Oklahoma Panhandle regional regression equations produce more accurate peak-streamflow statistic estimates for the irrigated period of record in the Oklahoma Panhandle than do the Oklahoma statewide regression equations. The regression equations developed in this report are applicable to streams that are not substantially affected by regulation, impoundment, or surface-water withdrawals. These regression equations are intended for use for stream sites with contributing drainage areas less than or equal to about 2,060 square miles, the maximum value for the independent variable used in the regression analysis.

Estimating multilevel logistic regression models when the number of clusters is low: a comparison of different statistical software procedures.

PubMed

Austin, Peter C

2010-04-22

Multilevel logistic regression models are increasingly being used to analyze clustered data in medical, public health, epidemiological, and educational research. Procedures for estimating the parameters of such models are available in many statistical software packages. There is currently little evidence on the minimum number of clusters necessary to reliably fit multilevel regression models. We conducted a Monte Carlo study to compare the performance of different statistical software procedures for estimating multilevel logistic regression models when the number of clusters was low. We examined procedures available in BUGS, HLM, R, SAS, and Stata. We found that there were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low. Among the likelihood-based procedures, estimation methods based on adaptive Gauss-Hermite approximations to the likelihood (glmer in R and xtlogit in Stata) or adaptive Gaussian quadrature (Proc NLMIXED in SAS) tended to have superior performance for estimating variance components when the number of clusters was small, compared to software procedures based on penalized quasi-likelihood. However, only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters. For all statistical software procedures, estimation of variance components tended to be poor when there were only five subjects per cluster, regardless of the number of clusters.

A new statistical approach to climate change detection and attribution

NASA Astrophysics Data System (ADS)

Ribes, Aurélien; Zwiers, Francis W.; Azaïs, Jean-Marc; Naveau, Philippe

2017-01-01

We propose here a new statistical approach to climate change detection and attribution that is based on additive decomposition and simple hypothesis testing. Most current statistical methods for detection and attribution rely on linear regression models where the observations are regressed onto expected response patterns to different external forcings. These methods do not use physical information provided by climate models regarding the expected response magnitudes to constrain the estimated responses to the forcings. Climate modelling uncertainty is difficult to take into account with regression based methods and is almost never treated explicitly. As an alternative to this approach, our statistical model is only based on the additivity assumption; the proposed method does not regress observations onto expected response patterns. We introduce estimation and testing procedures based on likelihood maximization, and show that climate modelling uncertainty can easily be accounted for. Some discussion is provided on how to practically estimate the climate modelling uncertainty based on an ensemble of opportunity. Our approach is based on the " models are statistically indistinguishable from the truth" paradigm, where the difference between any given model and the truth has the same distribution as the difference between any pair of models, but other choices might also be considered. The properties of this approach are illustrated and discussed based on synthetic data. Lastly, the method is applied to the linear trend in global mean temperature over the period 1951-2010. Consistent with the last IPCC assessment report, we find that most of the observed warming over this period (+0.65 K) is attributable to anthropogenic forcings (+0.67 ± 0.12 K, 90 % confidence range), with a very limited contribution from natural forcings (-0.01± 0.02 K).

Modelling nitrate pollution pressure using a multivariate statistical approach: the case of Kinshasa groundwater body, Democratic Republic of Congo

NASA Astrophysics Data System (ADS)

Mfumu Kihumba, Antoine; Ndembo Longo, Jean; Vanclooster, Marnik

2016-03-01

A multivariate statistical modelling approach was applied to explain the anthropogenic pressure of nitrate pollution on the Kinshasa groundwater body (Democratic Republic of Congo). Multiple regression and regression tree models were compared and used to identify major environmental factors that control the groundwater nitrate concentration in this region. The analyses were made in terms of physical attributes related to the topography, land use, geology and hydrogeology in the capture zone of different groundwater sampling stations. For the nitrate data, groundwater datasets from two different surveys were used. The statistical models identified the topography, the residential area, the service land (cemetery), and the surface-water land-use classes as major factors explaining nitrate occurrence in the groundwater. Also, groundwater nitrate pollution depends not on one single factor but on the combined influence of factors representing nitrogen loading sources and aquifer susceptibility characteristics. The groundwater nitrate pressure was better predicted with the regression tree model than with the multiple regression model. Furthermore, the results elucidated the sensitivity of the model performance towards the method of delineation of the capture zones. For pollution modelling at the monitoring points, therefore, it is better to identify capture-zone shapes based on a conceptual hydrogeological model rather than to adopt arbitrary circular capture zones.

Spatial Statistical Network Models for Stream and River Temperature in the Chesapeake Bay Watershed, USA

EPA Science Inventory

Regional temperature models are needed for characterizing and mapping stream thermal regimes, establishing reference conditions, predicting future impacts and identifying critical thermal refugia. Spatial statistical models have been developed to improve regression modeling techn...

A Constrained Linear Estimator for Multiple Regression

ERIC Educational Resources Information Center

Davis-Stober, Clintin P.; Dana, Jason; Budescu, David V.

2010-01-01

"Improper linear models" (see Dawes, Am. Psychol. 34:571-582, "1979"), such as equal weighting, have garnered interest as alternatives to standard regression models. We analyze the general circumstances under which these models perform well by recasting a class of "improper" linear models as "proper" statistical models with a single predictor. We…

Validation of a heteroscedastic hazards regression model.

PubMed

Wu, Hong-Dar Isaac; Hsieh, Fushing; Chen, Chen-Hsin

2002-03-01

A Cox-type regression model accommodating heteroscedasticity, with a power factor of the baseline cumulative hazard, is investigated for analyzing data with crossing hazards behavior. Since the approach of partial likelihood cannot eliminate the baseline hazard, an overidentified estimating equation (OEE) approach is introduced in the estimation procedure. It by-product, a model checking statistic, is presented to test for the overall adequacy of the heteroscedastic model. Further, under the heteroscedastic model setting, we propose two statistics to test the proportional hazards assumption. Implementation of this model is illustrated in a data analysis of a cancer clinical trial.

[Quantitative structure-gas chromatographic retention relationship of polycyclic aromatic sulfur heterocycles using molecular electronegativity-distance vector].

PubMed

Li, Zhenghua; Cheng, Fansheng; Xia, Zhining

2011-01-01

The chemical structures of 114 polycyclic aromatic sulfur heterocycles (PASHs) have been studied by molecular electronegativity-distance vector (MEDV). The linear relationships between gas chromatographic retention index and the MEDV have been established by a multiple linear regression (MLR) model. The results of variable selection by stepwise multiple regression (SMR) and the powerful predictive abilities of the optimization model appraised by leave-one-out cross-validation showed that the optimization model with the correlation coefficient (R) of 0.994 7 and the cross-validated correlation coefficient (Rcv) of 0.994 0 possessed the best statistical quality. Furthermore, when the 114 PASHs compounds were divided into calibration and test sets in the ratio of 2:1, the statistical analysis showed our models possesses almost equal statistical quality, the very similar regression coefficients and the good robustness. The quantitative structure-retention relationship (QSRR) model established may provide a convenient and powerful method for predicting the gas chromatographic retention of PASHs.

Obscure phenomena in statistical analysis of quantitative structure-activity relationships. Part 1: Multicollinearity of physicochemical descriptors.

PubMed

Mager, P P; Rothe, H

1990-10-01

Multicollinearity of physicochemical descriptors leads to serious consequences in quantitative structure-activity relationship (QSAR) analysis, such as incorrect estimators and test statistics of regression coefficients of the ordinary least-squares (OLS) model applied usually to QSARs. Beside the diagnosis of the known simple collinearity, principal component regression analysis (PCRA) also allows the diagnosis of various types of multicollinearity. Only if the absolute values of PCRA estimators are order statistics that decrease monotonically, the effects of multicollinearity can be circumvented. Otherwise, obscure phenomena may be observed, such as good data recognition but low predictive model power of a QSAR model.

Correlation and simple linear regression.

PubMed

Eberly, Lynn E

2007-01-01

This chapter highlights important steps in using correlation and simple linear regression to address scientific questions about the association of two continuous variables with each other. These steps include estimation and inference, assessing model fit, the connection between regression and ANOVA, and study design. Examples in microbiology are used throughout. This chapter provides a framework that is helpful in understanding more complex statistical techniques, such as multiple linear regression, linear mixed effects models, logistic regression, and proportional hazards regression.

Multivariate Regression Analysis and Slaughter Livestock,

DTIC Science & Technology

AGRICULTURE, *ECONOMICS), (*MEAT, PRODUCTION), MULTIVARIATE ANALYSIS, REGRESSION ANALYSIS , ANIMALS, WEIGHT, COSTS, PREDICTIONS, STABILITY, MATHEMATICAL MODELS, STORAGE, BEEF, PORK, FOOD, STATISTICAL DATA, ACCURACY

Using "Excel" for White's Test--An Important Technique for Evaluating the Equality of Variance Assumption and Model Specification in a Regression Analysis

ERIC Educational Resources Information Center

Berenson, Mark L.

2013-01-01

There is consensus in the statistical literature that severe departures from its assumptions invalidate the use of regression modeling for purposes of inference. The assumptions of regression modeling are usually evaluated subjectively through visual, graphic displays in a residual analysis but such an approach, taken alone, may be insufficient…

Statistical downscaling of precipitation using long short-term memory recurrent neural networks

NASA Astrophysics Data System (ADS)

Misra, Saptarshi; Sarkar, Sudeshna; Mitra, Pabitra

2017-11-01

Hydrological impacts of global climate change on regional scale are generally assessed by downscaling large-scale climatic variables, simulated by General Circulation Models (GCMs), to regional, small-scale hydrometeorological variables like precipitation, temperature, etc. In this study, we propose a new statistical downscaling model based on Recurrent Neural Network with Long Short-Term Memory which captures the spatio-temporal dependencies in local rainfall. The previous studies have used several other methods such as linear regression, quantile regression, kernel regression, beta regression, and artificial neural networks. Deep neural networks and recurrent neural networks have been shown to be highly promising in modeling complex and highly non-linear relationships between input and output variables in different domains and hence we investigated their performance in the task of statistical downscaling. We have tested this model on two datasets—one on precipitation in Mahanadi basin in India and the second on precipitation in Campbell River basin in Canada. Our autoencoder coupled long short-term memory recurrent neural network model performs the best compared to other existing methods on both the datasets with respect to temporal cross-correlation, mean squared error, and capturing the extremes.

Detection of crossover time scales in multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Ge, Erjia; Leung, Yee

2013-04-01

Fractal is employed in this paper as a scale-based method for the identification of the scaling behavior of time series. Many spatial and temporal processes exhibiting complex multi(mono)-scaling behaviors are fractals. One of the important concepts in fractals is crossover time scale(s) that separates distinct regimes having different fractal scaling behaviors. A common method is multifractal detrended fluctuation analysis (MF-DFA). The detection of crossover time scale(s) is, however, relatively subjective since it has been made without rigorous statistical procedures and has generally been determined by eye balling or subjective observation. Crossover time scales such determined may be spurious and problematic. It may not reflect the genuine underlying scaling behavior of a time series. The purpose of this paper is to propose a statistical procedure to model complex fractal scaling behaviors and reliably identify the crossover time scales under MF-DFA. The scaling-identification regression model, grounded on a solid statistical foundation, is first proposed to describe multi-scaling behaviors of fractals. Through the regression analysis and statistical inference, we can (1) identify the crossover time scales that cannot be detected by eye-balling observation, (2) determine the number and locations of the genuine crossover time scales, (3) give confidence intervals for the crossover time scales, and (4) establish the statistically significant regression model depicting the underlying scaling behavior of a time series. To substantive our argument, the regression model is applied to analyze the multi-scaling behaviors of avian-influenza outbreaks, water consumption, daily mean temperature, and rainfall of Hong Kong. Through the proposed model, we can have a deeper understanding of fractals in general and a statistical approach to identify multi-scaling behavior under MF-DFA in particular.

Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

ERIC Educational Resources Information Center

Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

2013-01-01

In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

Introduction to the use of regression models in epidemiology.

PubMed

Bender, Ralf

2009-01-01

Regression modeling is one of the most important statistical techniques used in analytical epidemiology. By means of regression models the effect of one or several explanatory variables (e.g., exposures, subject characteristics, risk factors) on a response variable such as mortality or cancer can be investigated. From multiple regression models, adjusted effect estimates can be obtained that take the effect of potential confounders into account. Regression methods can be applied in all epidemiologic study designs so that they represent a universal tool for data analysis in epidemiology. Different kinds of regression models have been developed in dependence on the measurement scale of the response variable and the study design. The most important methods are linear regression for continuous outcomes, logistic regression for binary outcomes, Cox regression for time-to-event data, and Poisson regression for frequencies and rates. This chapter provides a nontechnical introduction to these regression models with illustrating examples from cancer research.

Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.

PubMed

Faul, Franz; Erdfelder, Edgar; Buchner, Axel; Lang, Albert-Georg

2009-11-01

G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.

Evaluation of three statistical prediction models for forensic age prediction based on DNA methylation.

PubMed

Smeers, Inge; Decorte, Ronny; Van de Voorde, Wim; Bekaert, Bram

2018-05-01

DNA methylation is a promising biomarker for forensic age prediction. A challenge that has emerged in recent studies is the fact that prediction errors become larger with increasing age due to interindividual differences in epigenetic ageing rates. This phenomenon of non-constant variance or heteroscedasticity violates an assumption of the often used method of ordinary least squares (OLS) regression. The aim of this study was to evaluate alternative statistical methods that do take heteroscedasticity into account in order to provide more accurate, age-dependent prediction intervals. A weighted least squares (WLS) regression is proposed as well as a quantile regression model. Their performances were compared against an OLS regression model based on the same dataset. Both models provided age-dependent prediction intervals which account for the increasing variance with age, but WLS regression performed better in terms of success rate in the current dataset. However, quantile regression might be a preferred method when dealing with a variance that is not only non-constant, but also not normally distributed. Ultimately the choice of which model to use should depend on the observed characteristics of the data. Copyright © 2018 Elsevier B.V. All rights reserved.

External Tank Liquid Hydrogen (LH2) Prepress Regression Analysis Independent Review Technical Consultation Report

NASA Technical Reports Server (NTRS)

Parsons, Vickie s.

2009-01-01

The request to conduct an independent review of regression models, developed for determining the expected Launch Commit Criteria (LCC) External Tank (ET)-04 cycle count for the Space Shuttle ET tanking process, was submitted to the NASA Engineering and Safety Center NESC on September 20, 2005. The NESC team performed an independent review of regression models documented in Prepress Regression Analysis, Tom Clark and Angela Krenn, 10/27/05. This consultation consisted of a peer review by statistical experts of the proposed regression models provided in the Prepress Regression Analysis. This document is the consultation's final report.

Statistical analysis of water-quality data containing multiple detection limits: S-language software for regression on order statistics

USGS Publications Warehouse

Lee, L.; Helsel, D.

2005-01-01

Trace contaminants in water, including metals and organics, often are measured at sufficiently low concentrations to be reported only as values below the instrument detection limit. Interpretation of these "less thans" is complicated when multiple detection limits occur. Statistical methods for multiply censored, or multiple-detection limit, datasets have been developed for medical and industrial statistics, and can be employed to estimate summary statistics or model the distributions of trace-level environmental data. We describe S-language-based software tools that perform robust linear regression on order statistics (ROS). The ROS method has been evaluated as one of the most reliable procedures for developing summary statistics of multiply censored data. It is applicable to any dataset that has 0 to 80% of its values censored. These tools are a part of a software library, or add-on package, for the R environment for statistical computing. This library can be used to generate ROS models and associated summary statistics, plot modeled distributions, and predict exceedance probabilities of water-quality standards. ?? 2005 Elsevier Ltd. All rights reserved.

The relationship between the C-statistic of a risk-adjustment model and the accuracy of hospital report cards: a Monte Carlo Study.

PubMed

Austin, Peter C; Reeves, Mathew J

2013-03-01

Hospital report cards, in which outcomes following the provision of medical or surgical care are compared across health care providers, are being published with increasing frequency. Essential to the production of these reports is risk-adjustment, which allows investigators to account for differences in the distribution of patient illness severity across different hospitals. Logistic regression models are frequently used for risk adjustment in hospital report cards. Many applied researchers use the c-statistic (equivalent to the area under the receiver operating characteristic curve) of the logistic regression model as a measure of the credibility and accuracy of hospital report cards. To determine the relationship between the c-statistic of a risk-adjustment model and the accuracy of hospital report cards. Monte Carlo simulations were used to examine this issue. We examined the influence of 3 factors on the accuracy of hospital report cards: the c-statistic of the logistic regression model used for risk adjustment, the number of hospitals, and the number of patients treated at each hospital. The parameters used to generate the simulated datasets came from analyses of patients hospitalized with a diagnosis of acute myocardial infarction in Ontario, Canada. The c-statistic of the risk-adjustment model had, at most, a very modest impact on the accuracy of hospital report cards, whereas the number of patients treated at each hospital had a much greater impact. The c-statistic of a risk-adjustment model should not be used to assess the accuracy of a hospital report card.

The relationship between the c-statistic of a risk-adjustment model and the accuracy of hospital report cards: A Monte Carlo study

PubMed Central

Austin, Peter C.; Reeves, Mathew J.

2015-01-01

Background Hospital report cards, in which outcomes following the provision of medical or surgical care are compared across health care providers, are being published with increasing frequency. Essential to the production of these reports is risk-adjustment, which allows investigators to account for differences in the distribution of patient illness severity across different hospitals. Logistic regression models are frequently used for risk-adjustment in hospital report cards. Many applied researchers use the c-statistic (equivalent to the area under the receiver operating characteristic curve) of the logistic regression model as a measure of the credibility and accuracy of hospital report cards. Objectives To determine the relationship between the c-statistic of a risk-adjustment model and the accuracy of hospital report cards. Research Design Monte Carlo simulations were used to examine this issue. We examined the influence of three factors on the accuracy of hospital report cards: the c-statistic of the logistic regression model used for risk-adjustment, the number of hospitals, and the number of patients treated at each hospital. The parameters used to generate the simulated datasets came from analyses of patients hospitalized with a diagnosis of acute myocardial infarction in Ontario, Canada. Results The c-statistic of the risk-adjustment model had, at most, a very modest impact on the accuracy of hospital report cards, whereas the number of patients treated at each hospital had a much greater impact. Conclusions The c-statistic of a risk-adjustment model should not be used to assess the accuracy of a hospital report card. PMID:23295579

SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression *

PubMed Central

Sun, Qiang; Zhu, Hongtu; Liu, Yufeng; Ibrahim, Joseph G.

2014-01-01

The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling’s T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods. PMID:26527844

Testing homogeneity in Weibull-regression models.

PubMed

Bolfarine, Heleno; Valença, Dione M

2005-10-01

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data.

Short-term Forecasting of the Prevalence of Trachoma: Expert Opinion, Statistical Regression, versus Transmission Models

PubMed Central

Liu, Fengchen; Porco, Travis C.; Amza, Abdou; Kadri, Boubacar; Nassirou, Baido; West, Sheila K.; Bailey, Robin L.; Keenan, Jeremy D.; Solomon, Anthony W.; Emerson, Paul M.; Gambhir, Manoj; Lietman, Thomas M.

2015-01-01

Background Trachoma programs rely on guidelines made in large part using expert opinion of what will happen with and without intervention. Large community-randomized trials offer an opportunity to actually compare forecasting methods in a masked fashion. Methods The Program for the Rapid Elimination of Trachoma trials estimated longitudinal prevalence of ocular chlamydial infection from 24 communities treated annually with mass azithromycin. Given antibiotic coverage and biannual assessments from baseline through 30 months, forecasts of the prevalence of infection in each of the 24 communities at 36 months were made by three methods: the sum of 15 experts’ opinion, statistical regression of the square-root-transformed prevalence, and a stochastic hidden Markov model of infection transmission (Susceptible-Infectious-Susceptible, or SIS model). All forecasters were masked to the 36-month results and to the other forecasts. Forecasts of the 24 communities were scored by the likelihood of the observed results and compared using Wilcoxon’s signed-rank statistic. Findings Regression and SIS hidden Markov models had significantly better likelihood than community expert opinion (p = 0.004 and p = 0.01, respectively). All forecasts scored better when perturbed to decrease Fisher’s information. Each individual expert’s forecast was poorer than the sum of experts. Interpretation Regression and SIS models performed significantly better than expert opinion, although all forecasts were overly confident. Further model refinements may score better, although would need to be tested and compared in new masked studies. Construction of guidelines that rely on forecasting future prevalence could consider use of mathematical and statistical models. PMID:26302380

Short-term Forecasting of the Prevalence of Trachoma: Expert Opinion, Statistical Regression, versus Transmission Models.

PubMed

Liu, Fengchen; Porco, Travis C; Amza, Abdou; Kadri, Boubacar; Nassirou, Baido; West, Sheila K; Bailey, Robin L; Keenan, Jeremy D; Solomon, Anthony W; Emerson, Paul M; Gambhir, Manoj; Lietman, Thomas M

2015-08-01

Trachoma programs rely on guidelines made in large part using expert opinion of what will happen with and without intervention. Large community-randomized trials offer an opportunity to actually compare forecasting methods in a masked fashion. The Program for the Rapid Elimination of Trachoma trials estimated longitudinal prevalence of ocular chlamydial infection from 24 communities treated annually with mass azithromycin. Given antibiotic coverage and biannual assessments from baseline through 30 months, forecasts of the prevalence of infection in each of the 24 communities at 36 months were made by three methods: the sum of 15 experts' opinion, statistical regression of the square-root-transformed prevalence, and a stochastic hidden Markov model of infection transmission (Susceptible-Infectious-Susceptible, or SIS model). All forecasters were masked to the 36-month results and to the other forecasts. Forecasts of the 24 communities were scored by the likelihood of the observed results and compared using Wilcoxon's signed-rank statistic. Regression and SIS hidden Markov models had significantly better likelihood than community expert opinion (p = 0.004 and p = 0.01, respectively). All forecasts scored better when perturbed to decrease Fisher's information. Each individual expert's forecast was poorer than the sum of experts. Regression and SIS models performed significantly better than expert opinion, although all forecasts were overly confident. Further model refinements may score better, although would need to be tested and compared in new masked studies. Construction of guidelines that rely on forecasting future prevalence could consider use of mathematical and statistical models. Clinicaltrials.gov NCT00792922.

Watershed Regressions for Pesticides (WARP) for Predicting Annual Maximum and Annual Maximum Moving-Average Concentrations of Atrazine in Streams

USGS Publications Warehouse

Stone, Wesley W.; Gilliom, Robert J.; Crawford, Charles G.

2008-01-01

Regression models were developed for predicting annual maximum and selected annual maximum moving-average concentrations of atrazine in streams using the Watershed Regressions for Pesticides (WARP) methodology developed by the National Water-Quality Assessment Program (NAWQA) of the U.S. Geological Survey (USGS). The current effort builds on the original WARP models, which were based on the annual mean and selected percentiles of the annual frequency distribution of atrazine concentrations. Estimates of annual maximum and annual maximum moving-average concentrations for selected durations are needed to characterize the levels of atrazine and other pesticides for comparison to specific water-quality benchmarks for evaluation of potential concerns regarding human health or aquatic life. Separate regression models were derived for the annual maximum and annual maximum 21-day, 60-day, and 90-day moving-average concentrations. Development of the regression models used the same explanatory variables, transformations, model development data, model validation data, and regression methods as those used in the original development of WARP. The models accounted for 72 to 75 percent of the variability in the concentration statistics among the 112 sampling sites used for model development. Predicted concentration statistics from the four models were within a factor of 10 of the observed concentration statistics for most of the model development and validation sites. Overall, performance of the models for the development and validation sites supports the application of the WARP models for predicting annual maximum and selected annual maximum moving-average atrazine concentration in streams and provides a framework to interpret the predictions in terms of uncertainty. For streams with inadequate direct measurements of atrazine concentrations, the WARP model predictions for the annual maximum and the annual maximum moving-average atrazine concentrations can be used to characterize the probable levels of atrazine for comparison to specific water-quality benchmarks. Sites with a high probability of exceeding a benchmark for human health or aquatic life can be prioritized for monitoring.

INTRODUCTION TO A COMBINED MULTIPLE LINEAR REGRESSION AND ARMA MODELING APPROACH FOR BEACH BACTERIA PREDICTION

EPA Science Inventory

Due to the complexity of the processes contributing to beach bacteria concentrations, many researchers rely on statistical modeling, among which multiple linear regression (MLR) modeling is most widely used. Despite its ease of use and interpretation, there may be time dependence...

Advanced statistics: linear regression, part II: multiple linear regression.

PubMed

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Evaluating the utility of companion animal tick surveillance practices for monitoring spread and occurrence of human Lyme disease in West Virginia, 2014-2016.

PubMed

Hendricks, Brian; Mark-Carew, Miguella; Conley, Jamison

2017-11-13

Domestic dogs and cats are potentially effective sentinel populations for monitoring occurrence and spread of Lyme disease. Few studies have evaluated the public health utility of sentinel programmes using geo-analytic approaches. Confirmed Lyme disease cases diagnosed by physicians and ticks submitted by veterinarians to the West Virginia State Health Department were obtained for 2014-2016. Ticks were identified to species, and only Ixodes scapularis were incorporated in the analysis. Separate ordinary least squares (OLS) and spatial lag regression models were conducted to estimate the association between average numbers of Ix. scapularis collected on pets and human Lyme disease incidence. Regression residuals were visualised using Local Moran's I as a diagnostic tool to identify spatial dependence. Statistically significant associations were identified between average numbers of Ix. scapularis collected from dogs and human Lyme disease in the OLS (β=20.7, P<0.001) and spatial lag (β=12.0, P=0.002) regression. No significant associations were identified for cats in either regression model. Statistically significant (P≤0.05) spatial dependence was identified in all regression models. Local Moran's I maps produced for spatial lag regression residuals indicated a decrease in model over- and under-estimation, but identified a higher number of statistically significant outliers than OLS regression. Results support previous conclusions that dogs are effective sentinel populations for monitoring risk of human exposure to Lyme disease. Findings reinforce the utility of spatial analysis of surveillance data, and highlight West Virginia's unique position within the eastern United States in regards to Lyme disease occurrence.

Generalized linear and generalized additive models in studies of species distributions: Setting the scene

USGS Publications Warehouse

Guisan, Antoine; Edwards, T.C.; Hastie, T.

2002-01-01

An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we introduce a series of papers prepared within the framework of an international workshop entitled: Advances in GLMs/GAMs modeling: from species distribution to environmental management, held in Riederalp, Switzerland, 6-11 August 2001. We first discuss some general uses of statistical models in ecology, as well as provide a short review of several key examples of the use of GLMs and GAMs in ecological modeling efforts. We next present an overview of GLMs and GAMs, and discuss some of their related statistics used for predictor selection, model diagnostics, and evaluation. Included is a discussion of several new approaches applicable to GLMs and GAMs, such as ridge regression, an alternative to stepwise selection of predictors, and methods for the identification of interactions by a combined use of regression trees and several other approaches. We close with an overview of the papers and how we feel they advance our understanding of their application to ecological modeling. ?? 2002 Elsevier Science B.V. All rights reserved.

Statistical power to detect violation of the proportional hazards assumption when using the Cox regression model.

PubMed

Austin, Peter C

2018-01-01

The use of the Cox proportional hazards regression model is widespread. A key assumption of the model is that of proportional hazards. Analysts frequently test the validity of this assumption using statistical significance testing. However, the statistical power of such assessments is frequently unknown. We used Monte Carlo simulations to estimate the statistical power of two different methods for detecting violations of this assumption. When the covariate was binary, we found that a model-based method had greater power than a method based on cumulative sums of martingale residuals. Furthermore, the parametric nature of the distribution of event times had an impact on power when the covariate was binary. Statistical power to detect a strong violation of the proportional hazards assumption was low to moderate even when the number of observed events was high. In many data sets, power to detect a violation of this assumption is likely to be low to modest.

Statistical power to detect violation of the proportional hazards assumption when using the Cox regression model

PubMed Central

Austin, Peter C.

2017-01-01

The use of the Cox proportional hazards regression model is widespread. A key assumption of the model is that of proportional hazards. Analysts frequently test the validity of this assumption using statistical significance testing. However, the statistical power of such assessments is frequently unknown. We used Monte Carlo simulations to estimate the statistical power of two different methods for detecting violations of this assumption. When the covariate was binary, we found that a model-based method had greater power than a method based on cumulative sums of martingale residuals. Furthermore, the parametric nature of the distribution of event times had an impact on power when the covariate was binary. Statistical power to detect a strong violation of the proportional hazards assumption was low to moderate even when the number of observed events was high. In many data sets, power to detect a violation of this assumption is likely to be low to modest. PMID:29321694

An Investigation of the Fit of Linear Regression Models to Data from an SAT[R] Validity Study. Research Report 2011-3

ERIC Educational Resources Information Center

Kobrin, Jennifer L.; Sinharay, Sandip; Haberman, Shelby J.; Chajewski, Michael

2011-01-01

This study examined the adequacy of a multiple linear regression model for predicting first-year college grade point average (FYGPA) using SAT[R] scores and high school grade point average (HSGPA). A variety of techniques, both graphical and statistical, were used to examine if it is possible to improve on the linear regression model. The results…

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression.

PubMed

Chen, Yanguang

2016-01-01

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson's statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran's index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China's regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test.

Comparison and validation of statistical methods for predicting power outage durations in the event of hurricanes.

PubMed

Nateghi, Roshanak; Guikema, Seth D; Quiring, Steven M

2011-12-01

This article compares statistical methods for modeling power outage durations during hurricanes and examines the predictive accuracy of these methods. Being able to make accurate predictions of power outage durations is valuable because the information can be used by utility companies to plan their restoration efforts more efficiently. This information can also help inform customers and public agencies of the expected outage times, enabling better collective response planning, and coordination of restoration efforts for other critical infrastructures that depend on electricity. In the long run, outage duration estimates for future storm scenarios may help utilities and public agencies better allocate risk management resources to balance the disruption from hurricanes with the cost of hardening power systems. We compare the out-of-sample predictive accuracy of five distinct statistical models for estimating power outage duration times caused by Hurricane Ivan in 2004. The methods compared include both regression models (accelerated failure time (AFT) and Cox proportional hazard models (Cox PH)) and data mining techniques (regression trees, Bayesian additive regression trees (BART), and multivariate additive regression splines). We then validate our models against two other hurricanes. Our results indicate that BART yields the best prediction accuracy and that it is possible to predict outage durations with reasonable accuracy. © 2011 Society for Risk Analysis.

Semisupervised Clustering by Iterative Partition and Regression with Neuroscience Applications

PubMed Central

Qian, Guoqi; Wu, Yuehua; Ferrari, Davide; Qiao, Puxue; Hollande, Frédéric

2016-01-01

Regression clustering is a mixture of unsupervised and supervised statistical learning and data mining method which is found in a wide range of applications including artificial intelligence and neuroscience. It performs unsupervised learning when it clusters the data according to their respective unobserved regression hyperplanes. The method also performs supervised learning when it fits regression hyperplanes to the corresponding data clusters. Applying regression clustering in practice requires means of determining the underlying number of clusters in the data, finding the cluster label of each data point, and estimating the regression coefficients of the model. In this paper, we review the estimation and selection issues in regression clustering with regard to the least squares and robust statistical methods. We also provide a model selection based technique to determine the number of regression clusters underlying the data. We further develop a computing procedure for regression clustering estimation and selection. Finally, simulation studies are presented for assessing the procedure, together with analyzing a real data set on RGB cell marking in neuroscience to illustrate and interpret the method. PMID:27212939

Strengthening the Regression Discontinuity Design Using Additional Design Elements: A Within-Study Comparison

ERIC Educational Resources Information Center

Wing, Coady; Cook, Thomas D.

2013-01-01

The sharp regression discontinuity design (RDD) has three key weaknesses compared to the randomized clinical trial (RCT). It has lower statistical power, it is more dependent on statistical modeling assumptions, and its treatment effect estimates are limited to the narrow subpopulation of cases immediately around the cutoff, which is rarely of…

Assessing risk factors for periodontitis using regression

NASA Astrophysics Data System (ADS)

Lobo Pereira, J. A.; Ferreira, Maria Cristina; Oliveira, Teresa

2013-10-01

Multivariate statistical analysis is indispensable to assess the associations and interactions between different factors and the risk of periodontitis. Among others, regression analysis is a statistical technique widely used in healthcare to investigate and model the relationship between variables. In our work we study the impact of socio-demographic, medical and behavioral factors on periodontal health. Using regression, linear and logistic models, we can assess the relevance, as risk factors for periodontitis disease, of the following independent variables (IVs): Age, Gender, Diabetic Status, Education, Smoking status and Plaque Index. The multiple linear regression analysis model was built to evaluate the influence of IVs on mean Attachment Loss (AL). Thus, the regression coefficients along with respective p-values will be obtained as well as the respective p-values from the significance tests. The classification of a case (individual) adopted in the logistic model was the extent of the destruction of periodontal tissues defined by an Attachment Loss greater than or equal to 4 mm in 25% (AL≥4mm/≥25%) of sites surveyed. The association measures include the Odds Ratios together with the correspondent 95% confidence intervals.

Using Logistic Regression To Predict the Probability of Debris Flows Occurring in Areas Recently Burned By Wildland Fires

USGS Publications Warehouse

Rupert, Michael G.; Cannon, Susan H.; Gartner, Joseph E.

2003-01-01

Logistic regression was used to predict the probability of debris flows occurring in areas recently burned by wildland fires. Multiple logistic regression is conceptually similar to multiple linear regression because statistical relations between one dependent variable and several independent variables are evaluated. In logistic regression, however, the dependent variable is transformed to a binary variable (debris flow did or did not occur), and the actual probability of the debris flow occurring is statistically modeled. Data from 399 basins located within 15 wildland fires that burned during 2000-2002 in Colorado, Idaho, Montana, and New Mexico were evaluated. More than 35 independent variables describing the burn severity, geology, land surface gradient, rainfall, and soil properties were evaluated. The models were developed as follows: (1) Basins that did and did not produce debris flows were delineated from National Elevation Data using a Geographic Information System (GIS). (2) Data describing the burn severity, geology, land surface gradient, rainfall, and soil properties were determined for each basin. These data were then downloaded to a statistics software package for analysis using logistic regression. (3) Relations between the occurrence/non-occurrence of debris flows and burn severity, geology, land surface gradient, rainfall, and soil properties were evaluated and several preliminary multivariate logistic regression models were constructed. All possible combinations of independent variables were evaluated to determine which combination produced the most effective model. The multivariate model that best predicted the occurrence of debris flows was selected. (4) The multivariate logistic regression model was entered into a GIS, and a map showing the probability of debris flows was constructed. The most effective model incorporates the percentage of each basin with slope greater than 30 percent, percentage of land burned at medium and high burn severity in each basin, particle size sorting, average storm intensity (millimeters per hour), soil organic matter content, soil permeability, and soil drainage. The results of this study demonstrate that logistic regression is a valuable tool for predicting the probability of debris flows occurring in recently-burned landscapes.

Comparing Regression Coefficients between Nested Linear Models for Clustered Data with Generalized Estimating Equations

ERIC Educational Resources Information Center

Yan, Jun; Aseltine, Robert H., Jr.; Harel, Ofer

2013-01-01

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

Predicting risk for portal vein thrombosis in acute pancreatitis patients: A comparison of radical basis function artificial neural network and logistic regression models.

PubMed

Fei, Yang; Hu, Jian; Gao, Kun; Tu, Jianfeng; Li, Wei-Qin; Wang, Wei

2017-06-01

To construct a radical basis function (RBF) artificial neural networks (ANNs) model to predict the incidence of acute pancreatitis (AP)-induced portal vein thrombosis. The analysis included 353 patients with AP who had admitted between January 2011 and December 2015. RBF ANNs model and logistic regression model were constructed based on eleven factors relevant to AP respectively. Statistical indexes were used to evaluate the value of the prediction in two models. The predict sensitivity, specificity, positive predictive value, negative predictive value and accuracy by RBF ANNs model for PVT were 73.3%, 91.4%, 68.8%, 93.0% and 87.7%, respectively. There were significant differences between the RBF ANNs and logistic regression models in these parameters (P<0.05). In addition, a comparison of the area under receiver operating characteristic curves of the two models showed a statistically significant difference (P<0.05). The RBF ANNs model is more likely to predict the occurrence of PVT induced by AP than logistic regression model. D-dimer, AMY, Hct and PT were important prediction factors of approval for AP-induced PVT. Copyright © 2017 Elsevier Inc. All rights reserved.

SOME STATISTICAL ISSUES RELATED TO MULTIPLE LINEAR REGRESSION MODELING OF BEACH BACTERIA CONCENTRATIONS

EPA Science Inventory

As a fast and effective technique, the multiple linear regression (MLR) method has been widely used in modeling and prediction of beach bacteria concentrations. Among previous works on this subject, however, several issues were insufficiently or inconsistently addressed. Those is...

Detection of Cutting Tool Wear using Statistical Analysis and Regression Model

NASA Astrophysics Data System (ADS)

Ghani, Jaharah A.; Rizal, Muhammad; Nuawi, Mohd Zaki; Haron, Che Hassan Che; Ramli, Rizauddin

2010-10-01

This study presents a new method for detecting the cutting tool wear based on the measured cutting force signals. A statistical-based method called Integrated Kurtosis-based Algorithm for Z-Filter technique, called I-kaz was used for developing a regression model and 3D graphic presentation of I-kaz 3D coefficient during machining process. The machining tests were carried out using a CNC turning machine Colchester Master Tornado T4 in dry cutting condition. A Kistler 9255B dynamometer was used to measure the cutting force signals, which were transmitted, analyzed, and displayed in the DasyLab software. Various force signals from machining operation were analyzed, and each has its own I-kaz 3D coefficient. This coefficient was examined and its relationship with flank wear lands (VB) was determined. A regression model was developed due to this relationship, and results of the regression model shows that the I-kaz 3D coefficient value decreases as tool wear increases. The result then is used for real time tool wear monitoring.

Predicting lettuce canopy photosynthesis with statistical and neural network models

NASA Technical Reports Server (NTRS)

Frick, J.; Precetti, C.; Mitchell, C. A.

1998-01-01

An artificial neural network (NN) and a statistical regression model were developed to predict canopy photosynthetic rates (Pn) for 'Waldman's Green' leaf lettuce (Latuca sativa L.). All data used to develop and test the models were collected for crop stands grown hydroponically and under controlled-environment conditions. In the NN and regression models, canopy Pn was predicted as a function of three independent variables: shootzone CO2 concentration (600 to 1500 micromoles mol-1), photosynthetic photon flux (PPF) (600 to 1100 micromoles m-2 s-1), and canopy age (10 to 20 days after planting). The models were used to determine the combinations of CO2 and PPF setpoints required each day to maintain maximum canopy Pn. The statistical model (a third-order polynomial) predicted Pn more accurately than the simple NN (a three-layer, fully connected net). Over an 11-day validation period, average percent difference between predicted and actual Pn was 12.3% and 24.6% for the statistical and NN models, respectively. Both models lost considerable accuracy when used to determine relatively long-range Pn predictions (> or = 6 days into the future).

A generalized right truncated bivariate Poisson regression model with applications to health data.

PubMed

Islam, M Ataharul; Chowdhury, Rafiqul I

2017-01-01

A generalized right truncated bivariate Poisson regression model is proposed in this paper. Estimation and tests for goodness of fit and over or under dispersion are illustrated for both untruncated and right truncated bivariate Poisson regression models using marginal-conditional approach. Estimation and test procedures are illustrated for bivariate Poisson regression models with applications to Health and Retirement Study data on number of health conditions and the number of health care services utilized. The proposed test statistics are easy to compute and it is evident from the results that the models fit the data very well. A comparison between the right truncated and untruncated bivariate Poisson regression models using the test for nonnested models clearly shows that the truncated model performs significantly better than the untruncated model.

A generalized right truncated bivariate Poisson regression model with applications to health data

PubMed Central

Islam, M. Ataharul; Chowdhury, Rafiqul I.

2017-01-01

A generalized right truncated bivariate Poisson regression model is proposed in this paper. Estimation and tests for goodness of fit and over or under dispersion are illustrated for both untruncated and right truncated bivariate Poisson regression models using marginal-conditional approach. Estimation and test procedures are illustrated for bivariate Poisson regression models with applications to Health and Retirement Study data on number of health conditions and the number of health care services utilized. The proposed test statistics are easy to compute and it is evident from the results that the models fit the data very well. A comparison between the right truncated and untruncated bivariate Poisson regression models using the test for nonnested models clearly shows that the truncated model performs significantly better than the untruncated model. PMID:28586344

An adaptive two-stage analog/regression model for probabilistic prediction of small-scale precipitation in France

NASA Astrophysics Data System (ADS)

Chardon, Jérémy; Hingray, Benoit; Favre, Anne-Catherine

2018-01-01

Statistical downscaling models (SDMs) are often used to produce local weather scenarios from large-scale atmospheric information. SDMs include transfer functions which are based on a statistical link identified from observations between local weather and a set of large-scale predictors. As physical processes driving surface weather vary in time, the most relevant predictors and the regression link are likely to vary in time too. This is well known for precipitation for instance and the link is thus often estimated after some seasonal stratification of the data. In this study, we present a two-stage analog/regression model where the regression link is estimated from atmospheric analogs of the current prediction day. Atmospheric analogs are identified from fields of geopotential heights at 1000 and 500 hPa. For the regression stage, two generalized linear models are further used to model the probability of precipitation occurrence and the distribution of non-zero precipitation amounts, respectively. The two-stage model is evaluated for the probabilistic prediction of small-scale precipitation over France. It noticeably improves the skill of the prediction for both precipitation occurrence and amount. As the analog days vary from one prediction day to another, the atmospheric predictors selected in the regression stage and the value of the corresponding regression coefficients can vary from one prediction day to another. The model allows thus for a day-to-day adaptive and tailored downscaling. It can also reveal specific predictors for peculiar and non-frequent weather configurations.

Modelling of binary logistic regression for obesity among secondary students in a rural area of Kedah

NASA Astrophysics Data System (ADS)

Kamaruddin, Ainur Amira; Ali, Zalila; Noor, Norlida Mohd.; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

2014-07-01

Logistic regression analysis examines the influence of various factors on a dichotomous outcome by estimating the probability of the event's occurrence. Logistic regression, also called a logit model, is a statistical procedure used to model dichotomous outcomes. In the logit model the log odds of the dichotomous outcome is modeled as a linear combination of the predictor variables. The log odds ratio in logistic regression provides a description of the probabilistic relationship of the variables and the outcome. In conducting logistic regression, selection procedures are used in selecting important predictor variables, diagnostics are used to check that assumptions are valid which include independence of errors, linearity in the logit for continuous variables, absence of multicollinearity, and lack of strongly influential outliers and a test statistic is calculated to determine the aptness of the model. This study used the binary logistic regression model to investigate overweight and obesity among rural secondary school students on the basis of their demographics profile, medical history, diet and lifestyle. The results indicate that overweight and obesity of students are influenced by obesity in family and the interaction between a student's ethnicity and routine meals intake. The odds of a student being overweight and obese are higher for a student having a family history of obesity and for a non-Malay student who frequently takes routine meals as compared to a Malay student.

Nowcasting of Low-Visibility Procedure States with Ordered Logistic Regression at Vienna International Airport

NASA Astrophysics Data System (ADS)

Kneringer, Philipp; Dietz, Sebastian; Mayr, Georg J.; Zeileis, Achim

2017-04-01

Low-visibility conditions have a large impact on aviation safety and economic efficiency of airports and airlines. To support decision makers, we develop a statistical probabilistic nowcasting tool for the occurrence of capacity-reducing operations related to low visibility. The probabilities of four different low visibility classes are predicted with an ordered logistic regression model based on time series of meteorological point measurements. Potential predictor variables for the statistical models are visibility, humidity, temperature and wind measurements at several measurement sites. A stepwise variable selection method indicates that visibility and humidity measurements are the most important model inputs. The forecasts are tested with a 30 minute forecast interval up to two hours, which is a sufficient time span for tactical planning at Vienna Airport. The ordered logistic regression models outperform persistence and are competitive with human forecasters.

Additive hazards regression and partial likelihood estimation for ecological monitoring data across space.

PubMed

Lin, Feng-Chang; Zhu, Jun

2012-01-01

We develop continuous-time models for the analysis of environmental or ecological monitoring data such that subjects are observed at multiple monitoring time points across space. Of particular interest are additive hazards regression models where the baseline hazard function can take on flexible forms. We consider time-varying covariates and take into account spatial dependence via autoregression in space and time. We develop statistical inference for the regression coefficients via partial likelihood. Asymptotic properties, including consistency and asymptotic normality, are established for parameter estimates under suitable regularity conditions. Feasible algorithms utilizing existing statistical software packages are developed for computation. We also consider a simpler additive hazards model with homogeneous baseline hazard and develop hypothesis testing for homogeneity. A simulation study demonstrates that the statistical inference using partial likelihood has sound finite-sample properties and offers a viable alternative to maximum likelihood estimation. For illustration, we analyze data from an ecological study that monitors bark beetle colonization of red pines in a plantation of Wisconsin.

Quantifying the statistical importance of utilizing regression over classic energy intensity calculations for tracking efficiency improvements in industry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nimbalkar, Sachin U.; Wenning, Thomas J.; Guo, Wei

In the United States, manufacturing facilities account for about 32% of total domestic energy consumption in 2014. Robust energy tracking methodologies are critical to understanding energy performance in manufacturing facilities. Due to its simplicity and intuitiveness, the classic energy intensity method (i.e. the ratio of total energy use over total production) is the most widely adopted. However, the classic energy intensity method does not take into account the variation of other relevant parameters (i.e. product type, feed stock type, weather, etc.). Furthermore, the energy intensity method assumes that the facilities’ base energy consumption (energy use at zero production) is zero,more » which rarely holds true. Therefore, it is commonly recommended to utilize regression models rather than the energy intensity approach for tracking improvements at the facility level. Unfortunately, many energy managers have difficulties understanding why regression models are statistically better than utilizing the classic energy intensity method. While anecdotes and qualitative information may convince some, many have major reservations about the accuracy of regression models and whether it is worth the time and effort to gather data and build quality regression models. This paper will explain why regression models are theoretically and quantitatively more accurate for tracking energy performance improvements. Based on the analysis of data from 114 manufacturing plants over 12 years, this paper will present quantitative results on the importance of utilizing regression models over the energy intensity methodology. This paper will also document scenarios where regression models do not have significant relevance over the energy intensity method.« less

Estimation of variance in Cox's regression model with shared gamma frailties.

PubMed

Andersen, P K; Klein, J P; Knudsen, K M; Tabanera y Palacios, R

1997-12-01

The Cox regression model with a shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. Estimation in this model when the frailties are assumed to follow a gamma distribution is reviewed, and we address the problem of obtaining variance estimates for regression coefficients, frailty parameter, and cumulative baseline hazards using the observed nonparametric information matrix. A number of examples are given comparing this approach with fully parametric inference in models with piecewise constant baseline hazards.

Does transport time help explain the high trauma mortality rates in rural areas? New and traditional predictors assessed by new and traditional statistical methods

PubMed Central

Røislien, Jo; Lossius, Hans Morten; Kristiansen, Thomas

2015-01-01

Background Trauma is a leading global cause of death. Trauma mortality rates are higher in rural areas, constituting a challenge for quality and equality in trauma care. The aim of the study was to explore population density and transport time to hospital care as possible predictors of geographical differences in mortality rates, and to what extent choice of statistical method might affect the analytical results and accompanying clinical conclusions. Methods Using data from the Norwegian Cause of Death registry, deaths from external causes 1998–2007 were analysed. Norway consists of 434 municipalities, and municipality population density and travel time to hospital care were entered as predictors of municipality mortality rates in univariate and multiple regression models of increasing model complexity. We fitted linear regression models with continuous and categorised predictors, as well as piecewise linear and generalised additive models (GAMs). Models were compared using Akaike's information criterion (AIC). Results Population density was an independent predictor of trauma mortality rates, while the contribution of transport time to hospital care was highly dependent on choice of statistical model. A multiple GAM or piecewise linear model was superior, and similar, in terms of AIC. However, while transport time was statistically significant in multiple models with piecewise linear or categorised predictors, it was not in GAM or standard linear regression. Conclusions Population density is an independent predictor of trauma mortality rates. The added explanatory value of transport time to hospital care is marginal and model-dependent, highlighting the importance of exploring several statistical models when studying complex associations in observational data. PMID:25972600

The Application of Censored Regression Models in Low Streamflow Analyses

NASA Astrophysics Data System (ADS)

Kroll, C.; Luz, J.

2003-12-01

Estimation of low streamflow statistics at gauged and ungauged river sites is often a daunting task. This process is further confounded by the presence of intermittent streamflows, where streamflow is sometimes reported as zero, within a region. Streamflows recorded as zero may be zero, or may be less than the measurement detection limit. Such data is often referred to as censored data. Numerous methods have been developed to characterize intermittent streamflow series. Logit regression has been proposed to develop regional models of the probability annual lowflows series (such as 7-day lowflows) are zero. In addition, Tobit regression, a method of regression that allows for censored dependent variables, has been proposed for lowflow regional regression models in regions where the lowflow statistic of interest estimated as zero at some sites in the region. While these methods have been proposed, their use in practice has been limited. Here a delete-one jackknife simulation is presented to examine the performance of Logit and Tobit models of 7-day annual minimum flows in 6 USGS water resource regions in the United States. For the Logit model, an assessment is made of whether sites are correctly classified as having at least 10% of 7-day annual lowflows equal to zero. In such a situation, the 7-day, 10-year lowflow (Q710), a commonly employed low streamflow statistic, would be reported as zero. For the Tobit model, a comparison is made between results from the Tobit model, and from performing either ordinary least squares (OLS) or principal component regression (PCR) after the zero sites are dropped from the analysis. Initial results for the Logit model indicate this method to have a high probability of correctly classifying sites into groups with Q710s as zero and non-zero. Initial results also indicate the Tobit model produces better results than PCR and OLS when more than 5% of the sites in the region have Q710 values calculated as zero.

Estimating current and future streamflow characteristics at ungaged sites, central and eastern Montana, with application to evaluating effects of climate change on fish populations

USGS Publications Warehouse

Sando, Roy; Chase, Katherine J.

2017-03-23

A common statistical procedure for estimating streamflow statistics at ungaged locations is to develop a relational model between streamflow and drainage basin characteristics at gaged locations using least squares regression analysis; however, least squares regression methods are parametric and make constraining assumptions about the data distribution. The random forest regression method provides an alternative nonparametric method for estimating streamflow characteristics at ungaged sites and requires that the data meet fewer statistical conditions than least squares regression methods.Random forest regression analysis was used to develop predictive models for 89 streamflow characteristics using Precipitation-Runoff Modeling System simulated streamflow data and drainage basin characteristics at 179 sites in central and eastern Montana. The predictive models were developed from streamflow data simulated for current (baseline, water years 1982–99) conditions and three future periods (water years 2021–38, 2046–63, and 2071–88) under three different climate-change scenarios. These predictive models were then used to predict streamflow characteristics for baseline conditions and three future periods at 1,707 fish sampling sites in central and eastern Montana. The average root mean square error for all predictive models was about 50 percent. When streamflow predictions at 23 fish sampling sites were compared to nearby locations with simulated data, the mean relative percent difference was about 43 percent. When predictions were compared to streamflow data recorded at 21 U.S. Geological Survey streamflow-gaging stations outside of the calibration basins, the average mean absolute percent error was about 73 percent.

Potential pitfalls when denoising resting state fMRI data using nuisance regression.

PubMed

Bright, Molly G; Tench, Christopher R; Murphy, Kevin

2017-07-01

In resting state fMRI, it is necessary to remove signal variance associated with noise sources, leaving cleaned fMRI time-series that more accurately reflect the underlying intrinsic brain fluctuations of interest. This is commonly achieved through nuisance regression, in which the fit is calculated of a noise model of head motion and physiological processes to the fMRI data in a General Linear Model, and the "cleaned" residuals of this fit are used in further analysis. We examine the statistical assumptions and requirements of the General Linear Model, and whether these are met during nuisance regression of resting state fMRI data. Using toy examples and real data we show how pre-whitening, temporal filtering and temporal shifting of regressors impact model fit. Based on our own observations, existing literature, and statistical theory, we make the following recommendations when employing nuisance regression: pre-whitening should be applied to achieve valid statistical inference of the noise model fit parameters; temporal filtering should be incorporated into the noise model to best account for changes in degrees of freedom; temporal shifting of regressors, although merited, should be achieved via optimisation and validation of a single temporal shift. We encourage all readers to make simple, practical changes to their fMRI denoising pipeline, and to regularly assess the appropriateness of the noise model used. By negotiating the potential pitfalls described in this paper, and by clearly reporting the details of nuisance regression in future manuscripts, we hope that the field will achieve more accurate and precise noise models for cleaning the resting state fMRI time-series. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Bias in logistic regression due to imperfect diagnostic test results and practical correction approaches.

PubMed

Valle, Denis; Lima, Joanna M Tucker; Millar, Justin; Amratia, Punam; Haque, Ubydul

2015-11-04

Logistic regression is a statistical model widely used in cross-sectional and cohort studies to identify and quantify the effects of potential disease risk factors. However, the impact of imperfect tests on adjusted odds ratios (and thus on the identification of risk factors) is under-appreciated. The purpose of this article is to draw attention to the problem associated with modelling imperfect diagnostic tests, and propose simple Bayesian models to adequately address this issue. A systematic literature review was conducted to determine the proportion of malaria studies that appropriately accounted for false-negatives/false-positives in a logistic regression setting. Inference from the standard logistic regression was also compared with that from three proposed Bayesian models using simulations and malaria data from the western Brazilian Amazon. A systematic literature review suggests that malaria epidemiologists are largely unaware of the problem of using logistic regression to model imperfect diagnostic test results. Simulation results reveal that statistical inference can be substantially improved when using the proposed Bayesian models versus the standard logistic regression. Finally, analysis of original malaria data with one of the proposed Bayesian models reveals that microscopy sensitivity is strongly influenced by how long people have lived in the study region, and an important risk factor (i.e., participation in forest extractivism) is identified that would have been missed by standard logistic regression. Given the numerous diagnostic methods employed by malaria researchers and the ubiquitous use of logistic regression to model the results of these diagnostic tests, this paper provides critical guidelines to improve data analysis practice in the presence of misclassification error. Easy-to-use code that can be readily adapted to WinBUGS is provided, enabling straightforward implementation of the proposed Bayesian models.

Logistic Regression with Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages.

PubMed

Kim, Yoonsang; Choi, Young-Ku; Emery, Sherry

2013-08-01

Several statistical packages are capable of estimating generalized linear mixed models and these packages provide one or more of three estimation methods: penalized quasi-likelihood, Laplace, and Gauss-Hermite. Many studies have investigated these methods' performance for the mixed-effects logistic regression model. However, the authors focused on models with one or two random effects and assumed a simple covariance structure between them, which may not be realistic. When there are multiple correlated random effects in a model, the computation becomes intensive, and often an algorithm fails to converge. Moreover, in our analysis of smoking status and exposure to anti-tobacco advertisements, we have observed that when a model included multiple random effects, parameter estimates varied considerably from one statistical package to another even when using the same estimation method. This article presents a comprehensive review of the advantages and disadvantages of each estimation method. In addition, we compare the performances of the three methods across statistical packages via simulation, which involves two- and three-level logistic regression models with at least three correlated random effects. We apply our findings to a real dataset. Our results suggest that two packages-SAS GLIMMIX Laplace and SuperMix Gaussian quadrature-perform well in terms of accuracy, precision, convergence rates, and computing speed. We also discuss the strengths and weaknesses of the two packages in regard to sample sizes.

Logistic Regression with Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages

PubMed Central

Kim, Yoonsang; Emery, Sherry

2013-01-01

Several statistical packages are capable of estimating generalized linear mixed models and these packages provide one or more of three estimation methods: penalized quasi-likelihood, Laplace, and Gauss-Hermite. Many studies have investigated these methods’ performance for the mixed-effects logistic regression model. However, the authors focused on models with one or two random effects and assumed a simple covariance structure between them, which may not be realistic. When there are multiple correlated random effects in a model, the computation becomes intensive, and often an algorithm fails to converge. Moreover, in our analysis of smoking status and exposure to anti-tobacco advertisements, we have observed that when a model included multiple random effects, parameter estimates varied considerably from one statistical package to another even when using the same estimation method. This article presents a comprehensive review of the advantages and disadvantages of each estimation method. In addition, we compare the performances of the three methods across statistical packages via simulation, which involves two- and three-level logistic regression models with at least three correlated random effects. We apply our findings to a real dataset. Our results suggest that two packages—SAS GLIMMIX Laplace and SuperMix Gaussian quadrature—perform well in terms of accuracy, precision, convergence rates, and computing speed. We also discuss the strengths and weaknesses of the two packages in regard to sample sizes. PMID:24288415

Parametric regression model for survival data: Weibull regression model as an example

PubMed Central

2016-01-01

Weibull regression model is one of the most popular forms of parametric regression model that it provides estimate of baseline hazard function, as well as coefficients for covariates. Because of technical difficulties, Weibull regression model is seldom used in medical literature as compared to the semi-parametric proportional hazard model. To make clinical investigators familiar with Weibull regression model, this article introduces some basic knowledge on Weibull regression model and then illustrates how to fit the model with R software. The SurvRegCensCov package is useful in converting estimated coefficients to clinical relevant statistics such as hazard ratio (HR) and event time ratio (ETR). Model adequacy can be assessed by inspecting Kaplan-Meier curves stratified by categorical variable. The eha package provides an alternative method to model Weibull regression model. The check.dist() function helps to assess goodness-of-fit of the model. Variable selection is based on the importance of a covariate, which can be tested using anova() function. Alternatively, backward elimination starting from a full model is an efficient way for model development. Visualization of Weibull regression model after model development is interesting that it provides another way to report your findings. PMID:28149846

Multinomial Logistic Regression Predicted Probability Map To Visualize The Influence Of Socio-Economic Factors On Breast Cancer Occurrence in Southern Karnataka

NASA Astrophysics Data System (ADS)

Madhu, B.; Ashok, N. C.; Balasubramanian, S.

2014-11-01

Multinomial logistic regression analysis was used to develop statistical model that can predict the probability of breast cancer in Southern Karnataka using the breast cancer occurrence data during 2007-2011. Independent socio-economic variables describing the breast cancer occurrence like age, education, occupation, parity, type of family, health insurance coverage, residential locality and socioeconomic status of each case was obtained. The models were developed as follows: i) Spatial visualization of the Urban- rural distribution of breast cancer cases that were obtained from the Bharat Hospital and Institute of Oncology. ii) Socio-economic risk factors describing the breast cancer occurrences were complied for each case. These data were then analysed using multinomial logistic regression analysis in a SPSS statistical software and relations between the occurrence of breast cancer across the socio-economic status and the influence of other socio-economic variables were evaluated and multinomial logistic regression models were constructed. iii) the model that best predicted the occurrence of breast cancer were identified. This multivariate logistic regression model has been entered into a geographic information system and maps showing the predicted probability of breast cancer occurrence in Southern Karnataka was created. This study demonstrates that Multinomial logistic regression is a valuable tool for developing models that predict the probability of breast cancer Occurrence in Southern Karnataka.

Estimating the impact of mineral aerosols on crop yields in food insecure regions using statistical crop models

NASA Astrophysics Data System (ADS)

Hoffman, A.; Forest, C. E.; Kemanian, A.

2016-12-01

A significant number of food-insecure nations exist in regions of the world where dust plays a large role in the climate system. While the impacts of common climate variables (e.g. temperature, precipitation, ozone, and carbon dioxide) on crop yields are relatively well understood, the impact of mineral aerosols on yields have not yet been thoroughly investigated. This research aims to develop the data and tools to progress our understanding of mineral aerosol impacts on crop yields. Suspended dust affects crop yields by altering the amount and type of radiation reaching the plant, modifying local temperature and precipitation. While dust events (i.e. dust storms) affect crop yields by depleting the soil of nutrients or by defoliation via particle abrasion. The impact of dust on yields is modeled statistically because we are uncertain which impacts will dominate the response on national and regional scales considered in this study. Multiple linear regression is used in a number of large-scale statistical crop modeling studies to estimate yield responses to various climate variables. In alignment with previous work, we develop linear crop models, but build upon this simple method of regression with machine-learning techniques (e.g. random forests) to identify important statistical predictors and isolate how dust affects yields on the scales of interest. To perform this analysis, we develop a crop-climate dataset for maize, soybean, groundnut, sorghum, rice, and wheat for the regions of West Africa, East Africa, South Africa, and the Sahel. Random forest regression models consistently model historic crop yields better than the linear models. In several instances, the random forest models accurately capture the temperature and precipitation threshold behavior in crops. Additionally, improving agricultural technology has caused a well-documented positive trend that dominates time series of global and regional yields. This trend is often removed before regression with traditional crop models, but likely at the cost of removing climate information. Our random forest models consistently discover the positive trend without removing any additional data. The application of random forests as a statistical crop model provides insight into understanding the impact of dust on yields in marginal food producing regions.

Prediction of Patient-Controlled Analgesic Consumption: A Multimodel Regression Tree Approach.

PubMed

Hu, Yuh-Jyh; Ku, Tien-Hsiung; Yang, Yu-Hung; Shen, Jia-Ying

2018-01-01

Several factors contribute to individual variability in postoperative pain, therefore, individuals consume postoperative analgesics at different rates. Although many statistical studies have analyzed postoperative pain and analgesic consumption, most have identified only the correlation and have not subjected the statistical model to further tests in order to evaluate its predictive accuracy. In this study involving 3052 patients, a multistrategy computational approach was developed for analgesic consumption prediction. This approach uses data on patient-controlled analgesia demand behavior over time and combines clustering, classification, and regression to mitigate the limitations of current statistical models. Cross-validation results indicated that the proposed approach significantly outperforms various existing regression methods. Moreover, a comparison between the predictions by anesthesiologists and medical specialists and those of the computational approach for an independent test data set of 60 patients further evidenced the superiority of the computational approach in predicting analgesic consumption because it produced markedly lower root mean squared errors.

Regression assumptions in clinical psychology research practice-a systematic review of common misconceptions.

PubMed

Ernst, Anja F; Albers, Casper J

2017-01-01

Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking.

Examination of influential observations in penalized spline regression

NASA Astrophysics Data System (ADS)

Türkan, Semra

2013-10-01

In parametric or nonparametric regression models, the results of regression analysis are affected by some anomalous observations in the data set. Thus, detection of these observations is one of the major steps in regression analysis. These observations are precisely detected by well-known influence measures. Pena's statistic is one of them. In this study, Pena's approach is formulated for penalized spline regression in terms of ordinary residuals and leverages. The real data and artificial data are used to see illustrate the effectiveness of Pena's statistic as to Cook's distance on detecting influential observations. The results of the study clearly reveal that the proposed measure is superior to Cook's Distance to detect these observations in large data set.

Regression assumptions in clinical psychology research practice—a systematic review of common misconceptions

PubMed Central

Ernst, Anja F.

2017-01-01

Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking. PMID:28533971

4D-Fingerprint Categorical QSAR Models for Skin Sensitization Based on Classification Local Lymph Node Assay Measures

PubMed Central

Li, Yi; Tseng, Yufeng J.; Pan, Dahua; Liu, Jianzhong; Kern, Petra S.; Gerberick, G. Frank; Hopfinger, Anton J.

2008-01-01

Currently, the only validated methods to identify skin sensitization effects are in vivo models, such as the Local Lymph Node Assay (LLNA) and guinea pig studies. There is a tremendous need, in particular due to novel legislation, to develop animal alternatives, eg. Quantitative Structure-Activity Relationship (QSAR) models. Here, QSAR models for skin sensitization using LLNA data have been constructed. The descriptors used to generate these models are derived from the 4D-molecular similarity paradigm and are referred to as universal 4D-fingerprints. A training set of 132 structurally diverse compounds and a test set of 15 structurally diverse compounds were used in this study. The statistical methodologies used to build the models are logistic regression (LR), and partial least square coupled logistic regression (PLS-LR), which prove to be effective tools for studying skin sensitization measures expressed in the two categorical terms of sensitizer and non-sensitizer. QSAR models with low values of the Hosmer-Lemeshow goodness-of-fit statistic, χHL2, are significant and predictive. For the training set, the cross-validated prediction accuracy of the logistic regression models ranges from 77.3% to 78.0%, while that of PLS-logistic regression models ranges from 87.1% to 89.4%. For the test set, the prediction accuracy of logistic regression models ranges from 80.0%-86.7%, while that of PLS-logistic regression models ranges from 73.3%-80.0%. The QSAR models are made up of 4D-fingerprints related to aromatic atoms, hydrogen bond acceptors and negatively partially charged atoms. PMID:17226934

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

PubMed Central

Chen, Yanguang

2016-01-01

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test. PMID:26800271

Application of Semiparametric Spline Regression Model in Analyzing Factors that In uence Population Density in Central Java

NASA Astrophysics Data System (ADS)

Sumantari, Y. D.; Slamet, I.; Sugiyanto

2017-06-01

Semiparametric regression is a statistical analysis method that consists of parametric and nonparametric regression. There are various approach techniques in nonparametric regression. One of the approach techniques is spline. Central Java is one of the most densely populated province in Indonesia. Population density in this province can be modeled by semiparametric regression because it consists of parametric and nonparametric component. Therefore, the purpose of this paper is to determine the factors that in uence population density in Central Java using the semiparametric spline regression model. The result shows that the factors which in uence population density in Central Java is Family Planning (FP) active participants and district minimum wage.

Identifying the Factors That Influence Change in SEBD Using Logistic Regression Analysis

ERIC Educational Resources Information Center

Camilleri, Liberato; Cefai, Carmel

2013-01-01

Multiple linear regression and ANOVA models are widely used in applications since they provide effective statistical tools for assessing the relationship between a continuous dependent variable and several predictors. However these models rely heavily on linearity and normality assumptions and they do not accommodate categorical dependent…

A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence

USDA-ARS?s Scientific Manuscript database

Parametric non-linear regression (PNR) techniques commonly are used to develop weed seedling emergence models. Such techniques, however, require statistical assumptions that are difficult to meet. To examine and overcome these limitations, we compared PNR with a nonparametric estimation technique. F...

Functional Relationships and Regression Analysis.

ERIC Educational Resources Information Center

Preece, Peter F. W.

1978-01-01

Using a degenerate multivariate normal model for the distribution of organismic variables, the form of least-squares regression analysis required to estimate a linear functional relationship between variables is derived. It is suggested that the two conventional regression lines may be considered to describe functional, not merely statistical,…

Estimating maize production in Kenya using NDVI: Some statistical considerations

USGS Publications Warehouse

Lewis, J.E.; Rowland, James; Nadeau , A.

1998-01-01

A regression model approach using a normalized difference vegetation index (NDVI) has the potential for estimating crop production in East Africa. However, before production estimation can become a reality, the underlying model assumptions and statistical nature of the sample data (NDVI and crop production) must be examined rigorously. Annual maize production statistics from 1982-90 for 36 agricultural districts within Kenya were used as the dependent variable; median area NDVI (independent variable) values from each agricultural district and year were extracted from the annual maximum NDVI data set. The input data and the statistical association of NDVI with maize production for Kenya were tested systematically for the following items: (1) homogeneity of the data when pooling the sample, (2) gross data errors and influence points, (3) serial (time) correlation, (4) spatial autocorrelation and (5) stability of the regression coefficients. The results of using a simple regression model with NDVI as the only independent variable are encouraging (r 0.75, p 0.05) and illustrate that NDVI can be a responsive indicator of maize production, especially in areas of high NDVI spatial variability, which coincide with areas of production variability in Kenya.

Replica analysis of overfitting in regression models for time-to-event data

NASA Astrophysics Data System (ADS)

Coolen, A. C. C.; Barrett, J. E.; Paga, P.; Perez-Vicente, C. J.

2017-09-01

Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine presents us with data of unprecedented dimensionality, these data cannot yet be used effectively for clinical outcome prediction. Standard error measures in maximum likelihood regression, such as p-values and z-scores, are blind to overfitting, and even for Cox’s proportional hazards model (the main tool of medical statisticians), one finds in literature only rules of thumb on the number of samples required to avoid overfitting. In this paper we present a mathematical theory of overfitting in regression models for time-to-event data, which aims to increase our quantitative understanding of the problem and provide practical tools with which to correct regression outcomes for the impact of overfitting. It is based on the replica method, a statistical mechanical technique for the analysis of heterogeneous many-variable systems that has been used successfully for several decades in physics, biology, and computer science, but not yet in medical statistics. We develop the theory initially for arbitrary regression models for time-to-event data, and verify its predictions in detail for the popular Cox model.

Support vector methods for survival analysis: a comparison between ranking and regression approaches.

PubMed

Van Belle, Vanya; Pelckmans, Kristiaan; Van Huffel, Sabine; Suykens, Johan A K

2011-10-01

To compare and evaluate ranking, regression and combined machine learning approaches for the analysis of survival data. The literature describes two approaches based on support vector machines to deal with censored observations. In the first approach the key idea is to rephrase the task as a ranking problem via the concordance index, a problem which can be solved efficiently in a context of structural risk minimization and convex optimization techniques. In a second approach, one uses a regression approach, dealing with censoring by means of inequality constraints. The goal of this paper is then twofold: (i) introducing a new model combining the ranking and regression strategy, which retains the link with existing survival models such as the proportional hazards model via transformation models; and (ii) comparison of the three techniques on 6 clinical and 3 high-dimensional datasets and discussing the relevance of these techniques over classical approaches fur survival data. We compare svm-based survival models based on ranking constraints, based on regression constraints and models based on both ranking and regression constraints. The performance of the models is compared by means of three different measures: (i) the concordance index, measuring the model's discriminating ability; (ii) the logrank test statistic, indicating whether patients with a prognostic index lower than the median prognostic index have a significant different survival than patients with a prognostic index higher than the median; and (iii) the hazard ratio after normalization to restrict the prognostic index between 0 and 1. Our results indicate a significantly better performance for models including regression constraints above models only based on ranking constraints. This work gives empirical evidence that svm-based models using regression constraints perform significantly better than svm-based models based on ranking constraints. Our experiments show a comparable performance for methods including only regression or both regression and ranking constraints on clinical data. On high dimensional data, the former model performs better. However, this approach does not have a theoretical link with standard statistical models for survival data. This link can be made by means of transformation models when ranking constraints are included. Copyright © 2011 Elsevier B.V. All rights reserved.

Survival Data and Regression Models

NASA Astrophysics Data System (ADS)

Grégoire, G.

2014-12-01

We start this chapter by introducing some basic elements for the analysis of censored survival data. Then we focus on right censored data and develop two types of regression models. The first one concerns the so-called accelerated failure time models (AFT), which are parametric models where a function of a parameter depends linearly on the covariables. The second one is a semiparametric model, where the covariables enter in a multiplicative form in the expression of the hazard rate function. The main statistical tool for analysing these regression models is the maximum likelihood methodology and, in spite we recall some essential results about the ML theory, we refer to the chapter "Logistic Regression" for a more detailed presentation.

Finite-sample and asymptotic sign-based tests for parameters of non-linear quantile regression with Markov noise

NASA Astrophysics Data System (ADS)

Sirenko, M. A.; Tarasenko, P. F.; Pushkarev, M. I.

2017-01-01

One of the most noticeable features of sign-based statistical procedures is an opportunity to build an exact test for simple hypothesis testing of parameters in a regression model. In this article, we expanded a sing-based approach to the nonlinear case with dependent noise. The examined model is a multi-quantile regression, which makes it possible to test hypothesis not only of regression parameters, but of noise parameters as well.

Statistical model to perform error analysis of curve fits of wind tunnel test data using the techniques of analysis of variance and regression analysis

NASA Technical Reports Server (NTRS)

Alston, D. W.

1981-01-01

The considered research had the objective to design a statistical model that could perform an error analysis of curve fits of wind tunnel test data using analysis of variance and regression analysis techniques. Four related subproblems were defined, and by solving each of these a solution to the general research problem was obtained. The capabilities of the evolved true statistical model are considered. The least squares fit is used to determine the nature of the force, moment, and pressure data. The order of the curve fit is increased in order to delete the quadratic effect in the residuals. The analysis of variance is used to determine the magnitude and effect of the error factor associated with the experimental data.

Calibration transfer of a Raman spectroscopic quantification method for the assessment of liquid detergent compositions from at-line laboratory to in-line industrial scale.

PubMed

Brouckaert, D; Uyttersprot, J-S; Broeckx, W; De Beer, T

2018-03-01

Calibration transfer or standardisation aims at creating a uniform spectral response on different spectroscopic instruments or under varying conditions, without requiring a full recalibration for each situation. In the current study, this strategy is applied to construct at-line multivariate calibration models and consequently employ them in-line in a continuous industrial production line, using the same spectrometer. Firstly, quantitative multivariate models are constructed at-line at laboratory scale for predicting the concentration of two main ingredients in hard surface cleaners. By regressing the Raman spectra of a set of small-scale calibration samples against their reference concentration values, partial least squares (PLS) models are developed to quantify the surfactant levels in the liquid detergent compositions under investigation. After evaluating the models performance with a set of independent validation samples, a univariate slope/bias correction is applied in view of transporting these at-line calibration models to an in-line manufacturing set-up. This standardisation technique allows a fast and easy transfer of the PLS regression models, by simply correcting the model predictions on the in-line set-up, without adjusting anything to the original multivariate calibration models. An extensive statistical analysis is performed in order to assess the predictive quality of the transferred regression models. Before and after transfer, the R 2 and RMSEP of both models is compared for evaluating if their magnitude is similar. T-tests are then performed to investigate whether the slope and intercept of the transferred regression line are not statistically different from 1 and 0, respectively. Furthermore, it is inspected whether no significant bias can be noted. F-tests are executed as well, for assessing the linearity of the transfer regression line and for investigating the statistical coincidence of the transfer and validation regression line. Finally, a paired t-test is performed to compare the original at-line model to the slope/bias corrected in-line model, using interval hypotheses. It is shown that the calibration models of Surfactant 1 and Surfactant 2 yield satisfactory in-line predictions after slope/bias correction. While Surfactant 1 passes seven out of eight statistical tests, the recommended validation parameters are 100% successful for Surfactant 2. It is hence concluded that the proposed strategy for transferring at-line calibration models to an in-line industrial environment via a univariate slope/bias correction of the predicted values offers a successful standardisation approach. Copyright © 2017 Elsevier B.V. All rights reserved.

Disconcordance in Statistical Models of Bisphenol A and Chronic Disease Outcomes in NHANES 2003-08

PubMed Central

Casey, Martin F.; Neidell, Matthew

2013-01-01

Background Bisphenol A (BPA), a high production chemical commonly found in plastics, has drawn great attention from researchers due to the substance’s potential toxicity. Using data from three National Health and Nutrition Examination Survey (NHANES) cycles, we explored the consistency and robustness of BPA’s reported effects on coronary heart disease and diabetes. Methods And Findings We report the use of three different statistical models in the analysis of BPA: (1) logistic regression, (2) log-linear regression, and (3) dose-response logistic regression. In each variation, confounders were added in six blocks to account for demographics, urinary creatinine, source of BPA exposure, healthy behaviours, and phthalate exposure. Results were sensitive to the variations in functional form of our statistical models, but no single model yielded consistent results across NHANES cycles. Reported ORs were also found to be sensitive to inclusion/exclusion criteria. Further, observed effects, which were most pronounced in NHANES 2003-04, could not be explained away by confounding. Conclusions Limitations in the NHANES data and a poor understanding of the mode of action of BPA have made it difficult to develop informative statistical models. Given the sensitivity of effect estimates to functional form, researchers should report results using multiple specifications with different assumptions about BPA measurement, thus allowing for the identification of potential discrepancies in the data. PMID:24223205

Using regression equations built from summary data in the psychological assessment of the individual case: extension to multiple regression.

PubMed

Crawford, John R; Garthwaite, Paul H; Denham, Annie K; Chelune, Gordon J

2012-12-01

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because (a) not all psychologists are aware that regression equations can be built not only from raw data but also using only basic summary data for a sample, and (b) the computations involved are tedious and prone to error. In an attempt to overcome these barriers, Crawford and Garthwaite (2007) provided methods to build and apply simple linear regression models using summary statistics as data. In the present study, we extend this work to set out the steps required to build multiple regression models from sample summary statistics and the further steps required to compute the associated statistics for drawing inferences concerning an individual case. We also develop, describe, and make available a computer program that implements these methods. Although there are caveats associated with the use of the methods, these need to be balanced against pragmatic considerations and against the alternative of either entirely ignoring a pertinent data set or using it informally to provide a clinical "guesstimate." Upgraded versions of earlier programs for regression in the single case are also provided; these add the point and interval estimates of effect size developed in the present article.

Simulation of parametric model towards the fixed covariate of right censored lung cancer data

NASA Astrophysics Data System (ADS)

Afiqah Muhamad Jamil, Siti; Asrul Affendi Abdullah, M.; Kek, Sie Long; Ridwan Olaniran, Oyebayo; Enera Amran, Syahila

2017-09-01

In this study, simulation procedure was applied to measure the fixed covariate of right censored data by using parametric survival model. The scale and shape parameter were modified to differentiate the analysis of parametric regression survival model. Statistically, the biases, mean biases and the coverage probability were used in this analysis. Consequently, different sample sizes were employed to distinguish the impact of parametric regression model towards right censored data with 50, 100, 150 and 200 number of sample. R-statistical software was utilised to develop the coding simulation with right censored data. Besides, the final model of right censored simulation was compared with the right censored lung cancer data in Malaysia. It was found that different values of shape and scale parameter with different sample size, help to improve the simulation strategy for right censored data and Weibull regression survival model is suitable fit towards the simulation of survival of lung cancer patients data in Malaysia.

Regression Commonality Analysis: A Technique for Quantitative Theory Building

ERIC Educational Resources Information Center

Nimon, Kim; Reio, Thomas G., Jr.

2011-01-01

When it comes to multiple linear regression analysis (MLR), it is common for social and behavioral science researchers to rely predominately on beta weights when evaluating how predictors contribute to a regression model. Presenting an underutilized statistical technique, this article describes how organizational researchers can use commonality…

Goodness-Of-Fit Test for Nonparametric Regression Models: Smoothing Spline ANOVA Models as Example.

PubMed

Teran Hidalgo, Sebastian J; Wu, Michael C; Engel, Stephanie M; Kosorok, Michael R

2018-06-01

Nonparametric regression models do not require the specification of the functional form between the outcome and the covariates. Despite their popularity, the amount of diagnostic statistics, in comparison to their parametric counter-parts, is small. We propose a goodness-of-fit test for nonparametric regression models with linear smoother form. In particular, we apply this testing framework to smoothing spline ANOVA models. The test can consider two sources of lack-of-fit: whether covariates that are not currently in the model need to be included, and whether the current model fits the data well. The proposed method derives estimated residuals from the model. Then, statistical dependence is assessed between the estimated residuals and the covariates using the HSIC. If dependence exists, the model does not capture all the variability in the outcome associated with the covariates, otherwise the model fits the data well. The bootstrap is used to obtain p-values. Application of the method is demonstrated with a neonatal mental development data analysis. We demonstrate correct type I error as well as power performance through simulations.

[Methodology of the description of atmospheric air pollution by nitrogen dioxide by land use regression method in Ekaterinburg].

PubMed

Antropov, K M; Varaksin, A N

2013-01-01

This paper provides the description of Land Use Regression (LUR) modeling and the result of its application in the study of nitrogen dioxide air pollution in Ekaterinburg. The paper describes the difficulties of the modeling for air pollution caused by motor vehicles exhaust, and the ways to address these challenges. To create LUR model of the NO2 air pollution in Ekaterinburg, concentrations of NO2 were measured, data on factors affecting air pollution were collected, a statistical analysis of the data were held. A statistical model of NO2 air pollution (coefficient of determination R2 = 0.70) and a map of pollution were created.

Notes on power of normality tests of error terms in regression models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Střelec, Luboš

2015-03-10

Normality is one of the basic assumptions in applying statistical procedures. For example in linear regression most of the inferential procedures are based on the assumption of normality, i.e. the disturbance vector is assumed to be normally distributed. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Thus, error terms should be normally distributed in order to allow us to make exact inferences. As a consequence, normally distributed stochastic errors are necessary in order to make a not misleading inferences which explains a necessity and importancemore » of robust tests of normality. Therefore, the aim of this contribution is to discuss normality testing of error terms in regression models. In this contribution, we introduce the general RT class of robust tests for normality, and present and discuss the trade-off between power and robustness of selected classical and robust normality tests of error terms in regression models.« less

An operational GLS model for hydrologic regression

USGS Publications Warehouse

Tasker, Gary D.; Stedinger, J.R.

1989-01-01

Recent Monte Carlo studies have documented the value of generalized least squares (GLS) procedures to estimate empirical relationships between streamflow statistics and physiographic basin characteristics. This paper presents a number of extensions of the GLS method that deal with realities and complexities of regional hydrologic data sets that were not addressed in the simulation studies. These extensions include: (1) a more realistic model of the underlying model errors; (2) smoothed estimates of cross correlation of flows; (3) procedures for including historical flow data; (4) diagnostic statistics describing leverage and influence for GLS regression; and (5) the formulation of a mathematical program for evaluating future gaging activities. ?? 1989.

Predictors of the number of under-five malnourished children in Bangladesh: application of the generalized poisson regression model

PubMed Central

2013-01-01

Background Malnutrition is one of the principal causes of child mortality in developing countries including Bangladesh. According to our knowledge, most of the available studies, that addressed the issue of malnutrition among under-five children, considered the categorical (dichotomous/polychotomous) outcome variables and applied logistic regression (binary/multinomial) to find their predictors. In this study malnutrition variable (i.e. outcome) is defined as the number of under-five malnourished children in a family, which is a non-negative count variable. The purposes of the study are (i) to demonstrate the applicability of the generalized Poisson regression (GPR) model as an alternative of other statistical methods and (ii) to find some predictors of this outcome variable. Methods The data is extracted from the Bangladesh Demographic and Health Survey (BDHS) 2007. Briefly, this survey employs a nationally representative sample which is based on a two-stage stratified sample of households. A total of 4,460 under-five children is analysed using various statistical techniques namely Chi-square test and GPR model. Results The GPR model (as compared to the standard Poisson regression and negative Binomial regression) is found to be justified to study the above-mentioned outcome variable because of its under-dispersion (variance < mean) property. Our study also identify several significant predictors of the outcome variable namely mother’s education, father’s education, wealth index, sanitation status, source of drinking water, and total number of children ever born to a woman. Conclusions Consistencies of our findings in light of many other studies suggest that the GPR model is an ideal alternative of other statistical models to analyse the number of under-five malnourished children in a family. Strategies based on significant predictors may improve the nutritional status of children in Bangladesh. PMID:23297699

Comparing The Effectiveness of a90/95 Calculations (Preprint)

DTIC Science & Technology

2006-09-01

Nachtsheim, John Neter, William Li, Applied Linear Statistical Models , 5th ed., McGraw-Hill/Irwin, 2005 5. Mood, Graybill and Boes, Introduction...curves is based on methods that are only valid for ordinary linear regression. Requirements for a valid Ordinary Least-Squares Regression Model There... linear . For example is a linear model ; is not. 2. Uniform variance (homoscedasticity

Goodness-of-fit tests and model diagnostics for negative binomial regression of RNA sequencing data.

PubMed

Mi, Gu; Di, Yanming; Schafer, Daniel W

2015-01-01

This work is about assessing model adequacy for negative binomial (NB) regression, particularly (1) assessing the adequacy of the NB assumption, and (2) assessing the appropriateness of models for NB dispersion parameters. Tools for the first are appropriate for NB regression generally; those for the second are primarily intended for RNA sequencing (RNA-Seq) data analysis. The typically small number of biological samples and large number of genes in RNA-Seq analysis motivate us to address the trade-offs between robustness and statistical power using NB regression models. One widely-used power-saving strategy, for example, is to assume some commonalities of NB dispersion parameters across genes via simple models relating them to mean expression rates, and many such models have been proposed. As RNA-Seq analysis is becoming ever more popular, it is appropriate to make more thorough investigations into power and robustness of the resulting methods, and into practical tools for model assessment. In this article, we propose simulation-based statistical tests and diagnostic graphics to address model adequacy. We provide simulated and real data examples to illustrate that our proposed methods are effective for detecting the misspecification of the NB mean-variance relationship as well as judging the adequacy of fit of several NB dispersion models.

Testing Mediation Using Multiple Regression and Structural Equation Modeling Analyses in Secondary Data

ERIC Educational Resources Information Center

Li, Spencer D.

2011-01-01

Mediation analysis in child and adolescent development research is possible using large secondary data sets. This article provides an overview of two statistical methods commonly used to test mediated effects in secondary analysis: multiple regression and structural equation modeling (SEM). Two empirical studies are presented to illustrate the…

Conjoint Analysis: A Study of the Effects of Using Person Variables.

ERIC Educational Resources Information Center

Fraas, John W.; Newman, Isadore

Three statistical techniques--conjoint analysis, a multiple linear regression model, and a multiple linear regression model with a surrogate person variable--were used to estimate the relative importance of five university attributes for students in the process of selecting a college. The five attributes include: availability and variety of…

Suppressor Variables: The Difference between "Is" versus "Acting As"

ERIC Educational Resources Information Center

Ludlow, Larry; Klein, Kelsey

2014-01-01

Correlated predictors in regression models are a fact of life in applied social science research. The extent to which they are correlated will influence the estimates and statistics associated with the other variables they are modeled along with. These effects, for example, may include enhanced regression coefficients for the other variables--a…

A Comparison of Conventional Linear Regression Methods and Neural Networks for Forecasting Educational Spending.

ERIC Educational Resources Information Center

Baker, Bruce D.; Richards, Craig E.

1999-01-01

Applies neural network methods for forecasting 1991-95 per-pupil expenditures in U.S. public elementary and secondary schools. Forecasting models included the National Center for Education Statistics' multivariate regression model and three neural architectures. Regarding prediction accuracy, neural network results were comparable or superior to…

Minimizing bias in biomass allometry: Model selection and log transformation of data

Treesearch

Joseph Mascaro; undefined undefined; Flint Hughes; Amanda Uowolo; Stefan A. Schnitzer

2011-01-01

Nonlinear regression is increasingly used to develop allometric equations for forest biomass estimation (i.e., as opposed to the raditional approach of log-transformation followed by linear regression). Most statistical software packages, however, assume additive errors by default, violating a key assumption of allometric theory and possibly producing spurious models....

An open-access CMIP5 pattern library for temperature and precipitation: Description and methodology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lynch, Cary D.; Hartin, Corinne A.; Bond-Lamberty, Benjamin

Pattern scaling is used to efficiently emulate general circulation models and explore uncertainty in climate projections under multiple forcing scenarios. Pattern scaling methods assume that local climate changes scale with a global mean temperature increase, allowing for spatial patterns to be generated for multiple models for any future emission scenario. For uncertainty quantification and probabilistic statistical analysis, a library of patterns with descriptive statistics for each file would be beneficial, but such a library does not presently exist. Of the possible techniques used to generate patterns, the two most prominent are the delta and least squared regression methods. We exploremore » the differences and statistical significance between patterns generated by each method and assess performance of the generated patterns across methods and scenarios. Differences in patterns across seasons between methods and epochs were largest in high latitudes (60-90°N/S). Bias and mean errors between modeled and pattern predicted output from the linear regression method were smaller than patterns generated by the delta method. Across scenarios, differences in the linear regression method patterns were more statistically significant, especially at high latitudes. We found that pattern generation methodologies were able to approximate the forced signal of change to within ≤ 0.5°C, but choice of pattern generation methodology for pattern scaling purposes should be informed by user goals and criteria. As a result, this paper describes our library of least squared regression patterns from all CMIP5 models for temperature and precipitation on an annual and sub-annual basis, along with the code used to generate these patterns.« less

An open-access CMIP5 pattern library for temperature and precipitation: Description and methodology

DOE PAGES

Lynch, Cary D.; Hartin, Corinne A.; Bond-Lamberty, Benjamin; ...

2017-05-15

Pattern scaling is used to efficiently emulate general circulation models and explore uncertainty in climate projections under multiple forcing scenarios. Pattern scaling methods assume that local climate changes scale with a global mean temperature increase, allowing for spatial patterns to be generated for multiple models for any future emission scenario. For uncertainty quantification and probabilistic statistical analysis, a library of patterns with descriptive statistics for each file would be beneficial, but such a library does not presently exist. Of the possible techniques used to generate patterns, the two most prominent are the delta and least squared regression methods. We exploremore » the differences and statistical significance between patterns generated by each method and assess performance of the generated patterns across methods and scenarios. Differences in patterns across seasons between methods and epochs were largest in high latitudes (60-90°N/S). Bias and mean errors between modeled and pattern predicted output from the linear regression method were smaller than patterns generated by the delta method. Across scenarios, differences in the linear regression method patterns were more statistically significant, especially at high latitudes. We found that pattern generation methodologies were able to approximate the forced signal of change to within ≤ 0.5°C, but choice of pattern generation methodology for pattern scaling purposes should be informed by user goals and criteria. As a result, this paper describes our library of least squared regression patterns from all CMIP5 models for temperature and precipitation on an annual and sub-annual basis, along with the code used to generate these patterns.« less

Cocaine Dependence Treatment Data: Methods for Measurement Error Problems With Predictors Derived From Stationary Stochastic Processes

PubMed Central

Guan, Yongtao; Li, Yehua; Sinha, Rajita

2011-01-01

In a cocaine dependence treatment study, we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time. A subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories, such as baseline cocaine use frequency and average daily use amount. These summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients. Unlike classical measurement error problems, the error we encounter here is heteroscedastic with an unknown distribution, and there are no replicates for the error-prone variables or instrumental variables. We propose two robust methods to correct for the bias: a computationally efficient method-of-moments-based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models. Simulations and an application to the cocaine dependence treatment data are used to illustrate the efficacy of the proposed methods. Asymptotic theory and variance estimation for the proposed subsampling extrapolation method and some additional simulation results are described in the online supplementary material. PMID:21984854

Modeling Complex Phenomena Using Multiscale Time Sequences

DTIC Science & Technology

2009-08-24

measures based on Hurst and Holder exponents , auto-regressive methods and Fourier and wavelet decomposition methods. The applications for this technology...relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and Holder exponents , auto-regressive...different scales and how these scales relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harlim, John, E-mail: jharlim@psu.edu; Mahdi, Adam, E-mail: amahdi@ncsu.edu; Majda, Andrew J., E-mail: jonjon@cims.nyu.edu

2014-01-15

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partialmore » noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

MULTIVARIATE STATISTICAL MODELS FOR EFFECTS OF PM AND COPOLLUTANTS IN A DAILY TIME SERIES EPIDEMIOLOGY STUDY

EPA Science Inventory

Most analyses of daily time series epidemiology data relate mortality or morbidity counts to PM and other air pollutants by means of single-outcome regression models using multiple predictors, without taking into account the complex statistical structure of the predictor variable...

Multiple regression and Artificial Neural Network for long-term rainfall forecasting using large scale climate modes

NASA Astrophysics Data System (ADS)

Mekanik, F.; Imteaz, M. A.; Gato-Trinidad, S.; Elmahdi, A.

2013-10-01

In this study, the application of Artificial Neural Networks (ANN) and Multiple regression analysis (MR) to forecast long-term seasonal spring rainfall in Victoria, Australia was investigated using lagged El Nino Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) as potential predictors. The use of dual (combined lagged ENSO-IOD) input sets for calibrating and validating ANN and MR Models is proposed to investigate the simultaneous effect of past values of these two major climate modes on long-term spring rainfall prediction. The MR models that did not violate the limits of statistical significance and multicollinearity were selected for future spring rainfall forecast. The ANN was developed in the form of multilayer perceptron using Levenberg-Marquardt algorithm. Both MR and ANN modelling were assessed statistically using mean square error (MSE), mean absolute error (MAE), Pearson correlation (r) and Willmott index of agreement (d). The developed MR and ANN models were tested on out-of-sample test sets; the MR models showed very poor generalisation ability for east Victoria with correlation coefficients of -0.99 to -0.90 compared to ANN with correlation coefficients of 0.42-0.93; ANN models also showed better generalisation ability for central and west Victoria with correlation coefficients of 0.68-0.85 and 0.58-0.97 respectively. The ability of multiple regression models to forecast out-of-sample sets is compatible with ANN for Daylesford in central Victoria and Kaniva in west Victoria (r = 0.92 and 0.67 respectively). The errors of the testing sets for ANN models are generally lower compared to multiple regression models. The statistical analysis suggest the potential of ANN over MR models for rainfall forecasting using large scale climate modes.

Machine Learning Algorithms Outperform Conventional Regression Models in Predicting Development of Hepatocellular Carcinoma

PubMed Central

Singal, Amit G.; Mukherjee, Ashin; Elmunzer, B. Joseph; Higgins, Peter DR; Lok, Anna S.; Zhu, Ji; Marrero, Jorge A; Waljee, Akbar K

2015-01-01

Background Predictive models for hepatocellular carcinoma (HCC) have been limited by modest accuracy and lack of validation. Machine learning algorithms offer a novel methodology, which may improve HCC risk prognostication among patients with cirrhosis. Our study's aim was to develop and compare predictive models for HCC development among cirrhotic patients, using conventional regression analysis and machine learning algorithms. Methods We enrolled 442 patients with Child A or B cirrhosis at the University of Michigan between January 2004 and September 2006 (UM cohort) and prospectively followed them until HCC development, liver transplantation, death, or study termination. Regression analysis and machine learning algorithms were used to construct predictive models for HCC development, which were tested on an independent validation cohort from the Hepatitis C Antiviral Long-term Treatment against Cirrhosis (HALT-C) Trial. Both models were also compared to the previously published HALT-C model. Discrimination was assessed using receiver operating characteristic curve analysis and diagnostic accuracy was assessed with net reclassification improvement and integrated discrimination improvement statistics. Results After a median follow-up of 3.5 years, 41 patients developed HCC. The UM regression model had a c-statistic of 0.61 (95%CI 0.56-0.67), whereas the machine learning algorithm had a c-statistic of 0.64 (95%CI 0.60–0.69) in the validation cohort. The machine learning algorithm had significantly better diagnostic accuracy as assessed by net reclassification improvement (p<0.001) and integrated discrimination improvement (p=0.04). The HALT-C model had a c-statistic of 0.60 (95%CI 0.50-0.70) in the validation cohort and was outperformed by the machine learning algorithm (p=0.047). Conclusion Machine learning algorithms improve the accuracy of risk stratifying patients with cirrhosis and can be used to accurately identify patients at high-risk for developing HCC. PMID:24169273

Methods for identifying SNP interactions: a review on variations of Logic Regression, Random Forest and Bayesian logistic regression.

PubMed

Chen, Carla Chia-Ming; Schwender, Holger; Keith, Jonathan; Nunkesser, Robin; Mengersen, Kerrie; Macrossan, Paula

2011-01-01

Due to advancements in computational ability, enhanced technology and a reduction in the price of genotyping, more data are being generated for understanding genetic associations with diseases and disorders. However, with the availability of large data sets comes the inherent challenges of new methods of statistical analysis and modeling. Considering a complex phenotype may be the effect of a combination of multiple loci, various statistical methods have been developed for identifying genetic epistasis effects. Among these methods, logic regression (LR) is an intriguing approach incorporating tree-like structures. Various methods have built on the original LR to improve different aspects of the model. In this study, we review four variations of LR, namely Logic Feature Selection, Monte Carlo Logic Regression, Genetic Programming for Association Studies, and Modified Logic Regression-Gene Expression Programming, and investigate the performance of each method using simulated and real genotype data. We contrast these with another tree-like approach, namely Random Forests, and a Bayesian logistic regression with stochastic search variable selection.

The relationship between venture capital investment and macro economic variables via statistical computation method

NASA Astrophysics Data System (ADS)

Aygunes, Gunes

2017-07-01

The objective of this paper is to survey and determine the macroeconomic factors affecting the level of venture capital (VC) investments in a country. The literary depends on venture capitalists' quality and countries' venture capital investments. The aim of this paper is to give relationship between venture capital investment and macro economic variables via statistical computation method. We investigate the countries and macro economic variables. By using statistical computation method, we derive correlation between venture capital investments and macro economic variables. According to method of logistic regression model (logit regression or logit model), macro economic variables are correlated with each other in three group. Venture capitalists regard correlations as a indicator. Finally, we give correlation matrix of our results.

Linear regression models and k-means clustering for statistical analysis of fNIRS data.

PubMed

Bonomini, Viola; Zucchelli, Lucia; Re, Rebecca; Ieva, Francesca; Spinelli, Lorenzo; Contini, Davide; Paganoni, Anna; Torricelli, Alessandro

2015-02-01

We propose a new algorithm, based on a linear regression model, to statistically estimate the hemodynamic activations in fNIRS data sets. The main concern guiding the algorithm development was the minimization of assumptions and approximations made on the data set for the application of statistical tests. Further, we propose a K-means method to cluster fNIRS data (i.e. channels) as activated or not activated. The methods were validated both on simulated and in vivo fNIRS data. A time domain (TD) fNIRS technique was preferred because of its high performances in discriminating cortical activation and superficial physiological changes. However, the proposed method is also applicable to continuous wave or frequency domain fNIRS data sets.

Linear regression models and k-means clustering for statistical analysis of fNIRS data

PubMed Central

Bonomini, Viola; Zucchelli, Lucia; Re, Rebecca; Ieva, Francesca; Spinelli, Lorenzo; Contini, Davide; Paganoni, Anna; Torricelli, Alessandro

2015-01-01

We propose a new algorithm, based on a linear regression model, to statistically estimate the hemodynamic activations in fNIRS data sets. The main concern guiding the algorithm development was the minimization of assumptions and approximations made on the data set for the application of statistical tests. Further, we propose a K-means method to cluster fNIRS data (i.e. channels) as activated or not activated. The methods were validated both on simulated and in vivo fNIRS data. A time domain (TD) fNIRS technique was preferred because of its high performances in discriminating cortical activation and superficial physiological changes. However, the proposed method is also applicable to continuous wave or frequency domain fNIRS data sets. PMID:25780751

A methodology for the design of experiments in computational intelligence with multiple regression models.

PubMed

Fernandez-Lozano, Carlos; Gestal, Marcos; Munteanu, Cristian R; Dorado, Julian; Pazos, Alejandro

2016-01-01

The design of experiments and the validation of the results achieved with them are vital in any research study. This paper focuses on the use of different Machine Learning approaches for regression tasks in the field of Computational Intelligence and especially on a correct comparison between the different results provided for different methods, as those techniques are complex systems that require further study to be fully understood. A methodology commonly accepted in Computational intelligence is implemented in an R package called RRegrs. This package includes ten simple and complex regression models to carry out predictive modeling using Machine Learning and well-known regression algorithms. The framework for experimental design presented herein is evaluated and validated against RRegrs. Our results are different for three out of five state-of-the-art simple datasets and it can be stated that the selection of the best model according to our proposal is statistically significant and relevant. It is of relevance to use a statistical approach to indicate whether the differences are statistically significant using this kind of algorithms. Furthermore, our results with three real complex datasets report different best models than with the previously published methodology. Our final goal is to provide a complete methodology for the use of different steps in order to compare the results obtained in Computational Intelligence problems, as well as from other fields, such as for bioinformatics, cheminformatics, etc., given that our proposal is open and modifiable.

A methodology for the design of experiments in computational intelligence with multiple regression models

PubMed Central

Gestal, Marcos; Munteanu, Cristian R.; Dorado, Julian; Pazos, Alejandro

2016-01-01

The design of experiments and the validation of the results achieved with them are vital in any research study. This paper focuses on the use of different Machine Learning approaches for regression tasks in the field of Computational Intelligence and especially on a correct comparison between the different results provided for different methods, as those techniques are complex systems that require further study to be fully understood. A methodology commonly accepted in Computational intelligence is implemented in an R package called RRegrs. This package includes ten simple and complex regression models to carry out predictive modeling using Machine Learning and well-known regression algorithms. The framework for experimental design presented herein is evaluated and validated against RRegrs. Our results are different for three out of five state-of-the-art simple datasets and it can be stated that the selection of the best model according to our proposal is statistically significant and relevant. It is of relevance to use a statistical approach to indicate whether the differences are statistically significant using this kind of algorithms. Furthermore, our results with three real complex datasets report different best models than with the previously published methodology. Our final goal is to provide a complete methodology for the use of different steps in order to compare the results obtained in Computational Intelligence problems, as well as from other fields, such as for bioinformatics, cheminformatics, etc., given that our proposal is open and modifiable. PMID:27920952

Gene-Based Association Analysis for Censored Traits Via Fixed Effect Functional Regressions.

PubMed

Fan, Ruzong; Wang, Yifan; Yan, Qi; Ding, Ying; Weeks, Daniel E; Lu, Zhaohui; Ren, Haobo; Cook, Richard J; Xiong, Momiao; Swaroop, Anand; Chew, Emily Y; Chen, Wei

2016-02-01

Genetic studies of survival outcomes have been proposed and conducted recently, but statistical methods for identifying genetic variants that affect disease progression are rarely developed. Motivated by our ongoing real studies, here we develop Cox proportional hazard models using functional regression (FR) to perform gene-based association analysis of survival traits while adjusting for covariates. The proposed Cox models are fixed effect models where the genetic effects of multiple genetic variants are assumed to be fixed. We introduce likelihood ratio test (LRT) statistics to test for associations between the survival traits and multiple genetic variants in a genetic region. Extensive simulation studies demonstrate that the proposed Cox RF LRT statistics have well-controlled type I error rates. To evaluate power, we compare the Cox FR LRT with the previously developed burden test (BT) in a Cox model and sequence kernel association test (SKAT), which is based on mixed effect Cox models. The Cox FR LRT statistics have higher power than or similar power as Cox SKAT LRT except when 50%/50% causal variants had negative/positive effects and all causal variants are rare. In addition, the Cox FR LRT statistics have higher power than Cox BT LRT. The models and related test statistics can be useful in the whole genome and whole exome association studies. An age-related macular degeneration dataset was analyzed as an example. © 2016 WILEY PERIODICALS, INC.

Gene-based Association Analysis for Censored Traits Via Fixed Effect Functional Regressions

PubMed Central

Fan, Ruzong; Wang, Yifan; Yan, Qi; Ding, Ying; Weeks, Daniel E.; Lu, Zhaohui; Ren, Haobo; Cook, Richard J; Xiong, Momiao; Swaroop, Anand; Chew, Emily Y.; Chen, Wei

2015-01-01

Summary Genetic studies of survival outcomes have been proposed and conducted recently, but statistical methods for identifying genetic variants that affect disease progression are rarely developed. Motivated by our ongoing real studies, we develop here Cox proportional hazard models using functional regression (FR) to perform gene-based association analysis of survival traits while adjusting for covariates. The proposed Cox models are fixed effect models where the genetic effects of multiple genetic variants are assumed to be fixed. We introduce likelihood ratio test (LRT) statistics to test for associations between the survival traits and multiple genetic variants in a genetic region. Extensive simulation studies demonstrate that the proposed Cox RF LRT statistics have well-controlled type I error rates. To evaluate power, we compare the Cox FR LRT with the previously developed burden test (BT) in a Cox model and sequence kernel association test (SKAT) which is based on mixed effect Cox models. The Cox FR LRT statistics have higher power than or similar power as Cox SKAT LRT except when 50%/50% causal variants had negative/positive effects and all causal variants are rare. In addition, the Cox FR LRT statistics have higher power than Cox BT LRT. The models and related test statistics can be useful in the whole genome and whole exome association studies. An age-related macular degeneration dataset was analyzed as an example. PMID:26782979

Dynamic modelling of n-of-1 data: powerful and flexible data analytics applied to individualised studies.

PubMed

Vieira, Rute; McDonald, Suzanne; Araújo-Soares, Vera; Sniehotta, Falko F; Henderson, Robin

2017-09-01

N-of-1 studies are based on repeated observations within an individual or unit over time and are acknowledged as an important research method for generating scientific evidence about the health or behaviour of an individual. Statistical analyses of n-of-1 data require accurate modelling of the outcome while accounting for its distribution, time-related trend and error structures (e.g., autocorrelation) as well as reporting readily usable contextualised effect sizes for decision-making. A number of statistical approaches have been documented but no consensus exists on which method is most appropriate for which type of n-of-1 design. We discuss the statistical considerations for analysing n-of-1 studies and briefly review some currently used methodologies. We describe dynamic regression modelling as a flexible and powerful approach, adaptable to different types of outcomes and capable of dealing with the different challenges inherent to n-of-1 statistical modelling. Dynamic modelling borrows ideas from longitudinal and event history methodologies which explicitly incorporate the role of time and the influence of past on future. We also present an illustrative example of the use of dynamic regression on monitoring physical activity during the retirement transition. Dynamic modelling has the potential to expand researchers' access to robust and user-friendly statistical methods for individualised studies.

Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

PubMed Central

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-01-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

PubMed

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-12-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

Current state of the art for statistical modeling of species distributions [Chapter 16

Treesearch

Troy M. Hegel; Samuel A. Cushman; Jeffrey Evans; Falk Huettmann

2010-01-01

Over the past decade the number of statistical modelling tools available to ecologists to model species' distributions has increased at a rapid pace (e.g. Elith et al. 2006; Austin 2007), as have the number of species distribution models (SDM) published in the literature (e.g. Scott et al. 2002). Ten years ago, basic logistic regression (Hosmer and Lemeshow 2000)...

Watershed Regressions for Pesticides (WARP) models for predicting stream concentrations of multiple pesticides

USGS Publications Warehouse

Stone, Wesley W.; Crawford, Charles G.; Gilliom, Robert J.

2013-01-01

Watershed Regressions for Pesticides for multiple pesticides (WARP-MP) are statistical models developed to predict concentration statistics for a wide range of pesticides in unmonitored streams. The WARP-MP models use the national atrazine WARP models in conjunction with an adjustment factor for each additional pesticide. The WARP-MP models perform best for pesticides with application timing and methods similar to those used with atrazine. For other pesticides, WARP-MP models tend to overpredict concentration statistics for the model development sites. For WARP and WARP-MP, the less-than-ideal sampling frequency for the model development sites leads to underestimation of the shorter-duration concentration; hence, the WARP models tend to underpredict 4- and 21-d maximum moving-average concentrations, with median errors ranging from 9 to 38% As a result of this sampling bias, pesticides that performed well with the model development sites are expected to have predictions that are biased low for these shorter-duration concentration statistics. The overprediction by WARP-MP apparent for some of the pesticides is variably offset by underestimation of the model development concentration statistics. Of the 112 pesticides used in the WARP-MP application to stream segments nationwide, 25 were predicted to have concentration statistics with a 50% or greater probability of exceeding one or more aquatic life benchmarks in one or more stream segments. Geographically, many of the modeled streams in the Corn Belt Region were predicted to have one or more pesticides that exceeded an aquatic life benchmark during 2009, indicating the potential vulnerability of streams in this region.

Progress of statistical analysis in biomedical research through the historical review of the development of the Framingham score.

PubMed

Ignjatović, Aleksandra; Stojanović, Miodrag; Milošević, Zoran; Anđelković Apostolović, Marija

2017-12-02

The interest in developing risk models in medicine not only is appealing, but also associated with many obstacles in different aspects of predictive model development. Initially, the association of biomarkers or the association of more markers with the specific outcome was proven by statistical significance, but novel and demanding questions required the development of new and more complex statistical techniques. Progress of statistical analysis in biomedical research can be observed the best through the history of the Framingham study and development of the Framingham score. Evaluation of predictive models comes from a combination of the facts which are results of several metrics. Using logistic regression and Cox proportional hazards regression analysis, the calibration test, and the ROC curve analysis should be mandatory and eliminatory, and the central place should be taken by some new statistical techniques. In order to obtain complete information related to the new marker in the model, recently, there is a recommendation to use the reclassification tables by calculating the net reclassification index and the integrated discrimination improvement. Decision curve analysis is a novel method for evaluating the clinical usefulness of a predictive model. It may be noted that customizing and fine-tuning of the Framingham risk score initiated the development of statistical analysis. Clinically applicable predictive model should be a trade-off between all abovementioned statistical metrics, a trade-off between calibration and discrimination, accuracy and decision-making, costs and benefits, and quality and quantity of patient's life.

Applying quantitative adiposity feature analysis models to predict benefit of bevacizumab-based chemotherapy in ovarian cancer patients

NASA Astrophysics Data System (ADS)

Wang, Yunzhi; Qiu, Yuchen; Thai, Theresa; More, Kathleen; Ding, Kai; Liu, Hong; Zheng, Bin

2016-03-01

How to rationally identify epithelial ovarian cancer (EOC) patients who will benefit from bevacizumab or other antiangiogenic therapies is a critical issue in EOC treatments. The motivation of this study is to quantitatively measure adiposity features from CT images and investigate the feasibility of predicting potential benefit of EOC patients with or without receiving bevacizumab-based chemotherapy treatment using multivariate statistical models built based on quantitative adiposity image features. A dataset involving CT images from 59 advanced EOC patients were included. Among them, 32 patients received maintenance bevacizumab after primary chemotherapy and the remaining 27 patients did not. We developed a computer-aided detection (CAD) scheme to automatically segment subcutaneous fat areas (VFA) and visceral fat areas (SFA) and then extracted 7 adiposity-related quantitative features. Three multivariate data analysis models (linear regression, logistic regression and Cox proportional hazards regression) were performed respectively to investigate the potential association between the model-generated prediction results and the patients' progression-free survival (PFS) and overall survival (OS). The results show that using all 3 statistical models, a statistically significant association was detected between the model-generated results and both of the two clinical outcomes in the group of patients receiving maintenance bevacizumab (p<0.01), while there were no significant association for both PFS and OS in the group of patients without receiving maintenance bevacizumab. Therefore, this study demonstrated the feasibility of using quantitative adiposity-related CT image features based statistical prediction models to generate a new clinical marker and predict the clinical outcome of EOC patients receiving maintenance bevacizumab-based chemotherapy.

Modified retrieval algorithm for three types of precipitation distribution using x-band synthetic aperture radar

NASA Astrophysics Data System (ADS)

Xie, Yanan; Zhou, Mingliang; Pan, Dengke

2017-10-01

The forward-scattering model is introduced to describe the response of normalized radar cross section (NRCS) of precipitation with synthetic aperture radar (SAR). Since the distribution of near-surface rainfall is related to the rate of near-surface rainfall and horizontal distribution factor, a retrieval algorithm called modified regression empirical and model-oriented statistical (M-M) based on the volterra integration theory is proposed. Compared with the model-oriented statistical and volterra integration (MOSVI) algorithm, the biggest difference is that the M-M algorithm is based on the modified regression empirical algorithm rather than the linear regression formula to retrieve the value of near-surface rainfall rate. Half of the empirical parameters are reduced in the weighted integral work and a smaller average relative error is received while the rainfall rate is less than 100 mm/h. Therefore, the algorithm proposed in this paper can obtain high-precision rainfall information.

Novel forecasting approaches using combination of machine learning and statistical models for flood susceptibility mapping.

PubMed

Shafizadeh-Moghadam, Hossein; Valavi, Roozbeh; Shahabi, Himan; Chapi, Kamran; Shirzadi, Ataollah

2018-07-01

In this research, eight individual machine learning and statistical models are implemented and compared, and based on their results, seven ensemble models for flood susceptibility assessment are introduced. The individual models included artificial neural networks, classification and regression trees, flexible discriminant analysis, generalized linear model, generalized additive model, boosted regression trees, multivariate adaptive regression splines, and maximum entropy, and the ensemble models were Ensemble Model committee averaging (EMca), Ensemble Model confidence interval Inferior (EMciInf), Ensemble Model confidence interval Superior (EMciSup), Ensemble Model to estimate the coefficient of variation (EMcv), Ensemble Model to estimate the mean (EMmean), Ensemble Model to estimate the median (EMmedian), and Ensemble Model based on weighted mean (EMwmean). The data set covered 201 flood events in the Haraz watershed (Mazandaran province in Iran) and 10,000 randomly selected non-occurrence points. Among the individual models, the Area Under the Receiver Operating Characteristic (AUROC), which showed the highest value, belonged to boosted regression trees (0.975) and the lowest value was recorded for generalized linear model (0.642). On the other hand, the proposed EMmedian resulted in the highest accuracy (0.976) among all models. In spite of the outstanding performance of some models, nevertheless, variability among the prediction of individual models was considerable. Therefore, to reduce uncertainty, creating more generalizable, more stable, and less sensitive models, ensemble forecasting approaches and in particular the EMmedian is recommended for flood susceptibility assessment. Copyright © 2018 Elsevier Ltd. All rights reserved.

Classical Statistics and Statistical Learning in Imaging Neuroscience

PubMed Central

Bzdok, Danilo

2017-01-01

Brain-imaging research has predominantly generated insight by means of classical statistics, including regression-type analyses and null-hypothesis testing using t-test and ANOVA. Throughout recent years, statistical learning methods enjoy increasing popularity especially for applications in rich and complex data, including cross-validated out-of-sample prediction using pattern classification and sparsity-inducing regression. This concept paper discusses the implications of inferential justifications and algorithmic methodologies in common data analysis scenarios in neuroimaging. It is retraced how classical statistics and statistical learning originated from different historical contexts, build on different theoretical foundations, make different assumptions, and evaluate different outcome metrics to permit differently nuanced conclusions. The present considerations should help reduce current confusion between model-driven classical hypothesis testing and data-driven learning algorithms for investigating the brain with imaging techniques. PMID:29056896

Statistical tools for transgene copy number estimation based on real-time PCR.

PubMed

Yuan, Joshua S; Burris, Jason; Stewart, Nathan R; Mentewab, Ayalew; Stewart, C Neal

2007-11-01

As compared with traditional transgene copy number detection technologies such as Southern blot analysis, real-time PCR provides a fast, inexpensive and high-throughput alternative. However, the real-time PCR based transgene copy number estimation tends to be ambiguous and subjective stemming from the lack of proper statistical analysis and data quality control to render a reliable estimation of copy number with a prediction value. Despite the recent progresses in statistical analysis of real-time PCR, few publications have integrated these advancements in real-time PCR based transgene copy number determination. Three experimental designs and four data quality control integrated statistical models are presented. For the first method, external calibration curves are established for the transgene based on serially-diluted templates. The Ct number from a control transgenic event and putative transgenic event are compared to derive the transgene copy number or zygosity estimation. Simple linear regression and two group T-test procedures were combined to model the data from this design. For the second experimental design, standard curves were generated for both an internal reference gene and the transgene, and the copy number of transgene was compared with that of internal reference gene. Multiple regression models and ANOVA models can be employed to analyze the data and perform quality control for this approach. In the third experimental design, transgene copy number is compared with reference gene without a standard curve, but rather, is based directly on fluorescence data. Two different multiple regression models were proposed to analyze the data based on two different approaches of amplification efficiency integration. Our results highlight the importance of proper statistical treatment and quality control integration in real-time PCR-based transgene copy number determination. These statistical methods allow the real-time PCR-based transgene copy number estimation to be more reliable and precise with a proper statistical estimation. Proper confidence intervals are necessary for unambiguous prediction of trangene copy number. The four different statistical methods are compared for their advantages and disadvantages. Moreover, the statistical methods can also be applied for other real-time PCR-based quantification assays including transfection efficiency analysis and pathogen quantification.

A review and comparison of Bayesian and likelihood-based inferences in beta regression and zero-or-one-inflated beta regression.

PubMed

Liu, Fang; Eugenio, Evercita C

2018-04-01

Beta regression is an increasingly popular statistical technique in medical research for modeling of outcomes that assume values in (0, 1), such as proportions and patient reported outcomes. When outcomes take values in the intervals [0,1), (0,1], or [0,1], zero-or-one-inflated beta (zoib) regression can be used. We provide a thorough review on beta regression and zoib regression in the modeling, inferential, and computational aspects via the likelihood-based and Bayesian approaches. We demonstrate the statistical and practical importance of correctly modeling the inflation at zero/one rather than ad hoc replacing them with values close to zero/one via simulation studies; the latter approach can lead to biased estimates and invalid inferences. We show via simulation studies that the likelihood-based approach is computationally faster in general than MCMC algorithms used in the Bayesian inferences, but runs the risk of non-convergence, large biases, and sensitivity to starting values in the optimization algorithm especially with clustered/correlated data, data with sparse inflation at zero and one, and data that warrant regularization of the likelihood. The disadvantages of the regular likelihood-based approach make the Bayesian approach an attractive alternative in these cases. Software packages and tools for fitting beta and zoib regressions in both the likelihood-based and Bayesian frameworks are also reviewed.

An open-access CMIP5 pattern library for temperature and precipitation: description and methodology

NASA Astrophysics Data System (ADS)

Lynch, Cary; Hartin, Corinne; Bond-Lamberty, Ben; Kravitz, Ben

2017-05-01

Pattern scaling is used to efficiently emulate general circulation models and explore uncertainty in climate projections under multiple forcing scenarios. Pattern scaling methods assume that local climate changes scale with a global mean temperature increase, allowing for spatial patterns to be generated for multiple models for any future emission scenario. For uncertainty quantification and probabilistic statistical analysis, a library of patterns with descriptive statistics for each file would be beneficial, but such a library does not presently exist. Of the possible techniques used to generate patterns, the two most prominent are the delta and least squares regression methods. We explore the differences and statistical significance between patterns generated by each method and assess performance of the generated patterns across methods and scenarios. Differences in patterns across seasons between methods and epochs were largest in high latitudes (60-90° N/S). Bias and mean errors between modeled and pattern-predicted output from the linear regression method were smaller than patterns generated by the delta method. Across scenarios, differences in the linear regression method patterns were more statistically significant, especially at high latitudes. We found that pattern generation methodologies were able to approximate the forced signal of change to within ≤ 0.5 °C, but the choice of pattern generation methodology for pattern scaling purposes should be informed by user goals and criteria. This paper describes our library of least squares regression patterns from all CMIP5 models for temperature and precipitation on an annual and sub-annual basis, along with the code used to generate these patterns. The dataset and netCDF data generation code are available at doi:10.5281/zenodo.495632.

Determinant of securitization asset pricing in Malaysia

NASA Astrophysics Data System (ADS)

Bakri, M. H.; Ali, R.; Ismail, S.; Sufian, F.; Baharom, A. H.

2014-12-01

Malaysian firms have been reported involve in Asset Back Securities since 1986s where Cagamas is a pioneer. This research aims to examine the factor influencing primary market spread. Least square method and regression analysis are applied for the study period 2004-2012. The result shows one determinants in internal regression model and three determinants in external regression influence or contribute to the primary market spread and are statistically significant in developing the securitization in Malaysia. It can be concluded that transaction size significantly contribute to the determinant primary market spread in internal regression model while liquidity, transaction size and crisis is significant in both regression model. From five hypotheses, three hypotheses support that the determinants have a relationship with primary market spread.

Statistical Approaches to Interpretation of Local, Regional, and National Highway-Runoff and Urban-Stormwater Data

USGS Publications Warehouse

Tasker, Gary D.; Granato, Gregory E.

2000-01-01

Decision makers need viable methods for the interpretation of local, regional, and national-highway runoff and urban-stormwater data including flows, concentrations and loads of chemical constituents and sediment, potential effects on receiving waters, and the potential effectiveness of various best management practices (BMPs). Valid (useful for intended purposes), current, and technically defensible stormwater-runoff models are needed to interpret data collected in field studies, to support existing highway and urban-runoffplanning processes, to meet National Pollutant Discharge Elimination System (NPDES) requirements, and to provide methods for computation of Total Maximum Daily Loads (TMDLs) systematically and economically. Historically, conceptual, simulation, empirical, and statistical models of varying levels of detail, complexity, and uncertainty have been used to meet various data-quality objectives in the decision-making processes necessary for the planning, design, construction, and maintenance of highways and for other land-use applications. Water-quality simulation models attempt a detailed representation of the physical processes and mechanisms at a given site. Empirical and statistical regional water-quality assessment models provide a more general picture of water quality or changes in water quality over a region. All these modeling techniques share one common aspect-their predictive ability is poor without suitable site-specific data for calibration. To properly apply the correct model, one must understand the classification of variables, the unique characteristics of water-resources data, and the concept of population structure and analysis. Classifying variables being used to analyze data may determine which statistical methods are appropriate for data analysis. An understanding of the characteristics of water-resources data is necessary to evaluate the applicability of different statistical methods, to interpret the results of these techniques, and to use tools and techniques that account for the unique nature of water-resources data sets. Populations of data on stormwater-runoff quantity and quality are often best modeled as logarithmic transformations. Therefore, these factors need to be considered to form valid, current, and technically defensible stormwater-runoff models. Regression analysis is an accepted method for interpretation of water-resources data and for prediction of current or future conditions at sites that fit the input data model. Regression analysis is designed to provide an estimate of the average response of a system as it relates to variation in one or more known variables. To produce valid models, however, regression analysis should include visual analysis of scatterplots, an examination of the regression equation, evaluation of the method design assumptions, and regression diagnostics. A number of statistical techniques are described in the text and in the appendixes to provide information necessary to interpret data by use of appropriate methods. Uncertainty is an important part of any decisionmaking process. In order to deal with uncertainty problems, the analyst needs to know the severity of the statistical uncertainty of the methods used to predict water quality. Statistical models need to be based on information that is meaningful, representative, complete, precise, accurate, and comparable to be deemed valid, up to date, and technically supportable. To assess uncertainty in the analytical tools, the modeling methods, and the underlying data set, all of these components need be documented and communicated in an accessible format within project publications.

Prediction of dimethyl disulfide levels from biosolids using statistical modeling.

PubMed

Gabriel, Steven A; Vilalai, Sirapong; Arispe, Susanna; Kim, Hyunook; McConnell, Laura L; Torrents, Alba; Peot, Christopher; Ramirez, Mark

2005-01-01

Two statistical models were used to predict the concentration of dimethyl disulfide (DMDS) released from biosolids produced by an advanced wastewater treatment plant (WWTP) located in Washington, DC, USA. The plant concentrates sludge from primary sedimentation basins in gravity thickeners (GT) and sludge from secondary sedimentation basins in dissolved air flotation (DAF) thickeners. The thickened sludge is pumped into blending tanks and then fed into centrifuges for dewatering. The dewatered sludge is then conditioned with lime before trucking out from the plant. DMDS, along with other volatile sulfur and nitrogen-containing chemicals, is known to contribute to biosolids odors. These models identified oxidation/reduction potential (ORP) values of a GT and DAF, the amount of sludge dewatered by centrifuges, and the blend ratio between GT thickened sludge and DAF thickened sludge in blending tanks as control variables. The accuracy of the developed regression models was evaluated by checking the adjusted R2 of the regression as well as the signs of coefficients associated with each variable. In general, both models explained observed DMDS levels in sludge headspace samples. The adjusted R2 value of the regression models 1 and 2 were 0.79 and 0.77, respectively. Coefficients for each regression model also had the correct sign. Using the developed models, plant operators can adjust the controllable variables to proactively decrease this odorant. Therefore, these models are a useful tool in biosolids management at WWTPs.

Web 2.0 Articles: Content Analysis and a Statistical Model to Predict Recognition of the Need for New Instructional Design Strategies

ERIC Educational Resources Information Center

Liu, Leping; Maddux, Cleborne D.

2008-01-01

This article presents a study of Web 2.0 articles intended to (a) analyze the content of what is written and (b) develop a statistical model to predict whether authors' write about the need for new instructional design strategies and models. Eighty-eight technology articles were subjected to lexical analysis and a logistic regression model was…

Intermediate and advanced topics in multilevel logistic regression analysis.

PubMed

Austin, Peter C; Merlo, Juan

2017-09-10

Multilevel data occur frequently in health services, population and public health, and epidemiologic research. In such research, binary outcomes are common. Multilevel logistic regression models allow one to account for the clustering of subjects within clusters of higher-level units when estimating the effect of subject and cluster characteristics on subject outcomes. A search of the PubMed database demonstrated that the use of multilevel or hierarchical regression models is increasing rapidly. However, our impression is that many analysts simply use multilevel regression models to account for the nuisance of within-cluster homogeneity that is induced by clustering. In this article, we describe a suite of analyses that can complement the fitting of multilevel logistic regression models. These ancillary analyses permit analysts to estimate the marginal or population-average effect of covariates measured at the subject and cluster level, in contrast to the within-cluster or cluster-specific effects arising from the original multilevel logistic regression model. We describe the interval odds ratio and the proportion of opposed odds ratios, which are summary measures of effect for cluster-level covariates. We describe the variance partition coefficient and the median odds ratio which are measures of components of variance and heterogeneity in outcomes. These measures allow one to quantify the magnitude of the general contextual effect. We describe an R 2 measure that allows analysts to quantify the proportion of variation explained by different multilevel logistic regression models. We illustrate the application and interpretation of these measures by analyzing mortality in patients hospitalized with a diagnosis of acute myocardial infarction. © 2017 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. © 2017 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Distributed Monitoring of the R(sup 2) Statistic for Linear Regression

NASA Technical Reports Server (NTRS)

Bhaduri, Kanishka; Das, Kamalika; Giannella, Chris R.

2011-01-01

The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and one or more dependent target variables. This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings. Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the updated model is broadcast back to all nodes. We show empirically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness.

Development and validation of a risk calculator predicting exercise-induced ventricular arrhythmia in patients with cardiovascular disease.

PubMed

Hermes, Ilarraza-Lomelí; Marianna, García-Saldivia; Jessica, Rojano-Castillo; Carlos, Barrera-Ramírez; Rafael, Chávez-Domínguez; María Dolores, Rius-Suárez; Pedro, Iturralde

2016-10-01

Mortality due to cardiovascular disease is often associated with ventricular arrhythmias. Nowadays, patients with cardiovascular disease are more encouraged to take part in physical training programs. Nevertheless, high-intensity exercise is associated to a higher risk for sudden death, even in apparently healthy people. During an exercise testing (ET), health care professionals provide patients, in a controlled scenario, an intense physiological stimulus that could precipitate cardiac arrhythmia in high risk individuals. There is still no clinical or statistical tool to predict this incidence. The aim of this study was to develop a statistical model to predict the incidence of exercise-induced potentially life-threatening ventricular arrhythmia (PLVA) during high intensity exercise. 6415 patients underwent a symptom-limited ET with a Balke ramp protocol. A multivariate logistic regression model where the primary outcome was PLVA was performed. Incidence of PLVA was 548 cases (8.5%). After a bivariate model, thirty one clinical or ergometric variables were statistically associated with PLVA and were included in the regression model. In the multivariate model, 13 of these variables were found to be statistically significant. A regression model (G) with a X(2) of 283.987 and a p<0.001, was constructed. Significant variables included: heart failure, antiarrhythmic drugs, myocardial lower-VD, age and use of digoxin, nitrates, among others. This study allows clinicians to identify patients at risk of ventricular tachycardia or couplets during exercise, and to take preventive measures or appropriate supervision. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Regression-Based Norms for a Bi-factor Model for Scoring the Brief Test of Adult Cognition by Telephone (BTACT).

PubMed

Gurnani, Ashita S; John, Samantha E; Gavett, Brandon E

2015-05-01

The current study developed regression-based normative adjustments for a bi-factor model of the The Brief Test of Adult Cognition by Telephone (BTACT). Archival data from the Midlife Development in the United States-II Cognitive Project were used to develop eight separate linear regression models that predicted bi-factor BTACT scores, accounting for age, education, gender, and occupation-alone and in various combinations. All regression models provided statistically significant fit to the data. A three-predictor regression model fit best and accounted for 32.8% of the variance in the global bi-factor BTACT score. The fit of the regression models was not improved by gender. Eight different regression models are presented to allow the user flexibility in applying demographic corrections to the bi-factor BTACT scores. Occupation corrections, while not widely used, may provide useful demographic adjustments for adult populations or for those individuals who have attained an occupational status not commensurate with expected educational attainment. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

The extension of total gain (TG) statistic in survival models: properties and applications.

PubMed

Choodari-Oskooei, Babak; Royston, Patrick; Parmar, Mahesh K B

2015-07-01

The results of multivariable regression models are usually summarized in the form of parameter estimates for the covariates, goodness-of-fit statistics, and the relevant p-values. These statistics do not inform us about whether covariate information will lead to any substantial improvement in prediction. Predictive ability measures can be used for this purpose since they provide important information about the practical significance of prognostic factors. R (2)-type indices are the most familiar forms of such measures in survival models, but they all have limitations and none is widely used. In this paper, we extend the total gain (TG) measure, proposed for a logistic regression model, to survival models and explore its properties using simulations and real data. TG is based on the binary regression quantile plot, otherwise known as the predictiveness curve. Standardised TG ranges from 0 (no explanatory power) to 1 ('perfect' explanatory power). The results of our simulations show that unlike many of the other R (2)-type predictive ability measures, TG is independent of random censoring. It increases as the effect of a covariate increases and can be applied to different types of survival models, including models with time-dependent covariate effects. We also apply TG to quantify the predictive ability of multivariable prognostic models developed in several disease areas. Overall, TG performs well in our simulation studies and can be recommended as a measure to quantify the predictive ability in survival models.

Watershed regressions for pesticides (warp) models for predicting atrazine concentrations in Corn Belt streams

USGS Publications Warehouse

Stone, Wesley W.; Gilliom, Robert J.

2012-01-01

Watershed Regressions for Pesticides (WARP) models, previously developed for atrazine at the national scale, are improved for application to the United States (U.S.) Corn Belt region by developing region-specific models that include watershed characteristics that are influential in predicting atrazine concentration statistics within the Corn Belt. WARP models for the Corn Belt (WARP-CB) were developed for annual maximum moving-average (14-, 21-, 30-, 60-, and 90-day durations) and annual 95th-percentile atrazine concentrations in streams of the Corn Belt region. The WARP-CB models accounted for 53 to 62% of the variability in the various concentration statistics among the model-development sites. Model predictions were within a factor of 5 of the observed concentration statistic for over 90% of the model-development sites. The WARP-CB residuals and uncertainty are lower than those of the National WARP model for the same sites. Although atrazine-use intensity is the most important explanatory variable in the National WARP models, it is not a significant variable in the WARP-CB models. The WARP-CB models provide improved predictions for Corn Belt streams draining watersheds with atrazine-use intensities of 17 kg/km2 of watershed area or greater.

Regression Models of Quarterly Overhead Costs for Six Government Aerospace Contractors.

DTIC Science & Technology

1986-03-01

34 Testing ,, for Serial Correlation After Least Squares %Regression, Econometrica, Vol. 36, No. 1, pp. 133-150, January 1968. Intrili8ator M.D., Econometric ...to be superior. These two estimators are both two-stage estimators that are calculated utilizing Wallis’s test statistic for fourth-order...utilizing Wallis’s test statistic for fourth-order autocorrelation. NTIS C F’,& D tI1C T - .1 I -. . . ..- rJ ,. *p J • - DA 3

Use of statistical study methods for the analysis of the results of the imitation modeling of radiation transfer

NASA Astrophysics Data System (ADS)

Alekseenko, M. A.; Gendrina, I. Yu.

2017-11-01

Recently, due to the abundance of various types of observational data in the systems of vision through the atmosphere and the need for their processing, the use of various methods of statistical research in the study of such systems as correlation-regression analysis, dynamic series, variance analysis, etc. is actual. We have attempted to apply elements of correlation-regression analysis for the study and subsequent prediction of the patterns of radiation transfer in these systems same as in the construction of radiation models of the atmosphere. In this paper, we present some results of statistical processing of the results of numerical simulation of the characteristics of vision systems through the atmosphere obtained with the help of a special software package.1

Quality of life in breast cancer patients--a quantile regression analysis.

PubMed

Pourhoseingholi, Mohamad Amin; Safaee, Azadeh; Moghimi-Dehkordi, Bijan; Zeighami, Bahram; Faghihzadeh, Soghrat; Tabatabaee, Hamid Reza; Pourhoseingholi, Asma

2008-01-01

Quality of life study has an important role in health care especially in chronic diseases, in clinical judgment and in medical resources supplying. Statistical tools like linear regression are widely used to assess the predictors of quality of life. But when the response is not normal the results are misleading. The aim of this study is to determine the predictors of quality of life in breast cancer patients, using quantile regression model and compare to linear regression. A cross-sectional study conducted on 119 breast cancer patients that admitted and treated in chemotherapy ward of Namazi hospital in Shiraz. We used QLQ-C30 questionnaire to assessment quality of life in these patients. A quantile regression was employed to assess the assocciated factors and the results were compared to linear regression. All analysis carried out using SAS. The mean score for the global health status for breast cancer patients was 64.92+/-11.42. Linear regression showed that only grade of tumor, occupational status, menopausal status, financial difficulties and dyspnea were statistically significant. In spite of linear regression, financial difficulties were not significant in quantile regression analysis and dyspnea was only significant for first quartile. Also emotion functioning and duration of disease statistically predicted the QOL score in the third quartile. The results have demonstrated that using quantile regression leads to better interpretation and richer inference about predictors of the breast cancer patient quality of life.

Advanced statistics: linear regression, part I: simple linear regression.

PubMed

Marill, Keith A

2004-01-01

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

Two-Year versus One-Year Head Start Program Impact: Addressing Selection Bias by Comparing Regression Modeling with Propensity Score Analysis

ERIC Educational Resources Information Center

Leow, Christine; Wen, Xiaoli; Korfmacher, Jon

2015-01-01

This article compares regression modeling and propensity score analysis as different types of statistical techniques used in addressing selection bias when estimating the impact of two-year versus one-year Head Start on children's school readiness. The analyses were based on the national Head Start secondary dataset. After controlling for…

[Statistical prediction methods in violence risk assessment and its application].

PubMed

Liu, Yuan-Yuan; Hu, Jun-Mei; Yang, Min; Li, Xiao-Song

2013-06-01

It is an urgent global problem how to improve the violence risk assessment. As a necessary part of risk assessment, statistical methods have remarkable impacts and effects. In this study, the predicted methods in violence risk assessment from the point of statistics are reviewed. The application of Logistic regression as the sample of multivariate statistical model, decision tree model as the sample of data mining technique, and neural networks model as the sample of artificial intelligence technology are all reviewed. This study provides data in order to contribute the further research of violence risk assessment.

Illuminating Tradespace Decisions Using Efficient Experimental Space-Filling Designs for the Engineered Resilient System Architecture

DTIC Science & Technology

2015-06-30

7. Building Statistical Metamodels using Simulation Experimental Designs ............................................... 34 7.1. Statistical Design...system design drivers across several different domain models, our methodology uses statistical metamodeling to approximate the simulations’ behavior. A...output. We build metamodels using a number of statistical methods that include stepwise regression, boosted trees, neural nets, and bootstrap forest

Illuminating Tradespace Decisions Using Efficient Experimental Space-Filling Designs for the Engineered Resilient System Architecture

DTIC Science & Technology

2015-06-01

7. Building Statistical Metamodels using Simulation Experimental Designs ............................................... 34 7.1. Statistical Design...system design drivers across several different domain models, our methodology uses statistical metamodeling to approximate the simulations’ behavior. A...output. We build metamodels using a number of statistical methods that include stepwise regression, boosted trees, neural nets, and bootstrap forest

Strengthen forensic entomology in court--the need for data exploration and the validation of a generalised additive mixed model.

PubMed

Baqué, Michèle; Amendt, Jens

2013-01-01

Developmental data of juvenile blow flies (Diptera: Calliphoridae) are typically used to calculate the age of immature stages found on or around a corpse and thus to estimate a minimum post-mortem interval (PMI(min)). However, many of those data sets don't take into account that immature blow flies grow in a non-linear fashion. Linear models do not supply a sufficient reliability on age estimates and may even lead to an erroneous determination of the PMI(min). According to the Daubert standard and the need for improvements in forensic science, new statistic tools like smoothing methods and mixed models allow the modelling of non-linear relationships and expand the field of statistical analyses. The present study introduces into the background and application of these statistical techniques by analysing a model which describes the development of the forensically important blow fly Calliphora vicina at different temperatures. The comparison of three statistical methods (linear regression, generalised additive modelling and generalised additive mixed modelling) clearly demonstrates that only the latter provided regression parameters that reflect the data adequately. We focus explicitly on both the exploration of the data--to assure their quality and to show the importance of checking it carefully prior to conducting the statistical tests--and the validation of the resulting models. Hence, we present a common method for evaluating and testing forensic entomological data sets by using for the first time generalised additive mixed models.

Inferring epidemiological parameters from phylogenies using regression-ABC: A comparative study

PubMed Central

Gascuel, Olivier

2017-01-01

Inferring epidemiological parameters such as the R0 from time-scaled phylogenies is a timely challenge. Most current approaches rely on likelihood functions, which raise specific issues that range from computing these functions to finding their maxima numerically. Here, we present a new regression-based Approximate Bayesian Computation (ABC) approach, which we base on a large variety of summary statistics intended to capture the information contained in the phylogeny and its corresponding lineage-through-time plot. The regression step involves the Least Absolute Shrinkage and Selection Operator (LASSO) method, which is a robust machine learning technique. It allows us to readily deal with the large number of summary statistics, while avoiding resorting to Markov Chain Monte Carlo (MCMC) techniques. To compare our approach to existing ones, we simulated target trees under a variety of epidemiological models and settings, and inferred parameters of interest using the same priors. We found that, for large phylogenies, the accuracy of our regression-ABC is comparable to that of likelihood-based approaches involving birth-death processes implemented in BEAST2. Our approach even outperformed these when inferring the host population size with a Susceptible-Infected-Removed epidemiological model. It also clearly outperformed a recent kernel-ABC approach when assuming a Susceptible-Infected epidemiological model with two host types. Lastly, by re-analyzing data from the early stages of the recent Ebola epidemic in Sierra Leone, we showed that regression-ABC provides more realistic estimates for the duration parameters (latency and infectiousness) than the likelihood-based method. Overall, ABC based on a large variety of summary statistics and a regression method able to perform variable selection and avoid overfitting is a promising approach to analyze large phylogenies. PMID:28263987

Probabilistic regional climate projection in Japan using a regression model with CMIP5 multi-model ensemble experiments

NASA Astrophysics Data System (ADS)

Ishizaki, N. N.; Dairaku, K.; Ueno, G.

2016-12-01

We have developed a statistical downscaling method for estimating probabilistic climate projection using CMIP5 multi general circulation models (GCMs). A regression model was established so that the combination of weights of GCMs reflects the characteristics of the variation of observations at each grid point. Cross validations were conducted to select GCMs and to evaluate the regression model to avoid multicollinearity. By using spatially high resolution observation system, we conducted statistically downscaled probabilistic climate projections with 20-km horizontal grid spacing. Root mean squared errors for monthly mean air surface temperature and precipitation estimated by the regression method were the smallest compared with the results derived from a simple ensemble mean of GCMs and a cumulative distribution function based bias correction method. Projected changes in the mean temperature and precipitation were basically similar to those of the simple ensemble mean of GCMs. Mean precipitation was generally projected to increase associated with increased temperature and consequent increased moisture content in the air. Weakening of the winter monsoon may affect precipitation decrease in some areas. Temperature increase in excess of 4 K was expected in most areas of Japan in the end of 21st century under RCP8.5 scenario. The estimated probability of monthly precipitation exceeding 300 mm would increase around the Pacific side during the summer and the Japan Sea side during the winter season. This probabilistic climate projection based on the statistical method can be expected to bring useful information to the impact studies and risk assessments.

Using meta-regression models to systematically evaluate data in the published literature: relative contributions of agricultural drift, para-occupational, and residential use exposure pathways to house dust pesticide concentrations

EPA Science Inventory

Background: Data reported in the published literature have been used qualitatively to aid exposure assessment activities in epidemiologic studies. Analyzing these data in computational models presents statistical challenges because these data are often reported as summary statist...

Modeling time-to-event (survival) data using classification tree analysis.

PubMed

Linden, Ariel; Yarnold, Paul R

2017-12-01

Time to the occurrence of an event is often studied in health research. Survival analysis differs from other designs in that follow-up times for individuals who do not experience the event by the end of the study (called censored) are accounted for in the analysis. Cox regression is the standard method for analysing censored data, but the assumptions required of these models are easily violated. In this paper, we introduce classification tree analysis (CTA) as a flexible alternative for modelling censored data. Classification tree analysis is a "decision-tree"-like classification model that provides parsimonious, transparent (ie, easy to visually display and interpret) decision rules that maximize predictive accuracy, derives exact P values via permutation tests, and evaluates model cross-generalizability. Using empirical data, we identify all statistically valid, reproducible, longitudinally consistent, and cross-generalizable CTA survival models and then compare their predictive accuracy to estimates derived via Cox regression and an unadjusted naïve model. Model performance is assessed using integrated Brier scores and a comparison between estimated survival curves. The Cox regression model best predicts average incidence of the outcome over time, whereas CTA survival models best predict either relatively high, or low, incidence of the outcome over time. Classification tree analysis survival models offer many advantages over Cox regression, such as explicit maximization of predictive accuracy, parsimony, statistical robustness, and transparency. Therefore, researchers interested in accurate prognoses and clear decision rules should consider developing models using the CTA-survival framework. © 2017 John Wiley & Sons, Ltd.

Evaluating differential effects using regression interactions and regression mixture models

PubMed Central

Van Horn, M. Lee; Jaki, Thomas; Masyn, Katherine; Howe, George; Feaster, Daniel J.; Lamont, Andrea E.; George, Melissa R. W.; Kim, Minjung

2015-01-01

Research increasingly emphasizes understanding differential effects. This paper focuses on understanding regression mixture models, a relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their formulation, and their assumptions are compared using Monte Carlo simulations and real data analysis. The capabilities of regression mixture models are described and specific issues to be addressed when conducting regression mixtures are proposed. The paper aims to clarify the role that regression mixtures can take in the estimation of differential effects and increase awareness of the benefits and potential pitfalls of this approach. Regression mixture models are shown to be a potentially effective exploratory method for finding differential effects when these effects can be defined by a small number of classes of respondents who share a typical relationship between a predictor and an outcome. It is also shown that the comparison between regression mixture models and interactions becomes substantially more complex as the number of classes increases. It is argued that regression interactions are well suited for direct tests of specific hypotheses about differential effects and regression mixtures provide a useful approach for exploring effect heterogeneity given adequate samples and study design. PMID:26556903

A gentle introduction to quantile regression for ecologists

USGS Publications Warehouse

Cade, B.S.; Noon, B.R.

2003-01-01

Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between variables in ecological processes. Typically, all the factors that affect ecological processes are not measured and included in the statistical models used to investigate relationships between variables associated with those processes. As a consequence, there may be a weak or no predictive relationship between the mean of the response variable (y) distribution and the measured predictive factors (X). Yet there may be stronger, useful predictive relationships with other parts of the response variable distribution. This primer relates quantile regression estimates to prediction intervals in parametric error distribution regression models (eg least squares), and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of the estimates for homogeneous and heterogeneous regression models.

A statistical method for predicting seizure onset zones from human single-neuron recordings

NASA Astrophysics Data System (ADS)

Valdez, André B.; Hickman, Erin N.; Treiman, David M.; Smith, Kris A.; Steinmetz, Peter N.

2013-02-01

Objective. Clinicians often use depth-electrode recordings to localize human epileptogenic foci. To advance the diagnostic value of these recordings, we applied logistic regression models to single-neuron recordings from depth-electrode microwires to predict seizure onset zones (SOZs). Approach. We collected data from 17 epilepsy patients at the Barrow Neurological Institute and developed logistic regression models to calculate the odds of observing SOZs in the hippocampus, amygdala and ventromedial prefrontal cortex, based on statistics such as the burst interspike interval (ISI). Main results. Analysis of these models showed that, for a single-unit increase in burst ISI ratio, the left hippocampus was approximately 12 times more likely to contain a SOZ; and the right amygdala, 14.5 times more likely. Our models were most accurate for the hippocampus bilaterally (at 85% average sensitivity), and performance was comparable with current diagnostics such as electroencephalography. Significance. Logistic regression models can be combined with single-neuron recording to predict likely SOZs in epilepsy patients being evaluated for resective surgery, providing an automated source of clinically useful information.

Predicting the potential distribution of invasive exotic species using GIS and information-theoretic approaches: A case of ragweed (Ambrosia artemisiifolia L.) distribution in China

USGS Publications Warehouse

Hao, Chen; LiJun, Chen; Albright, Thomas P.

2007-01-01

Invasive exotic species pose a growing threat to the economy, public health, and ecological integrity of nations worldwide. Explaining and predicting the spatial distribution of invasive exotic species is of great importance to prevention and early warning efforts. We are investigating the potential distribution of invasive exotic species, the environmental factors that influence these distributions, and the ability to predict them using statistical and information-theoretic approaches. For some species, detailed presence/absence occurrence data are available, allowing the use of a variety of standard statistical techniques. However, for most species, absence data are not available. Presented with the challenge of developing a model based on presence-only information, we developed an improved logistic regression approach using Information Theory and Frequency Statistics to produce a relative suitability map. This paper generated a variety of distributions of ragweed (Ambrosia artemisiifolia L.) from logistic regression models applied to herbarium specimen location data and a suite of GIS layers including climatic, topographic, and land cover information. Our logistic regression model was based on Akaike's Information Criterion (AIC) from a suite of ecologically reasonable predictor variables. Based on the results we provided a new Frequency Statistical method to compartmentalize habitat-suitability in the native range. Finally, we used the model and the compartmentalized criterion developed in native ranges to "project" a potential distribution onto the exotic ranges to build habitat-suitability maps. ?? Science in China Press 2007.

An improved portmanteau test for autocorrelated errors in interrupted time-series regression models.

PubMed

Huitema, Bradley E; McKean, Joseph W

2007-08-01

A new portmanteau test for autocorrelation among the errors of interrupted time-series regression models is proposed. Simulation results demonstrate that the inferential properties of the proposed Q(H-M) test statistic are considerably more satisfactory than those of the well known Ljung-Box test and moderately better than those of the Box-Pierce test. These conclusions generally hold for a wide variety of autoregressive (AR), moving averages (MA), and ARMA error processes that are associated with time-series regression models of the form described in Huitema and McKean (2000a, 2000b).

Prediction of biomechanical parameters of the proximal femur using statistical appearance models and support vector regression.

PubMed

Fritscher, Karl; Schuler, Benedikt; Link, Thomas; Eckstein, Felix; Suhm, Norbert; Hänni, Markus; Hengg, Clemens; Schubert, Rainer

2008-01-01

Fractures of the proximal femur are one of the principal causes of mortality among elderly persons. Traditional methods for the determination of femoral fracture risk use methods for measuring bone mineral density. However, BMD alone is not sufficient to predict bone failure load for an individual patient and additional parameters have to be determined for this purpose. In this work an approach that uses statistical models of appearance to identify relevant regions and parameters for the prediction of biomechanical properties of the proximal femur will be presented. By using Support Vector Regression the proposed model based approach is capable of predicting two different biomechanical parameters accurately and fully automatically in two different testing scenarios.

Transfer Student Success: Educationally Purposeful Activities Predictive of Undergraduate GPA

ERIC Educational Resources Information Center

Fauria, Renee M.; Fuller, Matthew B.

2015-01-01

Researchers evaluated the effects of Educationally Purposeful Activities (EPAs) on transfer and nontransfer students' cumulative GPAs. Hierarchical, linear, and multiple regression models yielded seven statistically significant educationally purposeful items that influenced undergraduate student GPAs. Statistically significant positive EPAs for…

Kepler AutoRegressive Planet Search: Motivation & Methodology

NASA Astrophysics Data System (ADS)

Caceres, Gabriel; Feigelson, Eric; Jogesh Babu, G.; Bahamonde, Natalia; Bertin, Karine; Christen, Alejandra; Curé, Michel; Meza, Cristian

2015-08-01

The Kepler AutoRegressive Planet Search (KARPS) project uses statistical methodology associated with autoregressive (AR) processes to model Kepler lightcurves in order to improve exoplanet transit detection in systems with high stellar variability. We also introduce a planet-search algorithm to detect transits in time-series residuals after application of the AR models. One of the main obstacles in detecting faint planetary transits is the intrinsic stellar variability of the host star. The variability displayed by many stars may have autoregressive properties, wherein later flux values are correlated with previous ones in some manner. Auto-Regressive Moving-Average (ARMA) models, Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH), and related models are flexible, phenomenological methods used with great success to model stochastic temporal behaviors in many fields of study, particularly econometrics. Powerful statistical methods are implemented in the public statistical software environment R and its many packages. Modeling involves maximum likelihood fitting, model selection, and residual analysis. These techniques provide a useful framework to model stellar variability and are used in KARPS with the objective of reducing stellar noise to enhance opportunities to find as-yet-undiscovered planets. Our analysis procedure consisting of three steps: pre-processing of the data to remove discontinuities, gaps and outliers; ARMA-type model selection and fitting; and transit signal search of the residuals using a new Transit Comb Filter (TCF) that replaces traditional box-finding algorithms. We apply the procedures to simulated Kepler-like time series with known stellar and planetary signals to evaluate the effectiveness of the KARPS procedures. The ARMA-type modeling is effective at reducing stellar noise, but also reduces and transforms the transit signal into ingress/egress spikes. A periodogram based on the TCF is constructed to concentrate the signal of these periodic spikes. When a periodic transit is found, the model is displayed on a standard period-folded averaged light curve. We also illustrate the efficient coding in R.

Logistic regression for risk factor modelling in stuttering research.

PubMed

Reed, Phil; Wu, Yaqionq

2013-06-01

To outline the uses of logistic regression and other statistical methods for risk factor analysis in the context of research on stuttering. The principles underlying the application of a logistic regression are illustrated, and the types of questions to which such a technique has been applied in the stuttering field are outlined. The assumptions and limitations of the technique are discussed with respect to existing stuttering research, and with respect to formulating appropriate research strategies to accommodate these considerations. Finally, some alternatives to the approach are briefly discussed. The way the statistical procedures are employed are demonstrated with some hypothetical data. Research into several practical issues concerning stuttering could benefit if risk factor modelling were used. Important examples are early diagnosis, prognosis (whether a child will recover or persist) and assessment of treatment outcome. After reading this article you will: (a) Summarize the situations in which logistic regression can be applied to a range of issues about stuttering; (b) Follow the steps in performing a logistic regression analysis; (c) Describe the assumptions of the logistic regression technique and the precautions that need to be checked when it is employed; (d) Be able to summarize its advantages over other techniques like estimation of group differences and simple regression. Copyright © 2012 Elsevier Inc. All rights reserved.

Quantifying discrimination of Framingham risk functions with different survival C statistics.

PubMed

Pencina, Michael J; D'Agostino, Ralph B; Song, Linye

2012-07-10

Cardiovascular risk prediction functions offer an important diagnostic tool for clinicians and patients themselves. They are usually constructed with the use of parametric or semi-parametric survival regression models. It is essential to be able to evaluate the performance of these models, preferably with summaries that offer natural and intuitive interpretations. The concept of discrimination, popular in the logistic regression context, has been extended to survival analysis. However, the extension is not unique. In this paper, we define discrimination in survival analysis as the model's ability to separate those with longer event-free survival from those with shorter event-free survival within some time horizon of interest. This definition remains consistent with that used in logistic regression, in the sense that it assesses how well the model-based predictions match the observed data. Practical and conceptual examples and numerical simulations are employed to examine four C statistics proposed in the literature to evaluate the performance of survival models. We observe that they differ in the numerical values and aspects of discrimination that they capture. We conclude that the index proposed by Harrell is the most appropriate to capture discrimination described by the above definition. We suggest researchers report which C statistic they are using, provide a rationale for their selection, and be aware that comparing different indices across studies may not be meaningful. Copyright © 2012 John Wiley & Sons, Ltd.

Summer and winter habitat suitability of Marco Polo argali in southeastern Tajikistan: A modeling approach.

PubMed

Salas, Eric Ariel L; Valdez, Raul; Michel, Stefan

2017-11-01

We modeled summer and winter habitat suitability of Marco Polo argali in the Pamir Mountains in southeastern Tajikistan using these statistical algorithms: Generalized Linear Model, Random Forest, Boosted Regression Tree, Maxent, and Multivariate Adaptive Regression Splines. Using sheep occurrence data collected from 2009 to 2015 and a set of selected habitat predictors, we produced summer and winter habitat suitability maps and determined the important habitat suitability predictors for both seasons. Our results demonstrated that argali selected proximity to riparian areas and greenness as the two most relevant variables for summer, and the degree of slope (gentler slopes between 0° to 20°) and Landsat temperature band for winter. The terrain roughness was also among the most important variables in summer and winter models. Aspect was only significant for winter habitat, with argali preferring south-facing mountain slopes. We evaluated various measures of model performance such as the Area Under the Curve (AUC) and the True Skill Statistic (TSS). Comparing the five algorithms, the AUC scored highest for Boosted Regression Tree in summer (AUC = 0.94) and winter model runs (AUC = 0.94). In contrast, Random Forest underperformed in both model runs.

Predicting the aquatic toxicity mode of action using logistic regression and linear discriminant analysis.

PubMed

Ren, Y Y; Zhou, L C; Yang, L; Liu, P Y; Zhao, B W; Liu, H X

2016-09-01

The paper highlights the use of the logistic regression (LR) method in the construction of acceptable statistically significant, robust and predictive models for the classification of chemicals according to their aquatic toxic modes of action. Essentials accounting for a reliable model were all considered carefully. The model predictors were selected by stepwise forward discriminant analysis (LDA) from a combined pool of experimental data and chemical structure-based descriptors calculated by the CODESSA and DRAGON software packages. Model predictive ability was validated both internally and externally. The applicability domain was checked by the leverage approach to verify prediction reliability. The obtained models are simple and easy to interpret. In general, LR performs much better than LDA and seems to be more attractive for the prediction of the more toxic compounds, i.e. compounds that exhibit excess toxicity versus non-polar narcotic compounds and more reactive compounds versus less reactive compounds. In addition, model fit and regression diagnostics was done through the influence plot which reflects the hat-values, studentized residuals, and Cook's distance statistics of each sample. Overdispersion was also checked for the LR model. The relationships between the descriptors and the aquatic toxic behaviour of compounds are also discussed.

Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition.

PubMed

Falgreen, Steffen; Laursen, Maria Bach; Bødker, Julie Støve; Kjeldsen, Malene Krag; Schmitz, Alexander; Nyegaard, Mette; Johnsen, Hans Erik; Dybkær, Karen; Bøgsted, Martin

2014-06-05

In vitro generated dose-response curves of human cancer cell lines are widely used to develop new therapeutics. The curves are summarised by simplified statistics that ignore the conventionally used dose-response curves' dependency on drug exposure time and growth kinetics. This may lead to suboptimal exploitation of data and biased conclusions on the potential of the drug in question. Therefore we set out to improve the dose-response assessments by eliminating the impact of time dependency. First, a mathematical model for drug induced cell growth inhibition was formulated and used to derive novel dose-response curves and improved summary statistics that are independent of time under the proposed model. Next, a statistical analysis workflow for estimating the improved statistics was suggested consisting of 1) nonlinear regression models for estimation of cell counts and doubling times, 2) isotonic regression for modelling the suggested dose-response curves, and 3) resampling based method for assessing variation of the novel summary statistics. We document that conventionally used summary statistics for dose-response experiments depend on time so that fast growing cell lines compared to slowly growing ones are considered overly sensitive. The adequacy of the mathematical model is tested for doxorubicin and found to fit real data to an acceptable degree. Dose-response data from the NCI60 drug screen were used to illustrate the time dependency and demonstrate an adjustment correcting for it. The applicability of the workflow was illustrated by simulation and application on a doxorubicin growth inhibition screen. The simulations show that under the proposed mathematical model the suggested statistical workflow results in unbiased estimates of the time independent summary statistics. Variance estimates of the novel summary statistics are used to conclude that the doxorubicin screen covers a significant diverse range of responses ensuring it is useful for biological interpretations. Time independent summary statistics may aid the understanding of drugs' action mechanism on tumour cells and potentially renew previous drug sensitivity evaluation studies.

Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition

PubMed Central

2014-01-01

Background In vitro generated dose-response curves of human cancer cell lines are widely used to develop new therapeutics. The curves are summarised by simplified statistics that ignore the conventionally used dose-response curves’ dependency on drug exposure time and growth kinetics. This may lead to suboptimal exploitation of data and biased conclusions on the potential of the drug in question. Therefore we set out to improve the dose-response assessments by eliminating the impact of time dependency. Results First, a mathematical model for drug induced cell growth inhibition was formulated and used to derive novel dose-response curves and improved summary statistics that are independent of time under the proposed model. Next, a statistical analysis workflow for estimating the improved statistics was suggested consisting of 1) nonlinear regression models for estimation of cell counts and doubling times, 2) isotonic regression for modelling the suggested dose-response curves, and 3) resampling based method for assessing variation of the novel summary statistics. We document that conventionally used summary statistics for dose-response experiments depend on time so that fast growing cell lines compared to slowly growing ones are considered overly sensitive. The adequacy of the mathematical model is tested for doxorubicin and found to fit real data to an acceptable degree. Dose-response data from the NCI60 drug screen were used to illustrate the time dependency and demonstrate an adjustment correcting for it. The applicability of the workflow was illustrated by simulation and application on a doxorubicin growth inhibition screen. The simulations show that under the proposed mathematical model the suggested statistical workflow results in unbiased estimates of the time independent summary statistics. Variance estimates of the novel summary statistics are used to conclude that the doxorubicin screen covers a significant diverse range of responses ensuring it is useful for biological interpretations. Conclusion Time independent summary statistics may aid the understanding of drugs’ action mechanism on tumour cells and potentially renew previous drug sensitivity evaluation studies. PMID:24902483

Estimation of stature from the foot and its segments in a sub-adult female population of North India

PubMed Central

2011-01-01

Background Establishing personal identity is one of the main concerns in forensic investigations. Estimation of stature forms a basic domain of the investigation process in unknown and co-mingled human remains in forensic anthropology case work. The objective of the present study was to set up standards for estimation of stature from the foot and its segments in a sub-adult female population. Methods The sample for the study constituted 149 young females from the Northern part of India. The participants were aged between 13 and 18 years. Besides stature, seven anthropometric measurements that included length of the foot from each toe (T1, T2, T3, T4, and T5 respectively), foot breadth at ball (BBAL) and foot breadth at heel (BHEL) were measured on both feet in each participant using standard methods and techniques. Results The results indicated that statistically significant differences (p < 0.05) between left and right feet occur in both the foot breadth measurements (BBAL and BHEL). Foot length measurements (T1 to T5 lengths) did not show any statistically significant bilateral asymmetry. The correlation between stature and all the foot measurements was found to be positive and statistically significant (p-value < 0.001). Linear regression models and multiple regression models were derived for estimation of stature from the measurements of the foot. The present study indicates that anthropometric measurements of foot and its segments are valuable in the estimation of stature. Foot length measurements estimate stature with greater accuracy when compared to foot breadth measurements. Conclusions The present study concluded that foot measurements have a strong relationship with stature in the sub-adult female population of North India. Hence, the stature of an individual can be successfully estimated from the foot and its segments using different regression models derived in the study. The regression models derived in the study may be applied successfully for the estimation of stature in sub-adult females, whenever foot remains are brought for forensic examination. Stepwise multiple regression models tend to estimate stature more accurately than linear regression models in female sub-adults. PMID:22104433

Estimation of stature from the foot and its segments in a sub-adult female population of North India.

PubMed

Krishan, Kewal; Kanchan, Tanuj; Passi, Neelam

2011-11-21

Establishing personal identity is one of the main concerns in forensic investigations. Estimation of stature forms a basic domain of the investigation process in unknown and co-mingled human remains in forensic anthropology case work. The objective of the present study was to set up standards for estimation of stature from the foot and its segments in a sub-adult female population. The sample for the study constituted 149 young females from the Northern part of India. The participants were aged between 13 and 18 years. Besides stature, seven anthropometric measurements that included length of the foot from each toe (T1, T2, T3, T4, and T5 respectively), foot breadth at ball (BBAL) and foot breadth at heel (BHEL) were measured on both feet in each participant using standard methods and techniques. The results indicated that statistically significant differences (p < 0.05) between left and right feet occur in both the foot breadth measurements (BBAL and BHEL). Foot length measurements (T1 to T5 lengths) did not show any statistically significant bilateral asymmetry. The correlation between stature and all the foot measurements was found to be positive and statistically significant (p-value < 0.001). Linear regression models and multiple regression models were derived for estimation of stature from the measurements of the foot. The present study indicates that anthropometric measurements of foot and its segments are valuable in the estimation of stature. Foot length measurements estimate stature with greater accuracy when compared to foot breadth measurements. The present study concluded that foot measurements have a strong relationship with stature in the sub-adult female population of North India. Hence, the stature of an individual can be successfully estimated from the foot and its segments using different regression models derived in the study. The regression models derived in the study may be applied successfully for the estimation of stature in sub-adult females, whenever foot remains are brought for forensic examination. Stepwise multiple regression models tend to estimate stature more accurately than linear regression models in female sub-adults.

Statistical-learning strategies generate only modestly performing predictive models for urinary symptoms following external beam radiotherapy of the prostate: A comparison of conventional and machine-learning methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yahya, Noorazrul, E-mail: noorazrul.yahya@research.uwa.edu.au; Ebert, Martin A.; Bulsara, Max

Purpose: Given the paucity of available data concerning radiotherapy-induced urinary toxicity, it is important to ensure derivation of the most robust models with superior predictive performance. This work explores multiple statistical-learning strategies for prediction of urinary symptoms following external beam radiotherapy of the prostate. Methods: The performance of logistic regression, elastic-net, support-vector machine, random forest, neural network, and multivariate adaptive regression splines (MARS) to predict urinary symptoms was analyzed using data from 754 participants accrued by TROG03.04-RADAR. Predictive features included dose-surface data, comorbidities, and medication-intake. Four symptoms were analyzed: dysuria, haematuria, incontinence, and frequency, each with three definitions (grade ≥more » 1, grade ≥ 2 and longitudinal) with event rate between 2.3% and 76.1%. Repeated cross-validations producing matched models were implemented. A synthetic minority oversampling technique was utilized in endpoints with rare events. Parameter optimization was performed on the training data. Area under the receiver operating characteristic curve (AUROC) was used to compare performance using sample size to detect differences of ≥0.05 at the 95% confidence level. Results: Logistic regression, elastic-net, random forest, MARS, and support-vector machine were the highest-performing statistical-learning strategies in 3, 3, 3, 2, and 1 endpoints, respectively. Logistic regression, MARS, elastic-net, random forest, neural network, and support-vector machine were the best, or were not significantly worse than the best, in 7, 7, 5, 5, 3, and 1 endpoints. The best-performing statistical model was for dysuria grade ≥ 1 with AUROC ± standard deviation of 0.649 ± 0.074 using MARS. For longitudinal frequency and dysuria grade ≥ 1, all strategies produced AUROC>0.6 while all haematuria endpoints and longitudinal incontinence models produced AUROC<0.6. Conclusions: Logistic regression and MARS were most likely to be the best-performing strategy for the prediction of urinary symptoms with elastic-net and random forest producing competitive results. The predictive power of the models was modest and endpoint-dependent. New features, including spatial dose maps, may be necessary to achieve better models.« less

Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho

USGS Publications Warehouse

Wood, Molly S.; Fosness, Ryan L.; Skinner, Kenneth D.; Veilleux, Andrea G.

2016-06-27

The U.S. Geological Survey, in cooperation with the Idaho Transportation Department, updated regional regression equations to estimate peak-flow statistics at ungaged sites on Idaho streams using recent streamflow (flow) data and new statistical techniques. Peak-flow statistics with 80-, 67-, 50-, 43-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (1.25-, 1.50-, 2.00-, 2.33-, 5.00-, 10.0-, 25.0-, 50.0-, 100-, 200-, and 500-year recurrence intervals, respectively) were estimated for 192 streamgages in Idaho and bordering States with at least 10 years of annual peak-flow record through water year 2013. The streamgages were selected from drainage basins with little or no flow diversion or regulation. The peak-flow statistics were estimated by fitting a log-Pearson type III distribution to records of annual peak flows and applying two additional statistical methods: (1) the Expected Moments Algorithm to help describe uncertainty in annual peak flows and to better represent missing and historical record; and (2) the generalized Multiple Grubbs Beck Test to screen out potentially influential low outliers and to better fit the upper end of the peak-flow distribution. Additionally, a new regional skew was estimated for the Pacific Northwest and used to weight at-station skew at most streamgages. The streamgages were grouped into six regions (numbered 1_2, 3, 4, 5, 6_8, and 7, to maintain consistency in region numbering with a previous study), and the estimated peak-flow statistics were related to basin and climatic characteristics to develop regional regression equations using a generalized least squares procedure. Four out of 24 evaluated basin and climatic characteristics were selected for use in the final regional peak-flow regression equations.Overall, the standard error of prediction for the regional peak-flow regression equations ranged from 22 to 132 percent. Among all regions, regression model fit was best for region 4 in west-central Idaho (average standard error of prediction=46.4 percent; pseudo-R2>92 percent) and region 5 in central Idaho (average standard error of prediction=30.3 percent; pseudo-R2>95 percent). Regression model fit was poor for region 7 in southern Idaho (average standard error of prediction=103 percent; pseudo-R2<78 percent) compared to other regions because few streamgages in region 7 met the criteria for inclusion in the study, and the region’s semi-arid climate and associated variability in precipitation patterns causes substantial variability in peak flows.A drainage area ratio-adjustment method, using ratio exponents estimated using generalized least-squares regression, was presented as an alternative to the regional regression equations if peak-flow estimates are desired at an ungaged site that is close to a streamgage selected for inclusion in this study. The alternative drainage area ratio-adjustment method is appropriate for use when the drainage area ratio between the ungaged and gaged sites is between 0.5 and 1.5.The updated regional peak-flow regression equations had lower total error (standard error of prediction) than all regression equations presented in a 1982 study and in four of six regions presented in 2002 and 2003 studies in Idaho. A more extensive streamgage screening process used in the current study resulted in fewer streamgages used in the current study than in the 1982, 2002, and 2003 studies. Fewer streamgages used and the selection of different explanatory variables were likely causes of increased error in some regions compared to previous studies, but overall, regional peak‑flow regression model fit was generally improved for Idaho. The revised statistical procedures and increased streamgage screening applied in the current study most likely resulted in a more accurate representation of natural peak-flow conditions.The updated, regional peak-flow regression equations will be integrated in the U.S. Geological Survey StreamStats program to allow users to estimate basin and climatic characteristics and peak-flow statistics at ungaged locations of interest. StreamStats estimates peak-flow statistics with quantifiable certainty only when used at sites with basin and climatic characteristics within the range of input variables used to develop the regional regression equations. Both the regional regression equations and StreamStats should be used to estimate peak-flow statistics only in naturally flowing, relatively unregulated streams without substantial local influences to flow, such as large seeps, springs, or other groundwater-surface water interactions that are not widespread or characteristic of the respective region.

Robust mislabel logistic regression without modeling mislabel probabilities.

PubMed

Hung, Hung; Jou, Zhi-Yu; Huang, Su-Yun

2018-03-01

Logistic regression is among the most widely used statistical methods for linear discriminant analysis. In many applications, we only observe possibly mislabeled responses. Fitting a conventional logistic regression can then lead to biased estimation. One common resolution is to fit a mislabel logistic regression model, which takes into consideration of mislabeled responses. Another common method is to adopt a robust M-estimation by down-weighting suspected instances. In this work, we propose a new robust mislabel logistic regression based on γ-divergence. Our proposal possesses two advantageous features: (1) It does not need to model the mislabel probabilities. (2) The minimum γ-divergence estimation leads to a weighted estimating equation without the need to include any bias correction term, that is, it is automatically bias-corrected. These features make the proposed γ-logistic regression more robust in model fitting and more intuitive for model interpretation through a simple weighting scheme. Our method is also easy to implement, and two types of algorithms are included. Simulation studies and the Pima data application are presented to demonstrate the performance of γ-logistic regression. © 2017, The International Biometric Society.

Guidelines 13 and 14—Prediction uncertainty

USGS Publications Warehouse

Hill, Mary C.; Tiedeman, Claire

2005-01-01

An advantage of using optimization for model development and calibration is that optimization provides methods for evaluating and quantifying prediction uncertainty. Both deterministic and statistical methods can be used. Guideline 13 discusses using regression and post-audits, which we classify as deterministic methods. Guideline 14 discusses inferential statistics and Monte Carlo methods, which we classify as statistical methods.

Determination of osteoporosis risk factors using a multiple logistic regression model in postmenopausal Turkish women.

PubMed

Akkus, Zeki; Camdeviren, Handan; Celik, Fatma; Gur, Ali; Nas, Kemal

2005-09-01

To determine the risk factors of osteoporosis using a multiple binary logistic regression method and to assess the risk variables for osteoporosis, which is a major and growing health problem in many countries. We presented a case-control study, consisting of 126 postmenopausal healthy women as control group and 225 postmenopausal osteoporotic women as the case group. The study was carried out in the Department of Physical Medicine and Rehabilitation, Dicle University, Diyarbakir, Turkey between 1999-2002. The data from the 351 participants were collected using a standard questionnaire that contains 43 variables. A multiple logistic regression model was then used to evaluate the data and to find the best regression model. We classified 80.1% (281/351) of the participants using the regression model. Furthermore, the specificity value of the model was 67% (84/126) of the control group while the sensitivity value was 88% (197/225) of the case group. We found the distribution of residual values standardized for final model to be exponential using the Kolmogorow-Smirnow test (p=0.193). The receiver operating characteristic curve was found successful to predict patients with risk for osteoporosis. This study suggests that low levels of dietary calcium intake, physical activity, education, and longer duration of menopause are independent predictors of the risk of low bone density in our population. Adequate dietary calcium intake in combination with maintaining a daily physical activity, increasing educational level, decreasing birth rate, and duration of breast-feeding may contribute to healthy bones and play a role in practical prevention of osteoporosis in Southeast Anatolia. In addition, the findings of the present study indicate that the use of multivariate statistical method as a multiple logistic regression in osteoporosis, which maybe influenced by many variables, is better than univariate statistical evaluation.

Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models.

PubMed

Chen, Baojiang; Qin, Jing

2014-05-10

In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study. Copyright © 2013 John Wiley & Sons, Ltd.

Data Mining Methods Applied to Flight Operations Quality Assurance Data: A Comparison to Standard Statistical Methods

NASA Technical Reports Server (NTRS)

Stolzer, Alan J.; Halford, Carl

2007-01-01

In a previous study, multiple regression techniques were applied to Flight Operations Quality Assurance-derived data to develop parsimonious model(s) for fuel consumption on the Boeing 757 airplane. The present study examined several data mining algorithms, including neural networks, on the fuel consumption problem and compared them to the multiple regression results obtained earlier. Using regression methods, parsimonious models were obtained that explained approximately 85% of the variation in fuel flow. In general data mining methods were more effective in predicting fuel consumption. Classification and Regression Tree methods reported correlation coefficients of .91 to .92, and General Linear Models and Multilayer Perceptron neural networks reported correlation coefficients of about .99. These data mining models show great promise for use in further examining large FOQA databases for operational and safety improvements.

A Powerful Test for Comparing Multiple Regression Functions.

PubMed

Maity, Arnab

2012-09-01

In this article, we address the important problem of comparison of two or more population regression functions. Recently, Pardo-Fernández, Van Keilegom and González-Manteiga (2007) developed test statistics for simple nonparametric regression models: Y(ij) = θ(j)(Z(ij)) + σ(j)(Z(ij))∊(ij), based on empirical distributions of the errors in each population j = 1, … , J. In this paper, we propose a test for equality of the θ(j)(·) based on the concept of generalized likelihood ratio type statistics. We also generalize our test for other nonparametric regression setups, e.g, nonparametric logistic regression, where the loglikelihood for population j is any general smooth function [Formula: see text]. We describe a resampling procedure to obtain the critical values of the test. In addition, we present a simulation study to evaluate the performance of the proposed test and compare our results to those in Pardo-Fernández et al. (2007).

Nonparametric estimation and testing of fixed effects panel data models

PubMed Central

Henderson, Daniel J.; Carroll, Raymond J.; Li, Qi

2009-01-01

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics. PMID:19444335

Relative Contributions of Agricultural Drift, Para-Occupational, and Residential Use Exposure Pathways to House Dust Pesticide Concentrations: Meta-Regression of Published Data.

PubMed

Deziel, Nicole C; Freeman, Laura E Beane; Graubard, Barry I; Jones, Rena R; Hoppin, Jane A; Thomas, Kent; Hines, Cynthia J; Blair, Aaron; Sandler, Dale P; Chen, Honglei; Lubin, Jay H; Andreotti, Gabriella; Alavanja, Michael C R; Friesen, Melissa C

2017-03-01

Increased pesticide concentrations in house dust in agricultural areas have been attributed to several exposure pathways, including agricultural drift, para-occupational, and residential use. To guide future exposure assessment efforts, we quantified relative contributions of these pathways using meta-regression models of published data on dust pesticide concentrations. From studies in North American agricultural areas published from 1995 to 2015, we abstracted dust pesticide concentrations reported as summary statistics [e.g., geometric means (GM)]. We analyzed these data using mixed-effects meta-regression models that weighted each summary statistic by its inverse variance. Dependent variables were either the log-transformed GM (drift) or the log-transformed ratio of GMs from two groups (para-occupational, residential use). For the drift pathway, predicted GMs decreased sharply and nonlinearly, with GMs 64% lower in homes 250 m versus 23 m from fields (interquartile range of published data) based on 52 statistics from seven studies. For the para-occupational pathway, GMs were 2.3 times higher [95% confidence interval (CI): 1.5, 3.3; 15 statistics, five studies] in homes of farmers who applied pesticides more recently or frequently versus less recently or frequently. For the residential use pathway, GMs were 1.3 (95% CI: 1.1, 1.4) and 1.5 (95% CI: 1.2, 1.9) times higher in treated versus untreated homes, when the probability that a pesticide was used for the pest treatment was 1-19% and ≥ 20%, respectively (88 statistics, five studies). Our quantification of the relative contributions of pesticide exposure pathways in agricultural populations could improve exposure assessments in epidemiologic studies. The meta-regression models can be updated when additional data become available. Citation: Deziel NC, Beane Freeman LE, Graubard BI, Jones RR, Hoppin JA, Thomas K, Hines CJ, Blair A, Sandler DP, Chen H, Lubin JH, Andreotti G, Alavanja MC, Friesen MC. 2017. Relative contributions of agricultural drift, para-occupational, and residential use exposure pathways to house dust pesticide concentrations: meta-regression of published data. Environ Health Perspect 125:296-305; http://dx.doi.org/10.1289/EHP426.

Relative Contributions of Agricultural Drift, Para-Occupational, and Residential Use Exposure Pathways to House Dust Pesticide Concentrations: Meta-Regression of Published Data

PubMed Central

Deziel, Nicole C.; Freeman, Laura E. Beane; Graubard, Barry I.; Jones, Rena R.; Hoppin, Jane A.; Thomas, Kent; Hines, Cynthia J.; Blair, Aaron; Sandler, Dale P.; Chen, Honglei; Lubin, Jay H.; Andreotti, Gabriella; Alavanja, Michael C. R.; Friesen, Melissa C.

2016-01-01

Background: Increased pesticide concentrations in house dust in agricultural areas have been attributed to several exposure pathways, including agricultural drift, para-occupational, and residential use. Objective: To guide future exposure assessment efforts, we quantified relative contributions of these pathways using meta-regression models of published data on dust pesticide concentrations. Methods: From studies in North American agricultural areas published from 1995 to 2015, we abstracted dust pesticide concentrations reported as summary statistics [e.g., geometric means (GM)]. We analyzed these data using mixed-effects meta-regression models that weighted each summary statistic by its inverse variance. Dependent variables were either the log-transformed GM (drift) or the log-transformed ratio of GMs from two groups (para-occupational, residential use). Results: For the drift pathway, predicted GMs decreased sharply and nonlinearly, with GMs 64% lower in homes 250 m versus 23 m from fields (interquartile range of published data) based on 52 statistics from seven studies. For the para-occupational pathway, GMs were 2.3 times higher [95% confidence interval (CI): 1.5, 3.3; 15 statistics, five studies] in homes of farmers who applied pesticides more recently or frequently versus less recently or frequently. For the residential use pathway, GMs were 1.3 (95% CI: 1.1, 1.4) and 1.5 (95% CI: 1.2, 1.9) times higher in treated versus untreated homes, when the probability that a pesticide was used for the pest treatment was 1–19% and ≥ 20%, respectively (88 statistics, five studies). Conclusion: Our quantification of the relative contributions of pesticide exposure pathways in agricultural populations could improve exposure assessments in epidemiologic studies. The meta-regression models can be updated when additional data become available. Citation: Deziel NC, Beane Freeman LE, Graubard BI, Jones RR, Hoppin JA, Thomas K, Hines CJ, Blair A, Sandler DP, Chen H, Lubin JH, Andreotti G, Alavanja MC, Friesen MC. 2017. Relative contributions of agricultural drift, para-occupational, and residential use exposure pathways to house dust pesticide concentrations: meta-regression of published data. Environ Health Perspect 125:296–305; http://dx.doi.org/10.1289/EHP426 PMID:27458779

THE DISTRIBUTION OF COOK’S D STATISTIC

PubMed Central

Muller, Keith E.; Mok, Mario Chen

2013-01-01

Cook (1977) proposed a diagnostic to quantify the impact of deleting an observation on the estimated regression coefficients of a General Linear Univariate Model (GLUM). Simulations of models with Gaussian response and predictors demonstrate that his suggestion of comparing the diagnostic to the median of the F for overall regression captures an erratically varying proportion of the values. We describe the exact distribution of Cook’s statistic for a GLUM with Gaussian predictors and response. We also present computational forms, simple approximations, and asymptotic results. A simulation supports the accuracy of the results. The methods allow accurate evaluation of a single value or the maximum value from a regression analysis. The approximations work well for a single value, but less well for the maximum. In contrast, the cut-point suggested by Cook provides widely varying tail probabilities. As with all diagnostics, the data analyst must use scientific judgment in deciding how to treat highlighted observations. PMID:24363487

Alternative Statistical Frameworks for Student Growth Percentile Estimation

ERIC Educational Resources Information Center

Lockwood, J. R.; Castellano, Katherine E.

2015-01-01

This article suggests two alternative statistical approaches for estimating student growth percentiles (SGP). The first is to estimate percentile ranks of current test scores conditional on past test scores directly, by modeling the conditional cumulative distribution functions, rather than indirectly through quantile regressions. This would…

SOCR Analyses - an Instructional Java Web-based Statistical Analysis Toolkit.

PubMed

Chu, Annie; Cui, Jenny; Dinov, Ivo D

2009-03-01

The Statistical Online Computational Resource (SOCR) designs web-based tools for educational use in a variety of undergraduate courses (Dinov 2006). Several studies have demonstrated that these resources significantly improve students' motivation and learning experiences (Dinov et al. 2008). SOCR Analyses is a new component that concentrates on data modeling and analysis using parametric and non-parametric techniques supported with graphical model diagnostics. Currently implemented analyses include commonly used models in undergraduate statistics courses like linear models (Simple Linear Regression, Multiple Linear Regression, One-Way and Two-Way ANOVA). In addition, we implemented tests for sample comparisons, such as t-test in the parametric category; and Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, in the non-parametric category. SOCR Analyses also include several hypothesis test models, such as Contingency tables, Friedman's test and Fisher's exact test.The code itself is open source (http://socr.googlecode.com/), hoping to contribute to the efforts of the statistical computing community. The code includes functionality for each specific analysis model and it has general utilities that can be applied in various statistical computing tasks. For example, concrete methods with API (Application Programming Interface) have been implemented in statistical summary, least square solutions of general linear models, rank calculations, etc. HTML interfaces, tutorials, source code, activities, and data are freely available via the web (www.SOCR.ucla.edu). Code examples for developers and demos for educators are provided on the SOCR Wiki website.In this article, the pedagogical utilization of the SOCR Analyses is discussed, as well as the underlying design framework. As the SOCR project is on-going and more functions and tools are being added to it, these resources are constantly improved. The reader is strongly encouraged to check the SOCR site for most updated information and newly added models.

A Statistical Multimodel Ensemble Approach to Improving Long-Range Forecasting in Pakistan

DTIC Science & Technology

2012-03-01

Impact of global warming on monsoon variability in Pakistan. J. Anim. Pl. Sci., 21, no. 1, 107–110. Gillies, S., T. Murphree, and D. Meyer, 2012...are generated by multiple regression models that relate globally distributed oceanic and atmospheric predictors to local predictands. The...generated by multiple regression models that relate globally distributed oceanic and atmospheric predictors to local predictands. The predictands are

Across-Platform Imputation of DNA Methylation Levels Incorporating Nonlocal Information Using Penalized Functional Regression.

PubMed

Zhang, Guosheng; Huang, Kuan-Chieh; Xu, Zheng; Tzeng, Jung-Ying; Conneely, Karen N; Guan, Weihua; Kang, Jian; Li, Yun

2016-05-01

DNA methylation is a key epigenetic mark involved in both normal development and disease progression. Recent advances in high-throughput technologies have enabled genome-wide profiling of DNA methylation. However, DNA methylation profiling often employs different designs and platforms with varying resolution, which hinders joint analysis of methylation data from multiple platforms. In this study, we propose a penalized functional regression model to impute missing methylation data. By incorporating functional predictors, our model utilizes information from nonlocal probes to improve imputation quality. Here, we compared the performance of our functional model to linear regression and the best single probe surrogate in real data and via simulations. Specifically, we applied different imputation approaches to an acute myeloid leukemia dataset consisting of 194 samples and our method showed higher imputation accuracy, manifested, for example, by a 94% relative increase in information content and up to 86% more CpG sites passing post-imputation filtering. Our simulated association study further demonstrated that our method substantially improves the statistical power to identify trait-associated methylation loci. These findings indicate that the penalized functional regression model is a convenient and valuable imputation tool for methylation data, and it can boost statistical power in downstream epigenome-wide association study (EWAS). © 2016 WILEY PERIODICALS, INC.

Statistical downscaling modeling with quantile regression using lasso to estimate extreme rainfall

NASA Astrophysics Data System (ADS)

Santri, Dewi; Wigena, Aji Hamim; Djuraidah, Anik

2016-02-01

Rainfall is one of the climatic elements with high diversity and has many negative impacts especially extreme rainfall. Therefore, there are several methods that required to minimize the damage that may occur. So far, Global circulation models (GCM) are the best method to forecast global climate changes include extreme rainfall. Statistical downscaling (SD) is a technique to develop the relationship between GCM output as a global-scale independent variables and rainfall as a local- scale response variable. Using GCM method will have many difficulties when assessed against observations because GCM has high dimension and multicollinearity between the variables. The common method that used to handle this problem is principal components analysis (PCA) and partial least squares regression. The new method that can be used is lasso. Lasso has advantages in simultaneuosly controlling the variance of the fitted coefficients and performing automatic variable selection. Quantile regression is a method that can be used to detect extreme rainfall in dry and wet extreme. Objective of this study is modeling SD using quantile regression with lasso to predict extreme rainfall in Indramayu. The results showed that the estimation of extreme rainfall (extreme wet in January, February and December) in Indramayu could be predicted properly by the model at quantile 90th.

Quantile regression models of animal habitat relationships

USGS Publications Warehouse

Cade, Brian S.

2003-01-01

Typically, all factors that limit an organism are not measured and included in statistical models used to investigate relationships with their environment. If important unmeasured variables interact multiplicatively with the measured variables, the statistical models often will have heterogeneous response distributions with unequal variances. Quantile regression is an approach for estimating the conditional quantiles of a response variable distribution in the linear model, providing a more complete view of possible causal relationships between variables in ecological processes. Chapter 1 introduces quantile regression and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of estimates for homogeneous and heterogeneous regression models. Chapter 2 evaluates performance of quantile rankscore tests used for hypothesis testing and constructing confidence intervals for linear quantile regression estimates (0 ≤ τ ≤ 1). A permutation F test maintained better Type I errors than the Chi-square T test for models with smaller n, greater number of parameters p, and more extreme quantiles τ. Both versions of the test required weighting to maintain correct Type I errors when there was heterogeneity under the alternative model. An example application related trout densities to stream channel width:depth. Chapter 3 evaluates a drop in dispersion, F-ratio like permutation test for hypothesis testing and constructing confidence intervals for linear quantile regression estimates (0 ≤ τ ≤ 1). Chapter 4 simulates from a large (N = 10,000) finite population representing grid areas on a landscape to demonstrate various forms of hidden bias that might occur when the effect of a measured habitat variable on some animal was confounded with the effect of another unmeasured variable (spatially and not spatially structured). Depending on whether interactions of the measured habitat and unmeasured variable were negative (interference interactions) or positive (facilitation interactions), either upper (τ > 0.5) or lower (τ < 0.5) quantile regression parameters were less biased than mean rate parameters. Sampling (n = 20 - 300) simulations demonstrated that confidence intervals constructed by inverting rankscore tests provided valid coverage of these biased parameters. Quantile regression was used to estimate effects of physical habitat resources on a bivalve mussel (Macomona liliana) in a New Zealand harbor by modeling the spatial trend surface as a cubic polynomial of location coordinates.

The value of a statistical life: a meta-analysis with a mixed effects regression model.

PubMed

Bellavance, François; Dionne, Georges; Lebeau, Martin

2009-03-01

The value of a statistical life (VSL) is a very controversial topic, but one which is essential to the optimization of governmental decisions. We see a great variability in the values obtained from different studies. The source of this variability needs to be understood, in order to offer public decision-makers better guidance in choosing a value and to set clearer guidelines for future research on the topic. This article presents a meta-analysis based on 39 observations obtained from 37 studies (from nine different countries) which all use a hedonic wage method to calculate the VSL. Our meta-analysis is innovative in that it is the first to use the mixed effects regression model [Raudenbush, S.W., 1994. Random effects models. In: Cooper, H., Hedges, L.V. (Eds.), The Handbook of Research Synthesis. Russel Sage Foundation, New York] to analyze studies on the value of a statistical life. We conclude that the variability found in the values studied stems in large part from differences in methodologies.

Linear regression analysis: part 14 of a series on evaluation of scientific publications.

PubMed

Schneider, Astrid; Hommel, Gerhard; Blettner, Maria

2010-11-01

Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication. This article is based on selected textbooks of statistics, a selective review of the literature, and our own experience. After a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the results should be interpreted. The reader should then be able to judge whether the method has been used correctly and interpret the results appropriately. The performance and interpretation of linear regression analysis are subject to a variety of pitfalls, which are discussed here in detail. The reader is made aware of common errors of interpretation through practical examples. Both the opportunities for applying linear regression analysis and its limitations are presented.

Estimating Flow-Duration and Low-Flow Frequency Statistics for Unregulated Streams in Oregon

USGS Publications Warehouse

Risley, John; Stonewall, Adam J.; Haluska, Tana

2008-01-01

Flow statistical datasets, basin-characteristic datasets, and regression equations were developed to provide decision makers with surface-water information needed for activities such as water-quality regulation, water-rights adjudication, biological habitat assessment, infrastructure design, and water-supply planning and management. The flow statistics, which included annual and monthly period of record flow durations (5th, 10th, 25th, 50th, and 95th percent exceedances) and annual and monthly 7-day, 10-year (7Q10) and 7-day, 2-year (7Q2) low flows, were computed at 466 streamflow-gaging stations at sites with unregulated flow conditions throughout Oregon and adjacent areas of neighboring States. Regression equations, created from the flow statistics and basin characteristics of the stations, can be used to estimate flow statistics at ungaged stream sites in Oregon. The study area was divided into 10 regression modeling regions based on ecological, topographic, geologic, hydrologic, and climatic criteria. In total, 910 annual and monthly regression equations were created to predict the 7 flow statistics in the 10 regions. Equations to predict the five flow-duration exceedance percentages and the two low-flow frequency statistics were created with Ordinary Least Squares and Generalized Least Squares regression, respectively. The standard errors of estimate of the equations created to predict the 5th and 95th percent exceedances had medians of 42.4 and 64.4 percent, respectively. The standard errors of prediction of the equations created to predict the 7Q2 and 7Q10 low-flow statistics had medians of 51.7 and 61.2 percent, respectively. Standard errors for regression equations for sites in western Oregon were smaller than those in eastern Oregon partly because of a greater density of available streamflow-gaging stations in western Oregon than eastern Oregon. High-flow regression equations (such as the 5th and 10th percent exceedances) also generally were more accurate than the low-flow regression equations (such as the 95th percent exceedance and 7Q10 low-flow statistic). The regression equations predict unregulated flow conditions in Oregon. Flow estimates need to be adjusted if they are used at ungaged sites that are regulated by reservoirs or affected by water-supply and agricultural withdrawals if actual flow conditions are of interest. The regression equations are installed in the USGS StreamStats Web-based tool (http://water.usgs.gov/osw/streamstats/index.html, accessed July 16, 2008). StreamStats provides users with a set of annual and monthly flow-duration and low-flow frequency estimates for ungaged sites in Oregon in addition to the basin characteristics for the sites. Prediction intervals at the 90-percent confidence level also are automatically computed.

Comparing statistical and machine learning classifiers: alternatives for predictive modeling in human factors research.

PubMed

Carnahan, Brian; Meyer, Gérard; Kuntz, Lois-Ann

2003-01-01

Multivariate classification models play an increasingly important role in human factors research. In the past, these models have been based primarily on discriminant analysis and logistic regression. Models developed from machine learning research offer the human factors professional a viable alternative to these traditional statistical classification methods. To illustrate this point, two machine learning approaches--genetic programming and decision tree induction--were used to construct classification models designed to predict whether or not a student truck driver would pass his or her commercial driver license (CDL) examination. The models were developed and validated using the curriculum scores and CDL exam performances of 37 student truck drivers who had completed a 320-hr driver training course. Results indicated that the machine learning classification models were superior to discriminant analysis and logistic regression in terms of predictive accuracy. Actual or potential applications of this research include the creation of models that more accurately predict human performance outcomes.

Assessing the prediction accuracy of a cure model for censored survival data with long-term survivors: Application to breast cancer data.

PubMed

Asano, Junichi; Hirakawa, Akihiro

2017-01-01

The Cox proportional hazards cure model is a survival model incorporating a cure rate with the assumption that the population contains both uncured and cured individuals. It contains a logistic regression for the cure rate, and a Cox regression to estimate the hazard for uncured patients. A single predictive model for both the cure and hazard can be developed by using a cure model that simultaneously predicts the cure rate and hazards for uncured patients; however, model selection is a challenge because of the lack of a measure for quantifying the predictive accuracy of a cure model. Recently, we developed an area under the receiver operating characteristic curve (AUC) for determining the cure rate in a cure model (Asano et al., 2014), but the hazards measure for uncured patients was not resolved. In this article, we propose novel C-statistics that are weighted by the patients' cure status (i.e., cured, uncured, or censored cases) for the cure model. The operating characteristics of the proposed C-statistics and their confidence interval were examined by simulation analyses. We also illustrate methods for predictive model selection and for further interpretation of variables using the proposed AUCs and C-statistics via application to breast cancer data.

Active Learning with Statistical Models.

DTIC Science & Technology

1995-01-01

Active Learning with Statistical Models ASC-9217041, NSF CDA-9309300 6. AUTHOR(S) David A. Cohn, Zoubin Ghahramani, and Michael I. Jordan 7. PERFORMING...TERMS 15. NUMBER OF PAGES Al, MIT, Artificial Intelligence, active learning , queries, locally weighted 6 regression, LOESS, mixtures of gaussians...COMPUTATIONAL LEARNING DEPARTMENT OF BRAIN AND COGNITIVE SCIENCES A.I. Memo No. 1522 January 9. 1995 C.B.C.L. Paper No. 110 Active Learning with

Statistical Package User’s Guide.

DTIC Science & Technology

1980-08-01

261 C. STACH Nonparametric Descriptive Statistics ... ......... ... 265 D. CHIRA Coefficient of Concordance...135 I.- -a - - W 7- Test Data: This program was tested using data from John Neter and William Wasserman, Applied Linear Statistical Models: Regression...length of data file e. new fileý name (not same as raw data file) 5. Printout as optioned for only. Comments: Ranked data are used for program CHIRA

Analysis of a Rocket Based Combined Cycle Engine during Rocket Only Operation

NASA Technical Reports Server (NTRS)

Smith, T. D.; Steffen, C. J., Jr.; Yungster, S.; Keller, D. J.

1998-01-01

The all rocket mode of operation is a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. However, outside of performing experiments or a full three dimensional analysis, there are no first order parametric models to estimate performance. As a result, an axisymmetric RBCC engine was used to analytically determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and statistical regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, percent of injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inject diameter ratio. A perfect gas computational fluid dynamics analysis was performed to obtain values of vacuum specific impulse. Statistical regression analysis was performed based on both full flow and gas generator engine cycles. Results were also found to be dependent upon the entire cycle assumptions. The statistical regression analysis determined that there were five significant linear effects, six interactions, and one second-order effect. Two parametric models were created to provide performance assessments of an RBCC engine in the all rocket mode of operation.

Hidden Connections between Regression Models of Strain-Gage Balance Calibration Data

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert

2013-01-01

Hidden connections between regression models of wind tunnel strain-gage balance calibration data are investigated. These connections become visible whenever balance calibration data is supplied in its design format and both the Iterative and Non-Iterative Method are used to process the data. First, it is shown how the regression coefficients of the fitted balance loads of a force balance can be approximated by using the corresponding regression coefficients of the fitted strain-gage outputs. Then, data from the manual calibration of the Ames MK40 six-component force balance is chosen to illustrate how estimates of the regression coefficients of the fitted balance loads can be obtained from the regression coefficients of the fitted strain-gage outputs. The study illustrates that load predictions obtained by applying the Iterative or the Non-Iterative Method originate from two related regression solutions of the balance calibration data as long as balance loads are given in the design format of the balance, gage outputs behave highly linear, strict statistical quality metrics are used to assess regression models of the data, and regression model term combinations of the fitted loads and gage outputs can be obtained by a simple variable exchange.

Using Multilevel Modeling in Language Assessment Research: A Conceptual Introduction

ERIC Educational Resources Information Center

Barkaoui, Khaled

2013-01-01

This article critiques traditional single-level statistical approaches (e.g., multiple regression analysis) to examining relationships between language test scores and variables in the assessment setting. It highlights the conceptual, methodological, and statistical problems associated with these techniques in dealing with multilevel or nested…

Modeling Longitudinal Data Containing Non-Normal Within Subject Errors

NASA Technical Reports Server (NTRS)

Feiveson, Alan; Glenn, Nancy L.

2013-01-01

The mission of the National Aeronautics and Space Administration’s (NASA) human research program is to advance safe human spaceflight. This involves conducting experiments, collecting data, and analyzing data. The data are longitudinal and result from a relatively few number of subjects; typically 10 – 20. A longitudinal study refers to an investigation where participant outcomes and possibly treatments are collected at multiple follow-up times. Standard statistical designs such as mean regression with random effects and mixed–effects regression are inadequate for such data because the population is typically not approximately normally distributed. Hence, more advanced data analysis methods are necessary. This research focuses on four such methods for longitudinal data analysis: the recently proposed linear quantile mixed models (lqmm) by Geraci and Bottai (2013), quantile regression, multilevel mixed–effects linear regression, and robust regression. This research also provides computational algorithms for longitudinal data that scientists can directly use for human spaceflight and other longitudinal data applications, then presents statistical evidence that verifies which method is best for specific situations. This advances the study of longitudinal data in a broad range of applications including applications in the sciences, technology, engineering and mathematics fields.

Genetic Programming Transforms in Linear Regression Situations

NASA Astrophysics Data System (ADS)

Castillo, Flor; Kordon, Arthur; Villa, Carlos

The chapter summarizes the use of Genetic Programming (GP) inMultiple Linear Regression (MLR) to address multicollinearity and Lack of Fit (LOF). The basis of the proposed method is applying appropriate input transforms (model respecification) that deal with these issues while preserving the information content of the original variables. The transforms are selected from symbolic regression models with optimal trade-off between accuracy of prediction and expressional complexity, generated by multiobjective Pareto-front GP. The chapter includes a comparative study of the GP-generated transforms with Ridge Regression, a variant of ordinary Multiple Linear Regression, which has been a useful and commonly employed approach for reducing multicollinearity. The advantages of GP-generated model respecification are clearly defined and demonstrated. Some recommendations for transforms selection are given as well. The application benefits of the proposed approach are illustrated with a real industrial application in one of the broadest empirical modeling areas in manufacturing - robust inferential sensors. The chapter contributes to increasing the awareness of the potential of GP in statistical model building by MLR.

A novel model incorporating two variability sources for describing motor evoked potentials

PubMed Central

Goetz, Stefan M.; Luber, Bruce; Lisanby, Sarah H.; Peterchev, Angel V.

2014-01-01

Objective Motor evoked potentials (MEPs) play a pivotal role in transcranial magnetic stimulation (TMS), e.g., for determining the motor threshold and probing cortical excitability. Sampled across the range of stimulation strengths, MEPs outline an input–output (IO) curve, which is often used to characterize the corticospinal tract. More detailed understanding of the signal generation and variability of MEPs would provide insight into the underlying physiology and aid correct statistical treatment of MEP data. Methods A novel regression model is tested using measured IO data of twelve subjects. The model splits MEP variability into two independent contributions, acting on both sides of a strong sigmoidal nonlinearity that represents neural recruitment. Traditional sigmoidal regression with a single variability source after the nonlinearity is used for comparison. Results The distribution of MEP amplitudes varied across different stimulation strengths, violating statistical assumptions in traditional regression models. In contrast to the conventional regression model, the dual variability source model better described the IO characteristics including phenomena such as changing distribution spread and skewness along the IO curve. Conclusions MEP variability is best described by two sources that most likely separate variability in the initial excitation process from effects occurring later on. The new model enables more accurate and sensitive estimation of the IO curve characteristics, enhancing its power as a detection tool, and may apply to other brain stimulation modalities. Furthermore, it extracts new information from the IO data concerning the neural variability—information that has previously been treated as noise. PMID:24794287

Partial Least Squares Regression Can Aid in Detecting Differential Abundance of Multiple Features in Sets of Metagenomic Samples

PubMed Central

Libiger, Ondrej; Schork, Nicholas J.

2015-01-01

It is now feasible to examine the composition and diversity of microbial communities (i.e., “microbiomes”) that populate different human organs and orifices using DNA sequencing and related technologies. To explore the potential links between changes in microbial communities and various diseases in the human body, it is essential to test associations involving different species within and across microbiomes, environmental settings and disease states. Although a number of statistical techniques exist for carrying out relevant analyses, it is unclear which of these techniques exhibit the greatest statistical power to detect associations given the complexity of most microbiome datasets. We compared the statistical power of principal component regression, partial least squares regression, regularized regression, distance-based regression, Hill's diversity measures, and a modified test implemented in the popular and widely used microbiome analysis methodology “Metastats” across a wide range of simulated scenarios involving changes in feature abundance between two sets of metagenomic samples. For this purpose, simulation studies were used to change the abundance of microbial species in a real dataset from a published study examining human hands. Each technique was applied to the same data, and its ability to detect the simulated change in abundance was assessed. We hypothesized that a small subset of methods would outperform the rest in terms of the statistical power. Indeed, we found that the Metastats technique modified to accommodate multivariate analysis and partial least squares regression yielded high power under the models and data sets we studied. The statistical power of diversity measure-based tests, distance-based regression and regularized regression was significantly lower. Our results provide insight into powerful analysis strategies that utilize information on species counts from large microbiome data sets exhibiting skewed frequency distributions obtained on a small to moderate number of samples. PMID:26734061

Eutrophication risk assessment in coastal embayments using simple statistical models.

PubMed

Arhonditsis, G; Eleftheriadou, M; Karydis, M; Tsirtsis, G

2003-09-01

A statistical methodology is proposed for assessing the risk of eutrophication in marine coastal embayments. The procedure followed was the development of regression models relating the levels of chlorophyll a (Chl) with the concentration of the limiting nutrient--usually nitrogen--and the renewal rate of the systems. The method was applied in the Gulf of Gera, Island of Lesvos, Aegean Sea and a surrogate for renewal rate was created using the Canberra metric as a measure of the resemblance between the Gulf and the oligotrophic waters of the open sea in terms of their physical, chemical and biological properties. The Chl-total dissolved nitrogen-renewal rate regression model was the most significant, accounting for 60% of the variation observed in Chl. Predicted distributions of Chl for various combinations of the independent variables, based on Bayesian analysis of the models, enabled comparison of the outcomes of specific scenarios of interest as well as further analysis of the system dynamics. The present statistical approach can be used as a methodological tool for testing the resilience of coastal ecosystems under alternative managerial schemes and levels of exogenous nutrient loading.

The potential of composite cognitive scores for tracking progression in Huntington's disease.

PubMed

Jones, Rebecca; Stout, Julie C; Labuschagne, Izelle; Say, Miranda; Justo, Damian; Coleman, Allison; Dumas, Eve M; Hart, Ellen; Owen, Gail; Durr, Alexandra; Leavitt, Blair R; Roos, Raymund; O'Regan, Alison; Langbehn, Doug; Tabrizi, Sarah J; Frost, Chris

2014-01-01

Composite scores derived from joint statistical modelling of individual risk factors are widely used to identify individuals who are at increased risk of developing disease or of faster disease progression. We investigated the ability of composite measures developed using statistical models to differentiate progressive cognitive deterioration in Huntington's disease (HD) from natural decline in healthy controls. Using longitudinal data from TRACK-HD, the optimal combinations of quantitative cognitive measures to differentiate premanifest and early stage HD individuals respectively from controls was determined using logistic regression. Composite scores were calculated from the parameters of each statistical model. Linear regression models were used to calculate effect sizes (ES) quantifying the difference in longitudinal change over 24 months between premanifest and early stage HD groups respectively and controls. ES for the composites were compared with ES for individual cognitive outcomes and other measures used in HD research. The 0.632 bootstrap was used to eliminate biases which result from developing and testing models in the same sample. In early HD, the composite score from the HD change prediction model produced an ES for difference in rate of 24-month change relative to controls of 1.14 (95% CI: 0.90 to 1.39), larger than the ES for any individual cognitive outcome and UHDRS Total Motor Score and Total Functional Capacity. In addition, this composite gave a statistically significant difference in rate of change in premanifest HD compared to controls over 24-months (ES: 0.24; 95% CI: 0.04 to 0.44), even though none of the individual cognitive outcomes produced statistically significant ES over this period. Composite scores developed using appropriate statistical modelling techniques have the potential to materially reduce required sample sizes for randomised controlled trials.

Coronary artery calcium distributions in older persons in the AGES-Reykjavik study

PubMed Central

Gudmundsson, Elias Freyr; Gudnason, Vilmundur; Sigurdsson, Sigurdur; Launer, Lenore J.; Harris, Tamara B.; Aspelund, Thor

2013-01-01

Coronary Artery Calcium (CAC) is a sign of advanced atherosclerosis and an independent risk factor for cardiac events. Here, we describe CAC-distributions in an unselected aged population and compare modelling methods to characterize CAC-distribution. CAC is difficult to model because it has a skewed and zero inflated distribution with over-dispersion. Data are from the AGES-Reykjavik sample, a large population based study [2002-2006] in Iceland of 5,764 persons aged 66-96 years. Linear regressions using logarithmic- and Box-Cox transformations on CAC+1, quantile regression and a Zero-Inflated Negative Binomial model (ZINB) were applied. Methods were compared visually and with the PRESS-statistic, R2 and number of detected associations with concurrently measured variables. There were pronounced differences in CAC according to sex, age, history of coronary events and presence of plaque in the carotid artery. Associations with conventional coronary artery disease (CAD) risk factors varied between the sexes. The ZINB model provided the best results with respect to the PRESS-statistic, R2, and predicted proportion of zero scores. The ZINB model detected similar numbers of associations as the linear regression on ln(CAC+1) and usually with the same risk factors. PMID:22990371

Application of linear regression analysis in accuracy assessment of rolling force calculations

NASA Astrophysics Data System (ADS)

Poliak, E. I.; Shim, M. K.; Kim, G. S.; Choo, W. Y.

1998-10-01

Efficient operation of the computational models employed in process control systems require periodical assessment of the accuracy of their predictions. Linear regression is proposed as a tool which allows separate systematic and random prediction errors from those related to measurements. A quantitative characteristic of the model predictive ability is introduced in addition to standard statistical tests for model adequacy. Rolling force calculations are considered as an example for the application. However, the outlined approach can be used to assess the performance of any computational model.

Using Patient Demographics and Statistical Modeling to Predict Knee Tibia Component Sizing in Total Knee Arthroplasty.

PubMed

Ren, Anna N; Neher, Robert E; Bell, Tyler; Grimm, James

2018-06-01

Preoperative planning is important to achieve successful implantation in primary total knee arthroplasty (TKA). However, traditional TKA templating techniques are not accurate enough to predict the component size to a very close range. With the goal of developing a general predictive statistical model using patient demographic information, ordinal logistic regression was applied to build a proportional odds model to predict the tibia component size. The study retrospectively collected the data of 1992 primary Persona Knee System TKA procedures. Of them, 199 procedures were randomly selected as testing data and the rest of the data were randomly partitioned between model training data and model evaluation data with a ratio of 7:3. Different models were trained and evaluated on the training and validation data sets after data exploration. The final model had patient gender, age, weight, and height as independent variables and predicted the tibia size within 1 size difference 96% of the time on the validation data, 94% of the time on the testing data, and 92% on a prospective cadaver data set. The study results indicated the statistical model built by ordinal logistic regression can increase the accuracy of tibia sizing information for Persona Knee preoperative templating. This research shows statistical modeling may be used with radiographs to dramatically enhance the templating accuracy, efficiency, and quality. In general, this methodology can be applied to other TKA products when the data are applicable. Copyright © 2018 Elsevier Inc. All rights reserved.

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool.

PubMed

Aqil, Muhammad; Kita, Ichiro; Yano, Akira; Nishiyama, Soichi

2007-10-01

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.

A New Approach of Juvenile Age Estimation using Measurements of the Ilium and Multivariate Adaptive Regression Splines (MARS) Models for Better Age Prediction.

PubMed

Corron, Louise; Marchal, François; Condemi, Silvana; Chaumoître, Kathia; Adalian, Pascal

2017-01-01

Juvenile age estimation methods used in forensic anthropology generally lack methodological consistency and/or statistical validity. Considering this, a standard approach using nonparametric Multivariate Adaptive Regression Splines (MARS) models were tested to predict age from iliac biometric variables of male and female juveniles from Marseilles, France, aged 0-12 years. Models using unidimensional (length and width) and bidimensional iliac data (module and surface) were constructed on a training sample of 176 individuals and validated on an independent test sample of 68 individuals. Results show that MARS prediction models using iliac width, module and area give overall better and statistically valid age estimates. These models integrate punctual nonlinearities of the relationship between age and osteometric variables. By constructing valid prediction intervals whose size increases with age, MARS models take into account the normal increase of individual variability. MARS models can qualify as a practical and standardized approach for juvenile age estimation. © 2016 American Academy of Forensic Sciences.

DEVELOPMENT OF THE VIRTUAL BEACH MODEL, PHASE 1: AN EMPIRICAL MODEL

EPA Science Inventory

With increasing attention focused on the use of multiple linear regression (MLR) modeling of beach fecal bacteria concentration, the validity of the entire statistical process should be carefully evaluated to assure satisfactory predictions. This work aims to identify pitfalls an...

Determination of riverbank erosion probability using Locally Weighted Logistic Regression

NASA Astrophysics Data System (ADS)

Ioannidou, Elena; Flori, Aikaterini; Varouchakis, Emmanouil A.; Giannakis, Georgios; Vozinaki, Anthi Eirini K.; Karatzas, George P.; Nikolaidis, Nikolaos

2015-04-01

Riverbank erosion is a natural geomorphologic process that affects the fluvial environment. The most important issue concerning riverbank erosion is the identification of the vulnerable locations. An alternative to the usual hydrodynamic models to predict vulnerable locations is to quantify the probability of erosion occurrence. This can be achieved by identifying the underlying relations between riverbank erosion and the geomorphological or hydrological variables that prevent or stimulate erosion. Thus, riverbank erosion can be determined by a regression model using independent variables that are considered to affect the erosion process. The impact of such variables may vary spatially, therefore, a non-stationary regression model is preferred instead of a stationary equivalent. Locally Weighted Regression (LWR) is proposed as a suitable choice. This method can be extended to predict the binary presence or absence of erosion based on a series of independent local variables by using the logistic regression model. It is referred to as Locally Weighted Logistic Regression (LWLR). Logistic regression is a type of regression analysis used for predicting the outcome of a categorical dependent variable (e.g. binary response) based on one or more predictor variables. The method can be combined with LWR to assign weights to local independent variables of the dependent one. LWR allows model parameters to vary over space in order to reflect spatial heterogeneity. The probabilities of the possible outcomes are modelled as a function of the independent variables using a logistic function. Logistic regression measures the relationship between a categorical dependent variable and, usually, one or several continuous independent variables by converting the dependent variable to probability scores. Then, a logistic regression is formed, which predicts success or failure of a given binary variable (e.g. erosion presence or absence) for any value of the independent variables. The erosion occurrence probability can be calculated in conjunction with the model deviance regarding the independent variables tested. The most straightforward measure for goodness of fit is the G statistic. It is a simple and effective way to study and evaluate the Logistic Regression model efficiency and the reliability of each independent variable. The developed statistical model is applied to the Koiliaris River Basin on the island of Crete, Greece. Two datasets of river bank slope, river cross-section width and indications of erosion were available for the analysis (12 and 8 locations). Two different types of spatial dependence functions, exponential and tricubic, were examined to determine the local spatial dependence of the independent variables at the measurement locations. The results show a significant improvement when the tricubic function is applied as the erosion probability is accurately predicted at all eight validation locations. Results for the model deviance show that cross-section width is more important than bank slope in the estimation of erosion probability along the Koiliaris riverbanks. The proposed statistical model is a useful tool that quantifies the erosion probability along the riverbanks and can be used to assist managing erosion and flooding events. Acknowledgements This work is part of an on-going THALES project (CYBERSENSORS - High Frequency Monitoring System for Integrated Water Resources Management of Rivers). The project has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.

Impact of multicollinearity on small sample hydrologic regression models

NASA Astrophysics Data System (ADS)

Kroll, Charles N.; Song, Peter

2013-06-01

Often hydrologic regression models are developed with ordinary least squares (OLS) procedures. The use of OLS with highly correlated explanatory variables produces multicollinearity, which creates highly sensitive parameter estimators with inflated variances and improper model selection. It is not clear how to best address multicollinearity in hydrologic regression models. Here a Monte Carlo simulation is developed to compare four techniques to address multicollinearity: OLS, OLS with variance inflation factor screening (VIF), principal component regression (PCR), and partial least squares regression (PLS). The performance of these four techniques was observed for varying sample sizes, correlation coefficients between the explanatory variables, and model error variances consistent with hydrologic regional regression models. The negative effects of multicollinearity are magnified at smaller sample sizes, higher correlations between the variables, and larger model error variances (smaller R2). The Monte Carlo simulation indicates that if the true model is known, multicollinearity is present, and the estimation and statistical testing of regression parameters are of interest, then PCR or PLS should be employed. If the model is unknown, or if the interest is solely on model predictions, is it recommended that OLS be employed since using more complicated techniques did not produce any improvement in model performance. A leave-one-out cross-validation case study was also performed using low-streamflow data sets from the eastern United States. Results indicate that OLS with stepwise selection generally produces models across study regions with varying levels of multicollinearity that are as good as biased regression techniques such as PCR and PLS.

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

PubMed

Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S

2017-06-01

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LET d based models should be further evaluated in clinically realistic scenarios. © 2017 American Association of Physicists in Medicine.

Quantile regression reveals hidden bias and uncertainty in habitat models

Treesearch

Brian S. Cade; Barry R. Noon; Curtis H. Flather

2005-01-01

We simulated the effects of missing information on statistical distributions of animal response that covaried with measured predictors of habitat to evaluate the utility and performance of quantile regression for providing more useful intervals of uncertainty in habitat relationships. These procedures were evaulated for conditions in which heterogeneity and hidden bias...

Statistical Power for a Simultaneous Test of Factorial and Predictive Invariance

ERIC Educational Resources Information Center

Olivera-Aguilar, Margarita; Millsap, Roger E.

2013-01-01

A common finding in studies of differential prediction across groups is that although regression slopes are the same or similar across groups, group differences exist in regression intercepts. Building on earlier work by Birnbaum (1979), Millsap (1998) presented an invariant factor model that would explain such intercept differences as arising due…

Beyond logistic regression: structural equations modelling for binary variables and its application to investigating unobserved confounders.

PubMed

Kupek, Emil

2006-03-15

Structural equation modelling (SEM) has been increasingly used in medical statistics for solving a system of related regression equations. However, a great obstacle for its wider use has been its difficulty in handling categorical variables within the framework of generalised linear models. A large data set with a known structure among two related outcomes and three independent variables was generated to investigate the use of Yule's transformation of odds ratio (OR) into Q-metric by (OR-1)/(OR+1) to approximate Pearson's correlation coefficients between binary variables whose covariance structure can be further analysed by SEM. Percent of correctly classified events and non-events was compared with the classification obtained by logistic regression. The performance of SEM based on Q-metric was also checked on a small (N = 100) random sample of the data generated and on a real data set. SEM successfully recovered the generated model structure. SEM of real data suggested a significant influence of a latent confounding variable which would have not been detectable by standard logistic regression. SEM classification performance was broadly similar to that of the logistic regression. The analysis of binary data can be greatly enhanced by Yule's transformation of odds ratios into estimated correlation matrix that can be further analysed by SEM. The interpretation of results is aided by expressing them as odds ratios which are the most frequently used measure of effect in medical statistics.

Length bias correction in gene ontology enrichment analysis using logistic regression.

PubMed

Mi, Gu; Di, Yanming; Emerson, Sarah; Cumbie, Jason S; Chang, Jeff H

2012-01-01

When assessing differential gene expression from RNA sequencing data, commonly used statistical tests tend to have greater power to detect differential expression of genes encoding longer transcripts. This phenomenon, called "length bias", will influence subsequent analyses such as Gene Ontology enrichment analysis. In the presence of length bias, Gene Ontology categories that include longer genes are more likely to be identified as enriched. These categories, however, are not necessarily biologically more relevant. We show that one can effectively adjust for length bias in Gene Ontology analysis by including transcript length as a covariate in a logistic regression model. The logistic regression model makes the statistical issue underlying length bias more transparent: transcript length becomes a confounding factor when it correlates with both the Gene Ontology membership and the significance of the differential expression test. The inclusion of the transcript length as a covariate allows one to investigate the direct correlation between the Gene Ontology membership and the significance of testing differential expression, conditional on the transcript length. We present both real and simulated data examples to show that the logistic regression approach is simple, effective, and flexible.

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

PubMed

Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

2016-01-01

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation. Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.

Handling nonnormality and variance heterogeneity for quantitative sublethal toxicity tests.

PubMed

Ritz, Christian; Van der Vliet, Leana

2009-09-01

The advantages of using regression-based techniques to derive endpoints from environmental toxicity data are clear, and slowly, this superior analytical technique is gaining acceptance. As use of regression-based analysis becomes more widespread, some of the associated nuances and potential problems come into sharper focus. Looking at data sets that cover a broad spectrum of standard test species, we noticed that some model fits to data failed to meet two key assumptions-variance homogeneity and normality-that are necessary for correct statistical analysis via regression-based techniques. Failure to meet these assumptions often is caused by reduced variance at the concentrations showing severe adverse effects. Although commonly used with linear regression analysis, transformation of the response variable only is not appropriate when fitting data using nonlinear regression techniques. Through analysis of sample data sets, including Lemna minor, Eisenia andrei (terrestrial earthworm), and algae, we show that both the so-called Box-Cox transformation and use of the Poisson distribution can help to correct variance heterogeneity and nonnormality and so allow nonlinear regression analysis to be implemented. Both the Box-Cox transformation and the Poisson distribution can be readily implemented into existing protocols for statistical analysis. By correcting for nonnormality and variance heterogeneity, these two statistical tools can be used to encourage the transition to regression-based analysis and the depreciation of less-desirable and less-flexible analytical techniques, such as linear interpolation.

Using Logistic Regression to Predict the Probability of Debris Flows in Areas Burned by Wildfires, Southern California, 2003-2006

USGS Publications Warehouse

Rupert, Michael G.; Cannon, Susan H.; Gartner, Joseph E.; Michael, John A.; Helsel, Dennis R.

2008-01-01

Logistic regression was used to develop statistical models that can be used to predict the probability of debris flows in areas recently burned by wildfires by using data from 14 wildfires that burned in southern California during 2003-2006. Twenty-eight independent variables describing the basin morphology, burn severity, rainfall, and soil properties of 306 drainage basins located within those burned areas were evaluated. The models were developed as follows: (1) Basins that did and did not produce debris flows soon after the 2003 to 2006 fires were delineated from data in the National Elevation Dataset using a geographic information system; (2) Data describing the basin morphology, burn severity, rainfall, and soil properties were compiled for each basin. These data were then input to a statistics software package for analysis using logistic regression; and (3) Relations between the occurrence or absence of debris flows and the basin morphology, burn severity, rainfall, and soil properties were evaluated, and five multivariate logistic regression models were constructed. All possible combinations of independent variables were evaluated to determine which combinations produced the most effective models, and the multivariate models that best predicted the occurrence of debris flows were identified. Percentage of high burn severity and 3-hour peak rainfall intensity were significant variables in all models. Soil organic matter content and soil clay content were significant variables in all models except Model 5. Soil slope was a significant variable in all models except Model 4. The most suitable model can be selected from these five models on the basis of the availability of independent variables in the particular area of interest and field checking of probability maps. The multivariate logistic regression models can be entered into a geographic information system, and maps showing the probability of debris flows can be constructed in recently burned areas of southern California. This study demonstrates that logistic regression is a valuable tool for developing models that predict the probability of debris flows occurring in recently burned landscapes.

Background stratified Poisson regression analysis of cohort data.

PubMed

Richardson, David B; Langholz, Bryan

2012-03-01

Background stratified Poisson regression is an approach that has been used in the analysis of data derived from a variety of epidemiologically important studies of radiation-exposed populations, including uranium miners, nuclear industry workers, and atomic bomb survivors. We describe a novel approach to fit Poisson regression models that adjust for a set of covariates through background stratification while directly estimating the radiation-disease association of primary interest. The approach makes use of an expression for the Poisson likelihood that treats the coefficients for stratum-specific indicator variables as 'nuisance' variables and avoids the need to explicitly estimate the coefficients for these stratum-specific parameters. Log-linear models, as well as other general relative rate models, are accommodated. This approach is illustrated using data from the Life Span Study of Japanese atomic bomb survivors and data from a study of underground uranium miners. The point estimate and confidence interval obtained from this 'conditional' regression approach are identical to the values obtained using unconditional Poisson regression with model terms for each background stratum. Moreover, it is shown that the proposed approach allows estimation of background stratified Poisson regression models of non-standard form, such as models that parameterize latency effects, as well as regression models in which the number of strata is large, thereby overcoming the limitations of previously available statistical software for fitting background stratified Poisson regression models.

Statistical procedures for evaluating daily and monthly hydrologic model predictions

USGS Publications Warehouse

Coffey, M.E.; Workman, S.R.; Taraba, J.L.; Fogle, A.W.

2004-01-01

The overall study objective was to evaluate the applicability of different qualitative and quantitative methods for comparing daily and monthly SWAT computer model hydrologic streamflow predictions to observed data, and to recommend statistical methods for use in future model evaluations. Statistical methods were tested using daily streamflows and monthly equivalent runoff depths. The statistical techniques included linear regression, Nash-Sutcliffe efficiency, nonparametric tests, t-test, objective functions, autocorrelation, and cross-correlation. None of the methods specifically applied to the non-normal distribution and dependence between data points for the daily predicted and observed data. Of the tested methods, median objective functions, sign test, autocorrelation, and cross-correlation were most applicable for the daily data. The robust coefficient of determination (CD*) and robust modeling efficiency (EF*) objective functions were the preferred methods for daily model results due to the ease of comparing these values with a fixed ideal reference value of one. Predicted and observed monthly totals were more normally distributed, and there was less dependence between individual monthly totals than was observed for the corresponding predicted and observed daily values. More statistical methods were available for comparing SWAT model-predicted and observed monthly totals. The 1995 monthly SWAT model predictions and observed data had a regression Rr2 of 0.70, a Nash-Sutcliffe efficiency of 0.41, and the t-test failed to reject the equal data means hypothesis. The Nash-Sutcliffe coefficient and the R r2 coefficient were the preferred methods for monthly results due to the ability to compare these coefficients to a set ideal value of one.

Using Artificial Neural Networks in Educational Research: Some Comparisons with Linear Statistical Models.

ERIC Educational Resources Information Center

Everson, Howard T.; And Others

This paper explores the feasibility of neural computing methods such as artificial neural networks (ANNs) and abductory induction mechanisms (AIM) for use in educational measurement. ANNs and AIMS methods are contrasted with more traditional statistical techniques, such as multiple regression and discriminant function analyses, for making…

Development of a funding, cost, and spending model for satellite projects

NASA Technical Reports Server (NTRS)

Johnson, Jesse P.

1989-01-01

The need for a predictive budget/funging model is obvious. The current models used by the Resource Analysis Office (RAO) are used to predict the total costs of satellite projects. An effort to extend the modeling capabilities from total budget analysis to total budget and budget outlays over time analysis was conducted. A statistical based and data driven methodology was used to derive and develop the model. Th budget data for the last 18 GSFC-sponsored satellite projects were analyzed and used to build a funding model which would describe the historical spending patterns. This raw data consisted of dollars spent in that specific year and their 1989 dollar equivalent. This data was converted to the standard format used by the RAO group and placed in a database. A simple statistical analysis was performed to calculate the gross statistics associated with project length and project cost ant the conditional statistics on project length and project cost. The modeling approach used is derived form the theory of embedded statistics which states that properly analyzed data will produce the underlying generating function. The process of funding large scale projects over extended periods of time is described by Life Cycle Cost Models (LCCM). The data was analyzed to find a model in the generic form of a LCCM. The model developed is based on a Weibull function whose parameters are found by both nonlinear optimization and nonlinear regression. In order to use this model it is necessary to transform the problem from a dollar/time space to a percentage of total budget/time space. This transformation is equivalent to moving to a probability space. By using the basic rules of probability, the validity of both the optimization and the regression steps are insured. This statistically significant model is then integrated and inverted. The resulting output represents a project schedule which relates the amount of money spent to the percentage of project completion.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Development of a statistical model for the determination of the probability of riverbank erosion in a Meditteranean river basin

NASA Astrophysics Data System (ADS)

Varouchakis, Emmanouil; Kourgialas, Nektarios; Karatzas, George; Giannakis, Georgios; Lilli, Maria; Nikolaidis, Nikolaos

2014-05-01

Riverbank erosion affects the river morphology and the local habitat and results in riparian land loss, damage to property and infrastructures, ultimately weakening flood defences. An important issue concerning riverbank erosion is the identification of the areas vulnerable to erosion, as it allows for predicting changes and assists with stream management and restoration. One way to predict the vulnerable to erosion areas is to determine the erosion probability by identifying the underlying relations between riverbank erosion and the geomorphological and/or hydrological variables that prevent or stimulate erosion. A statistical model for evaluating the probability of erosion based on a series of independent local variables and by using logistic regression is developed in this work. The main variables affecting erosion are vegetation index (stability), the presence or absence of meanders, bank material (classification), stream power, bank height, river bank slope, riverbed slope, cross section width and water velocities (Luppi et al. 2009). In statistics, logistic regression is a type of regression analysis used for predicting the outcome of a categorical dependent variable, e.g. binary response, based on one or more predictor variables (continuous or categorical). The probabilities of the possible outcomes are modelled as a function of independent variables using a logistic function. Logistic regression measures the relationship between a categorical dependent variable and, usually, one or several continuous independent variables by converting the dependent variable to probability scores. Then, a logistic regression is formed, which predicts success or failure of a given binary variable (e.g. 1 = "presence of erosion" and 0 = "no erosion") for any value of the independent variables. The regression coefficients are estimated by using maximum likelihood estimation. The erosion occurrence probability can be calculated in conjunction with the model deviance regarding the independent variables tested (Atkinson et al. 2003). The developed statistical model is applied to the Koiliaris River Basin in the island of Crete, Greece. The aim is to determine the probability of erosion along the Koiliaris' riverbanks considering a series of independent geomorphological and/or hydrological variables. Data for the river bank slope and for the river cross section width are available at ten locations along the river. The riverbank has indications of erosion at six of the ten locations while four has remained stable. Based on a recent work, measurements for the two independent variables and data regarding bank stability are available at eight different locations along the river. These locations were used as validation points for the proposed statistical model. The results show a very close agreement between the observed erosion indications and the statistical model as the probability of erosion was accurately predicted at seven out of the eight locations. The next step is to apply the model at more locations along the riverbanks. In November 2013, stakes were inserted at selected locations in order to be able to identify the presence or absence of erosion after the winter period. In April 2014 the presence or absence of erosion will be identified and the model results will be compared to the field data. Our intent is to extend the model by increasing the number of independent variables in order to indentify the key factors favouring erosion along the Koiliaris River. We aim at developing an easy to use statistical tool that will provide a quantified measure of the erosion probability along the riverbanks, which could consequently be used to prevent erosion and flooding events. Atkinson, P. M., German, S. E., Sear, D. A. and Clark, M. J. 2003. Exploring the relations between riverbank erosion and geomorphological controls using geographically weighted logistic regression. Geographical Analysis, 35 (1), 58-82. Luppi, L., Rinaldi, M., Teruggi, L. B., Darby, S. E. and Nardi, L. 2009. Monitoring and numerical modelling of riverbank erosion processes: A case study along the Cecina River (central Italy). Earth Surface Processes and Landforms, 34 (4), 530-546. Acknowledgements This work is part of an on-going THALES project (CYBERSENSORS - High Frequency Monitoring System for Integrated Water Resources Management of Rivers). The project has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.

Statistical validation of normal tissue complication probability models.

PubMed

Xu, Cheng-Jian; van der Schaaf, Arjen; Van't Veld, Aart A; Langendijk, Johannes A; Schilstra, Cornelis

2012-09-01

To investigate the applicability and value of double cross-validation and permutation tests as established statistical approaches in the validation of normal tissue complication probability (NTCP) models. A penalized regression method, LASSO (least absolute shrinkage and selection operator), was used to build NTCP models for xerostomia after radiation therapy treatment of head-and-neck cancer. Model assessment was based on the likelihood function and the area under the receiver operating characteristic curve. Repeated double cross-validation showed the uncertainty and instability of the NTCP models and indicated that the statistical significance of model performance can be obtained by permutation testing. Repeated double cross-validation and permutation tests are recommended to validate NTCP models before clinical use. Copyright © 2012 Elsevier Inc. All rights reserved.

Forecasting volatility with neural regression: a contribution to model adequacy.

PubMed

Refenes, A N; Holt, W T

2001-01-01

Neural nets' usefulness for forecasting is limited by problems of overfitting and the lack of rigorous procedures for model identification, selection and adequacy testing. This paper describes a methodology for neural model misspecification testing. We introduce a generalization of the Durbin-Watson statistic for neural regression and discuss the general issues of misspecification testing using residual analysis. We derive a generalized influence matrix for neural estimators which enables us to evaluate the distribution of the statistic. We deploy Monte Carlo simulation to compare the power of the test for neural and linear regressors. While residual testing is not a sufficient condition for model adequacy, it is nevertheless a necessary condition to demonstrate that the model is a good approximation to the data generating process, particularly as neural-network estimation procedures are susceptible to partial convergence. The work is also an important step toward developing rigorous procedures for neural model identification, selection and adequacy testing which have started to appear in the literature. We demonstrate its applicability in the nontrivial problem of forecasting implied volatility innovations using high-frequency stock index options. Each step of the model building process is validated using statistical tests to verify variable significance and model adequacy with the results confirming the presence of nonlinear relationships in implied volatility innovations.

A Comparison of the Performance of Advanced Statistical Techniques for the Refinement of Day-ahead and Longer NWP-based Wind Power Forecasts

NASA Astrophysics Data System (ADS)

Zack, J. W.

2015-12-01

Predictions from Numerical Weather Prediction (NWP) models are the foundation for wind power forecasts for day-ahead and longer forecast horizons. The NWP models directly produce three-dimensional wind forecasts on their respective computational grids. These can be interpolated to the location and time of interest. However, these direct predictions typically contain significant systematic errors ("biases"). This is due to a variety of factors including the limited space-time resolution of the NWP models and shortcomings in the model's representation of physical processes. It has become common practice to attempt to improve the raw NWP forecasts by statistically adjusting them through a procedure that is widely known as Model Output Statistics (MOS). The challenge is to identify complex patterns of systematic errors and then use this knowledge to adjust the NWP predictions. The MOS-based improvements are the basis for much of the value added by commercial wind power forecast providers. There are an enormous number of statistical approaches that can be used to generate the MOS adjustments to the raw NWP forecasts. In order to obtain insight into the potential value of some of the newer and more sophisticated statistical techniques often referred to as "machine learning methods" a MOS-method comparison experiment has been performed for wind power generation facilities in 6 wind resource areas of California. The underlying NWP models that provided the raw forecasts were the two primary operational models of the US National Weather Service: the GFS and NAM models. The focus was on 1- and 2-day ahead forecasts of the hourly wind-based generation. The statistical methods evaluated included: (1) screening multiple linear regression, which served as a baseline method, (2) artificial neural networks, (3) a decision-tree approach called random forests, (4) gradient boosted regression based upon an decision-tree algorithm, (5) support vector regression and (6) analog ensemble, which is a case-matching scheme. The presentation will provide (1) an overview of each method and the experimental design, (2) performance comparisons based on standard metrics such as bias, MAE and RMSE, (3) a summary of the performance characteristics of each approach and (4) a preview of further experiments to be conducted.

Kendall-Theil Robust Line (KTRLine--version 1.0)-A Visual Basic Program for Calculating and Graphing Robust Nonparametric Estimates of Linear-Regression Coefficients Between Two Continuous Variables

USGS Publications Warehouse

Granato, Gregory E.

2006-01-01

The Kendall-Theil Robust Line software (KTRLine-version 1.0) is a Visual Basic program that may be used with the Microsoft Windows operating system to calculate parameters for robust, nonparametric estimates of linear-regression coefficients between two continuous variables. The KTRLine software was developed by the U.S. Geological Survey, in cooperation with the Federal Highway Administration, for use in stochastic data modeling with local, regional, and national hydrologic data sets to develop planning-level estimates of potential effects of highway runoff on the quality of receiving waters. The Kendall-Theil robust line was selected because this robust nonparametric method is resistant to the effects of outliers and nonnormality in residuals that commonly characterize hydrologic data sets. The slope of the line is calculated as the median of all possible pairwise slopes between points. The intercept is calculated so that the line will run through the median of input data. A single-line model or a multisegment model may be specified. The program was developed to provide regression equations with an error component for stochastic data generation because nonparametric multisegment regression tools are not available with the software that is commonly used to develop regression models. The Kendall-Theil robust line is a median line and, therefore, may underestimate total mass, volume, or loads unless the error component or a bias correction factor is incorporated into the estimate. Regression statistics such as the median error, the median absolute deviation, the prediction error sum of squares, the root mean square error, the confidence interval for the slope, and the bias correction factor for median estimates are calculated by use of nonparametric methods. These statistics, however, may be used to formulate estimates of mass, volume, or total loads. The program is used to read a two- or three-column tab-delimited input file with variable names in the first row and data in subsequent rows. The user may choose the columns that contain the independent (X) and dependent (Y) variable. A third column, if present, may contain metadata such as the sample-collection location and date. The program screens the input files and plots the data. The KTRLine software is a graphical tool that facilitates development of regression models by use of graphs of the regression line with data, the regression residuals (with X or Y), and percentile plots of the cumulative frequency of the X variable, Y variable, and the regression residuals. The user may individually transform the independent and dependent variables to reduce heteroscedasticity and to linearize data. The program plots the data and the regression line. The program also prints model specifications and regression statistics to the screen. The user may save and print the regression results. The program can accept data sets that contain up to about 15,000 XY data points, but because the program must sort the array of all pairwise slopes, the program may be perceptibly slow with data sets that contain more than about 1,000 points.

Inferring gene regression networks with model trees

PubMed Central

2010-01-01

Background Novel strategies are required in order to handle the huge amount of data produced by microarray technologies. To infer gene regulatory networks, the first step is to find direct regulatory relationships between genes building the so-called gene co-expression networks. They are typically generated using correlation statistics as pairwise similarity measures. Correlation-based methods are very useful in order to determine whether two genes have a strong global similarity but do not detect local similarities. Results We propose model trees as a method to identify gene interaction networks. While correlation-based methods analyze each pair of genes, in our approach we generate a single regression tree for each gene from the remaining genes. Finally, a graph from all the relationships among output and input genes is built taking into account whether the pair of genes is statistically significant. For this reason we apply a statistical procedure to control the false discovery rate. The performance of our approach, named REGNET, is experimentally tested on two well-known data sets: Saccharomyces Cerevisiae and E.coli data set. First, the biological coherence of the results are tested. Second the E.coli transcriptional network (in the Regulon database) is used as control to compare the results to that of a correlation-based method. This experiment shows that REGNET performs more accurately at detecting true gene associations than the Pearson and Spearman zeroth and first-order correlation-based methods. Conclusions REGNET generates gene association networks from gene expression data, and differs from correlation-based methods in that the relationship between one gene and others is calculated simultaneously. Model trees are very useful techniques to estimate the numerical values for the target genes by linear regression functions. They are very often more precise than linear regression models because they can add just different linear regressions to separate areas of the search space favoring to infer localized similarities over a more global similarity. Furthermore, experimental results show the good performance of REGNET. PMID:20950452

Individual risk factors for deep infection and compromised fracture healing after intramedullary nailing of tibial shaft fractures: a single centre experience of 480 patients.

PubMed

Metsemakers, W-J; Handojo, K; Reynders, P; Sermon, A; Vanderschot, P; Nijs, S

2015-04-01

Despite modern advances in the treatment of tibial shaft fractures, complications including nonunion, malunion, and infection remain relatively frequent. A better understanding of these injuries and its complications could lead to prevention rather than treatment strategies. A retrospective study was performed to identify risk factors for deep infection and compromised fracture healing after intramedullary nailing (IMN) of tibial shaft fractures. Between January 2000 and January 2012, 480 consecutive patients with 486 tibial shaft fractures were enrolled in the study. Statistical analysis was performed to determine predictors of deep infection and compromised fracture healing. Compromised fracture healing was subdivided in delayed union and nonunion. The following independent variables were selected for analysis: age, sex, smoking, obesity, diabetes, American Society of Anaesthesiologists (ASA) classification, polytrauma, fracture type, open fractures, Gustilo type, primary external fixation (EF), time to nailing (TTN) and reaming. As primary statistical evaluation we performed a univariate analysis, followed by a multiple logistic regression model. Univariate regression analysis revealed similar risk factors for delayed union and nonunion, including fracture type, open fractures and Gustilo type. Factors affecting the occurrence of deep infection in this model were primary EF, a prolonged TTN, open fractures and Gustilo type. Multiple logistic regression analysis revealed polytrauma as the single risk factor for nonunion. With respect to delayed union, no risk factors could be identified. In the same statistical model, deep infection was correlated with primary EF. The purpose of this study was to evaluate risk factors of poor outcome after IMN of tibial shaft fractures. The univariate regression analysis showed that the nature of complications after tibial shaft nailing could be multifactorial. This was not confirmed in a multiple logistic regression model, which only revealed polytrauma and primary EF as risk factors for nonunion and deep infection, respectively. Future strategies should focus on prevention in high-risk populations such as polytrauma patients treated with EF. Copyright © 2014 Elsevier Ltd. All rights reserved.

Model Checking Techniques for Assessing Functional Form Specifications in Censored Linear Regression Models.

PubMed

León, Larry F; Cai, Tianxi

2012-04-01

In this paper we develop model checking techniques for assessing functional form specifications of covariates in censored linear regression models. These procedures are based on a censored data analog to taking cumulative sums of "robust" residuals over the space of the covariate under investigation. These cumulative sums are formed by integrating certain Kaplan-Meier estimators and may be viewed as "robust" censored data analogs to the processes considered by Lin, Wei & Ying (2002). The null distributions of these stochastic processes can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be generated by computer simulation. Each observed process can then be graphically compared with a few realizations from the Gaussian process. We also develop formal test statistics for numerical comparison. Such comparisons enable one to assess objectively whether an apparent trend seen in a residual plot reects model misspecification or natural variation. We illustrate the methods with a well known dataset. In addition, we examine the finite sample performance of the proposed test statistics in simulation experiments. In our simulation experiments, the proposed test statistics have good power of detecting misspecification while at the same time controlling the size of the test.

Fourier transform infrared reflectance spectra of latent fingerprints: a biometric gauge for the age of an individual.

PubMed

Hemmila, April; McGill, Jim; Ritter, David

2008-03-01

To determine if changes in fingerprint infrared spectra linear with age can be found, partial least squares (PLS1) regression of 155 fingerprint infrared spectra against the person's age was constructed. The regression produced a linear model of age as a function of spectrum with a root mean square error of calibration of less than 4 years, showing an inflection at about 25 years of age. The spectral ranges emphasized by the regression do not correspond to the highest concentration constituents of the fingerprints. Separate linear regression models for old and young people can be constructed with even more statistical rigor. The success of the regression demonstrates that a combination of constituents can be found that changes linearly with age, with a significant shift around puberty.

The Influence Factor Model for the Popularity of Mobile Phone without Considering the Price Factor

NASA Astrophysics Data System (ADS)

Long, Hongming; Peng, Diefei; Wu, Hailin; Yang, Zihui

2018-01-01

Based on the statistical data like economic development, social development, population indicator and so on, this paper establishes the linear regression model which influences the popularity rate of mobile phone users.

Estimating effects of limiting factors with regression quantiles

USGS Publications Warehouse

Cade, B.S.; Terrell, J.W.; Schroeder, R.L.

1999-01-01

In a recent Concepts paper in Ecology, Thomson et al. emphasized that assumptions of conventional correlation and regression analyses fundamentally conflict with the ecological concept of limiting factors, and they called for new statistical procedures to address this problem. The analytical issue is that unmeasured factors may be the active limiting constraint and may induce a pattern of unequal variation in the biological response variable through an interaction with the measured factors. Consequently, changes near the maxima, rather than at the center of response distributions, are better estimates of the effects expected when the observed factor is the active limiting constraint. Regression quantiles provide estimates for linear models fit to any part of a response distribution, including near the upper bounds, and require minimal assumptions about the form of the error distribution. Regression quantiles extend the concept of one-sample quantiles to the linear model by solving an optimization problem of minimizing an asymmetric function of absolute errors. Rank-score tests for regression quantiles provide tests of hypotheses and confidence intervals for parameters in linear models with heteroscedastic errors, conditions likely to occur in models of limiting ecological relations. We used selected regression quantiles (e.g., 5th, 10th, ..., 95th) and confidence intervals to test hypotheses that parameters equal zero for estimated changes in average annual acorn biomass due to forest canopy cover of oak (Quercus spp.) and oak species diversity. Regression quantiles also were used to estimate changes in glacier lily (Erythronium grandiflorum) seedling numbers as a function of lily flower numbers, rockiness, and pocket gopher (Thomomys talpoides fossor) activity, data that motivated the query by Thomson et al. for new statistical procedures. Both example applications showed that effects of limiting factors estimated by changes in some upper regression quantile (e.g., 90-95th) were greater than if effects were estimated by changes in the means from standard linear model procedures. Estimating a range of regression quantiles (e.g., 5-95th) provides a comprehensive description of biological response patterns for exploratory and inferential analyses in observational studies of limiting factors, especially when sampling large spatial and temporal scales.

[Application of SAS macro to evaluated multiplicative and additive interaction in logistic and Cox regression in clinical practices].

PubMed

Nie, Z Q; Ou, Y Q; Zhuang, J; Qu, Y J; Mai, J Z; Chen, J M; Liu, X Q

2016-05-01

Conditional logistic regression analysis and unconditional logistic regression analysis are commonly used in case control study, but Cox proportional hazard model is often used in survival data analysis. Most literature only refer to main effect model, however, generalized linear model differs from general linear model, and the interaction was composed of multiplicative interaction and additive interaction. The former is only statistical significant, but the latter has biological significance. In this paper, macros was written by using SAS 9.4 and the contrast ratio, attributable proportion due to interaction and synergy index were calculated while calculating the items of logistic and Cox regression interactions, and the confidence intervals of Wald, delta and profile likelihood were used to evaluate additive interaction for the reference in big data analysis in clinical epidemiology and in analysis of genetic multiplicative and additive interactions.

Improving satellite-based PM2.5 estimates in China using Gaussian processes modeling in a Bayesian hierarchical setting.

PubMed

Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun

2017-08-01

Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2  = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.

Comparison of Logistic Regression and Random Forests techniques for shallow landslide susceptibility assessment in Giampilieri (NE Sicily, Italy)

NASA Astrophysics Data System (ADS)

Trigila, Alessandro; Iadanza, Carla; Esposito, Carlo; Scarascia-Mugnozza, Gabriele

2015-11-01

The aim of this work is to define reliable susceptibility models for shallow landslides using Logistic Regression and Random Forests multivariate statistical techniques. The study area, located in North-East Sicily, was hit on October 1st 2009 by a severe rainstorm (225 mm of cumulative rainfall in 7 h) which caused flash floods and more than 1000 landslides. Several small villages, such as Giampilieri, were hit with 31 fatalities, 6 missing persons and damage to buildings and transportation infrastructures. Landslides, mainly types such as earth and debris translational slides evolving into debris flows, were triggered on steep slopes and involved colluvium and regolith materials which cover the underlying metamorphic bedrock. The work has been carried out with the following steps: i) realization of a detailed event landslide inventory map through field surveys coupled with observation of high resolution aerial colour orthophoto; ii) identification of landslide source areas; iii) data preparation of landslide controlling factors and descriptive statistics based on a bivariate method (Frequency Ratio) to get an initial overview on existing relationships between causative factors and shallow landslide source areas; iv) choice of criteria for the selection and sizing of the mapping unit; v) implementation of 5 multivariate statistical susceptibility models based on Logistic Regression and Random Forests techniques and focused on landslide source areas; vi) evaluation of the influence of sample size and type of sampling on results and performance of the models; vii) evaluation of the predictive capabilities of the models using ROC curve, AUC and contingency tables; viii) comparison of model results and obtained susceptibility maps; and ix) analysis of temporal variation of landslide susceptibility related to input parameter changes. Models based on Logistic Regression and Random Forests have demonstrated excellent predictive capabilities. Land use and wildfire variables were found to have a strong control on the occurrence of very rapid shallow landslides.

Accounting for spatial effects in land use regression for urban air pollution modeling.

PubMed

Bertazzon, Stefania; Johnson, Markey; Eccles, Kristin; Kaplan, Gilaad G

2015-01-01

In order to accurately assess air pollution risks, health studies require spatially resolved pollution concentrations. Land-use regression (LUR) models estimate ambient concentrations at a fine spatial scale. However, spatial effects such as spatial non-stationarity and spatial autocorrelation can reduce the accuracy of LUR estimates by increasing regression errors and uncertainty; and statistical methods for resolving these effects--e.g., spatially autoregressive (SAR) and geographically weighted regression (GWR) models--may be difficult to apply simultaneously. We used an alternate approach to address spatial non-stationarity and spatial autocorrelation in LUR models for nitrogen dioxide. Traditional models were re-specified to include a variable capturing wind speed and direction, and re-fit as GWR models. Mean R(2) values for the resulting GWR-wind models (summer: 0.86, winter: 0.73) showed a 10-20% improvement over traditional LUR models. GWR-wind models effectively addressed both spatial effects and produced meaningful predictive models. These results suggest a useful method for improving spatially explicit models. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Applied Prevalence Ratio estimation with different Regression models: An example from a cross-national study on substance use research.

PubMed

Espelt, Albert; Marí-Dell'Olmo, Marc; Penelo, Eva; Bosque-Prous, Marina

2016-06-14

To examine the differences between Prevalence Ratio (PR) and Odds Ratio (OR) in a cross-sectional study and to provide tools to calculate PR using two statistical packages widely used in substance use research (STATA and R). We used cross-sectional data from 41,263 participants of 16 European countries participating in the Survey on Health, Ageing and Retirement in Europe (SHARE). The dependent variable, hazardous drinking, was calculated using the Alcohol Use Disorders Identification Test - Consumption (AUDIT-C). The main independent variable was gender. Other variables used were: age, educational level and country of residence. PR of hazardous drinking in men with relation to women was estimated using Mantel-Haenszel method, log-binomial regression models and poisson regression models with robust variance. These estimations were compared to the OR calculated using logistic regression models. Prevalence of hazardous drinkers varied among countries. Generally, men have higher prevalence of hazardous drinking than women [PR=1.43 (1.38-1.47)]. Estimated PR was identical independently of the method and the statistical package used. However, OR overestimated PR, depending on the prevalence of hazardous drinking in the country. In cross-sectional studies, where comparisons between countries with differences in the prevalence of the disease or condition are made, it is advisable to use PR instead of OR.

Marginal regression approach for additive hazards models with clustered current status data.

PubMed

Su, Pei-Fang; Chi, Yunchan

2014-01-15

Current status data arise naturally from tumorigenicity experiments, epidemiology studies, biomedicine, econometrics and demographic and sociology studies. Moreover, clustered current status data may occur with animals from the same litter in tumorigenicity experiments or with subjects from the same family in epidemiology studies. Because the only information extracted from current status data is whether the survival times are before or after the monitoring or censoring times, the nonparametric maximum likelihood estimator of survival function converges at a rate of n(1/3) to a complicated limiting distribution. Hence, semiparametric regression models such as the additive hazards model have been extended for independent current status data to derive the test statistics, whose distributions converge at a rate of n(1/2) , for testing the regression parameters. However, a straightforward application of these statistical methods to clustered current status data is not appropriate because intracluster correlation needs to be taken into account. Therefore, this paper proposes two estimating functions for estimating the parameters in the additive hazards model for clustered current status data. The comparative results from simulation studies are presented, and the application of the proposed estimating functions to one real data set is illustrated. Copyright © 2013 John Wiley & Sons, Ltd.

Test anxiety and academic performance in chiropractic students.

PubMed

Zhang, Niu; Henderson, Charles N R

2014-01-01

Objective : We assessed the level of students' test anxiety, and the relationship between test anxiety and academic performance. Methods : We recruited 166 third-quarter students. The Test Anxiety Inventory (TAI) was administered to all participants. Total scores from written examinations and objective structured clinical examinations (OSCEs) were used as response variables. Results : Multiple regression analysis shows that there was a modest, but statistically significant negative correlation between TAI scores and written exam scores, but not OSCE scores. Worry and emotionality were the best predictive models for written exam scores. Mean total anxiety and emotionality scores for females were significantly higher than those for males, but not worry scores. Conclusion : Moderate-to-high test anxiety was observed in 85% of the chiropractic students examined. However, total test anxiety, as measured by the TAI score, was a very weak predictive model for written exam performance. Multiple regression analysis demonstrated that replacing total anxiety (TAI) with worry and emotionality (TAI subscales) produces a much more effective predictive model of written exam performance. Sex, age, highest current academic degree, and ethnicity contributed little additional predictive power in either regression model. Moreover, TAI scores were not found to be statistically significant predictors of physical exam skill performance, as measured by OSCEs.

Predicting Final GPA of Graduate School Students: Comparing Artificial Neural Networking and Simultaneous Multiple Regression

ERIC Educational Resources Information Center

Anderson, Joan L.

2006-01-01

Data from graduate student applications at a large Western university were used to determine which factors were the best predictors of success in graduate school, as defined by cumulative graduate grade point average. Two statistical models were employed and compared: artificial neural networking and simultaneous multiple regression. Both models…

Passing the Test: Ecological Regression Analysis in the Los Angeles County Case and Beyond.

ERIC Educational Resources Information Center

Lichtman, Allan J.

1991-01-01

Statistical analysis of racially polarized voting prepared for the Garza v County of Los Angeles (California) (1990) voting rights case is reviewed to demonstrate that ecological regression is a flexible, robust technique that illuminates the reality of ethnic voting, and superior to the neighborhood model supported by the defendants. (SLD)

10 CFR 436.31 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-01-01

... systems, building load simulation models, statistical regression analysis, or some combination of these..., excluding any cogeneration process for other than a federally owned building or buildings or other federally...

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert M.

2013-01-01

A new regression model search algorithm was developed that may be applied to both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The algorithm is a simplified version of a more complex algorithm that was originally developed for the NASA Ames Balance Calibration Laboratory. The new algorithm performs regression model term reduction to prevent overfitting of data. It has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a regression model search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression model. Therefore, the simplified algorithm is not intended to replace the original algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new search algorithm.

[How to fit and interpret multilevel models using SPSS].

PubMed

Pardo, Antonio; Ruiz, Miguel A; San Martín, Rafael

2007-05-01

Hierarchic or multilevel models are used to analyse data when cases belong to known groups and sample units are selected both from the individual level and from the group level. In this work, the multilevel models most commonly discussed in the statistic literature are described, explaining how to fit these models using the SPSS program (any version as of the 11 th ) and how to interpret the outcomes of the analysis. Five particular models are described, fitted, and interpreted: (1) one-way analysis of variance with random effects, (2) regression analysis with means-as-outcomes, (3) one-way analysis of covariance with random effects, (4) regression analysis with random coefficients, and (5) regression analysis with means- and slopes-as-outcomes. All models are explained, trying to make them understandable to researchers in health and behaviour sciences.

Estimating procedure times for surgeries by determining location parameters for the lognormal model.

PubMed

Spangler, William E; Strum, David P; Vargas, Luis G; May, Jerrold H

2004-05-01

We present an empirical study of methods for estimating the location parameter of the lognormal distribution. Our results identify the best order statistic to use, and indicate that using the best order statistic instead of the median may lead to less frequent incorrect rejection of the lognormal model, more accurate critical value estimates, and higher goodness-of-fit. Using simulation data, we constructed and compared two models for identifying the best order statistic, one based on conventional nonlinear regression and the other using a data mining/machine learning technique. Better surgical procedure time estimates may lead to improved surgical operations.

Forecasting defoliation by the gypsy moth in oak stands

Treesearch

Robert W. Campbell; Joseph P. Standaert

1974-01-01

A multiple-regression model is presented that reflects statistically significant correlations between defoliation by the gypsy moth, the dependent variable, and a series of biotic and physical independent variables. Both possible uses and shortcomings of this model are discussed.

Introduction to statistical modelling 2: categorical variables and interactions in linear regression.

PubMed

Lunt, Mark

2015-07-01

In the first article in this series we explored the use of linear regression to predict an outcome variable from a number of predictive factors. It assumed that the predictive factors were measured on an interval scale. However, this article shows how categorical variables can also be included in a linear regression model, enabling predictions to be made separately for different groups and allowing for testing the hypothesis that the outcome differs between groups. The use of interaction terms to measure whether the effect of a particular predictor variable differs between groups is also explained. An alternative approach to testing the difference between groups of the effect of a given predictor, which consists of measuring the effect in each group separately and seeing whether the statistical significance differs between the groups, is shown to be misleading. © The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Regression Analysis as a Cost Estimation Model for Unexploded Ordnance Cleanup at Former Military Installations

DTIC Science & Technology

2002-06-01

fits our actual data . To determine the goodness of fit, statisticians typically use the following four measures: R2 Statistic. The R2 statistic...reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of...mathematical model is developed to better estimate cleanup costs using historical cost data that could be used by the Defense Department prior to placing

Additive Genetic Variability and the Bayesian Alphabet

PubMed Central

Gianola, Daniel; de los Campos, Gustavo; Hill, William G.; Manfredi, Eduardo; Fernando, Rohan

2009-01-01

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called “Bayes A”) with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly. PMID:19620397

Discrete post-processing of total cloud cover ensemble forecasts

NASA Astrophysics Data System (ADS)

Hemri, Stephan; Haiden, Thomas; Pappenberger, Florian

2017-04-01

This contribution presents an approach to post-process ensemble forecasts for the discrete and bounded weather variable of total cloud cover. Two methods for discrete statistical post-processing of ensemble predictions are tested. The first approach is based on multinomial logistic regression, the second involves a proportional odds logistic regression model. Applying them to total cloud cover raw ensemble forecasts from the European Centre for Medium-Range Weather Forecasts improves forecast skill significantly. Based on station-wise post-processing of raw ensemble total cloud cover forecasts for a global set of 3330 stations over the period from 2007 to early 2014, the more parsimonious proportional odds logistic regression model proved to slightly outperform the multinomial logistic regression model. Reference Hemri, S., Haiden, T., & Pappenberger, F. (2016). Discrete post-processing of total cloud cover ensemble forecasts. Monthly Weather Review 144, 2565-2577.

Building and verifying a severity prediction model of acute pancreatitis (AP) based on BISAP, MEWS and routine test indexes.

PubMed

Ye, Jiang-Feng; Zhao, Yu-Xin; Ju, Jian; Wang, Wei

2017-10-01

To discuss the value of the Bedside Index for Severity in Acute Pancreatitis (BISAP), Modified Early Warning Score (MEWS), serum Ca2+, similarly hereinafter, and red cell distribution width (RDW) for predicting the severity grade of acute pancreatitis and to develop and verify a more accurate scoring system to predict the severity of AP. In 302 patients with AP, we calculated BISAP and MEWS scores and conducted regression analyses on the relationships of BISAP scoring, RDW, MEWS, and serum Ca2+ with the severity of AP using single-factor logistics. The variables with statistical significance in the single-factor logistic regression were used in a multi-factor logistic regression model; forward stepwise regression was used to screen variables and build a multi-factor prediction model. A receiver operating characteristic curve (ROC curve) was constructed, and the significance of multi- and single-factor prediction models in predicting the severity of AP using the area under the ROC curve (AUC) was evaluated. The internal validity of the model was verified through bootstrapping. Among 302 patients with AP, 209 had mild acute pancreatitis (MAP) and 93 had severe acute pancreatitis (SAP). According to single-factor logistic regression analysis, we found that BISAP, MEWS and serum Ca2+ are prediction indexes of the severity of AP (P-value<0.001), whereas RDW is not a prediction index of AP severity (P-value>0.05). The multi-factor logistic regression analysis showed that BISAP and serum Ca2+ are independent prediction indexes of AP severity (P-value<0.001), and MEWS is not an independent prediction index of AP severity (P-value>0.05); BISAP is negatively related to serum Ca2+ (r=-0.330, P-value<0.001). The constructed model is as follows: ln()=7.306+1.151*BISAP-4.516*serum Ca2+. The predictive ability of each model for SAP follows the order of the combined BISAP and serum Ca2+ prediction model>Ca2+>BISAP. There is no statistical significance for the predictive ability of BISAP and serum Ca2+ (P-value>0.05); however, there is remarkable statistical significance for the predictive ability using the newly built prediction model as well as BISAP and serum Ca2+ individually (P-value<0.01). Verification of the internal validity of the models by bootstrapping is favorable. BISAP and serum Ca2+ have high predictive value for the severity of AP. However, the model built by combining BISAP and serum Ca2+ is remarkably superior to those of BISAP and serum Ca2+ individually. Furthermore, this model is simple, practical and appropriate for clinical use. Copyright © 2016. Published by Elsevier Masson SAS.

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.

2012 Workplace and Gender Relations Survey of Reserve Component Members: Statistical Methodology Report

DTIC Science & Technology

2012-09-01

3,435 10,461 9.1 3.1 63 Unmarried with Children+ Unmarried without Children 439,495 0.01 10,350 43,870 10.1 2.2 64 Married with Children+ Married ...logistic regression model was used to predict the probability of eligibility for the survey (known eligibility vs . unknown eligibility). A second logistic...regression model was used to predict the probability of response among eligible sample members (complete response vs . non-response). CHAID (Chi

A Regional Analysis of Non-Methane Hydrocarbons And Meteorology of The Rural Southeast United States

DTIC Science & Technology

1996-01-01

Zt is an ARIMA time series. This is a typical regression model , except that it allows for autocorrelation in the error term Z. In this work, an ARMA...data=folder; var residual; run; II Statistical output of 1992 regression model on 1993 ozone data ARIMA Procedure Maximum Likelihood Estimation Approx...at each of the sites, and to show the effect of synoptic meteorology on high ozone by examining NOAA daily weather maps and climatic data

Systematic review of statistical approaches to quantify, or correct for, measurement error in a continuous exposure in nutritional epidemiology.

PubMed

Bennett, Derrick A; Landry, Denise; Little, Julian; Minelli, Cosetta

2017-09-19

Several statistical approaches have been proposed to assess and correct for exposure measurement error. We aimed to provide a critical overview of the most common approaches used in nutritional epidemiology. MEDLINE, EMBASE, BIOSIS and CINAHL were searched for reports published in English up to May 2016 in order to ascertain studies that described methods aimed to quantify and/or correct for measurement error for a continuous exposure in nutritional epidemiology using a calibration study. We identified 126 studies, 43 of which described statistical methods and 83 that applied any of these methods to a real dataset. The statistical approaches in the eligible studies were grouped into: a) approaches to quantify the relationship between different dietary assessment instruments and "true intake", which were mostly based on correlation analysis and the method of triads; b) approaches to adjust point and interval estimates of diet-disease associations for measurement error, mostly based on regression calibration analysis and its extensions. Two approaches (multiple imputation and moment reconstruction) were identified that can deal with differential measurement error. For regression calibration, the most common approach to correct for measurement error used in nutritional epidemiology, it is crucial to ensure that its assumptions and requirements are fully met. Analyses that investigate the impact of departures from the classical measurement error model on regression calibration estimates can be helpful to researchers in interpreting their findings. With regard to the possible use of alternative methods when regression calibration is not appropriate, the choice of method should depend on the measurement error model assumed, the availability of suitable calibration study data and the potential for bias due to violation of the classical measurement error model assumptions. On the basis of this review, we provide some practical advice for the use of methods to assess and adjust for measurement error in nutritional epidemiology.

SOCR Analyses – an Instructional Java Web-based Statistical Analysis Toolkit

PubMed Central

Chu, Annie; Cui, Jenny; Dinov, Ivo D.

2011-01-01

The Statistical Online Computational Resource (SOCR) designs web-based tools for educational use in a variety of undergraduate courses (Dinov 2006). Several studies have demonstrated that these resources significantly improve students' motivation and learning experiences (Dinov et al. 2008). SOCR Analyses is a new component that concentrates on data modeling and analysis using parametric and non-parametric techniques supported with graphical model diagnostics. Currently implemented analyses include commonly used models in undergraduate statistics courses like linear models (Simple Linear Regression, Multiple Linear Regression, One-Way and Two-Way ANOVA). In addition, we implemented tests for sample comparisons, such as t-test in the parametric category; and Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, in the non-parametric category. SOCR Analyses also include several hypothesis test models, such as Contingency tables, Friedman's test and Fisher's exact test. The code itself is open source (http://socr.googlecode.com/), hoping to contribute to the efforts of the statistical computing community. The code includes functionality for each specific analysis model and it has general utilities that can be applied in various statistical computing tasks. For example, concrete methods with API (Application Programming Interface) have been implemented in statistical summary, least square solutions of general linear models, rank calculations, etc. HTML interfaces, tutorials, source code, activities, and data are freely available via the web (www.SOCR.ucla.edu). Code examples for developers and demos for educators are provided on the SOCR Wiki website. In this article, the pedagogical utilization of the SOCR Analyses is discussed, as well as the underlying design framework. As the SOCR project is on-going and more functions and tools are being added to it, these resources are constantly improved. The reader is strongly encouraged to check the SOCR site for most updated information and newly added models. PMID:21546994

Modelling spruce bark beetle infestation probability

Treesearch

Paulius Zolubas; Jose Negron; A. Steven Munson

2009-01-01

Spruce bark beetle (Ips typographus L.) risk model, based on pure Norway spruce (Picea abies Karst.) stand characteristics in experimental and control plots was developed using classification and regression tree statistical technique under endemic pest population density. The most significant variable in spruce bark beetle...

Spatial prediction of soil texture in region Centre (France) from summary data

NASA Astrophysics Data System (ADS)

Dobarco, Mercedes Roman; Saby, Nicolas; Paroissien, Jean-Baptiste; Orton, Tom G.

2015-04-01

Soil texture is a key controlling factor of important soil functions like water and nutrient holding capacity, retention of pollutants, drainage, soil biodiversity, and C cycling. High resolution soil texture maps enhance our understanding of the spatial distribution of soil properties and provide valuable information for decision making and crop management, environmental protection, and hydrological planning. We predicted the soil texture of agricultural topsoils in the Region Centre (France) combining regression and area-to-point kriging. Soil texture data was collected from the French soil-test database (BDAT), which is populated with soil analysis performed by farmers' demand. To protect the anonymity of the farms the data was treated by commune. In a first step, summary statistics of environmental covariates by commune were used to develop prediction models with Cubist, boosted regression trees, and random forests. In a second step the residuals of each individual observation were summarized by commune and kriged following the method developed by Orton et al. (2012). This approach allowed to include non-linear relationships among covariates and soil texture while accounting for the uncertainty on areal means in the area-to-point kriging step. Independent validation of the models was done using data from the systematic soil monitoring network of French soils. Future work will compare the performance of these models with a non-stationary variance geostatistical model using the most important covariates and summary statistics of texture data. The results will inform on whether the later and statistically more-challenging approach improves significantly texture predictions or whether the more simple area-to-point regression kriging can offer satisfactory results. The application of area-to-point regression kriging at national level using BDAT data has the potential to improve soil texture predictions for agricultural topsoils, especially when combined with existing maps (i.e., model ensemble).

Hypothesis testing in functional linear regression models with Neyman's truncation and wavelet thresholding for longitudinal data.

PubMed

Yang, Xiaowei; Nie, Kun

2008-03-15

Longitudinal data sets in biomedical research often consist of large numbers of repeated measures. In many cases, the trajectories do not look globally linear or polynomial, making it difficult to summarize the data or test hypotheses using standard longitudinal data analysis based on various linear models. An alternative approach is to apply the approaches of functional data analysis, which directly target the continuous nonlinear curves underlying discretely sampled repeated measures. For the purposes of data exploration, many functional data analysis strategies have been developed based on various schemes of smoothing, but fewer options are available for making causal inferences regarding predictor-outcome relationships, a common task seen in hypothesis-driven medical studies. To compare groups of curves, two testing strategies with good power have been proposed for high-dimensional analysis of variance: the Fourier-based adaptive Neyman test and the wavelet-based thresholding test. Using a smoking cessation clinical trial data set, this paper demonstrates how to extend the strategies for hypothesis testing into the framework of functional linear regression models (FLRMs) with continuous functional responses and categorical or continuous scalar predictors. The analysis procedure consists of three steps: first, apply the Fourier or wavelet transform to the original repeated measures; then fit a multivariate linear model in the transformed domain; and finally, test the regression coefficients using either adaptive Neyman or thresholding statistics. Since a FLRM can be viewed as a natural extension of the traditional multiple linear regression model, the development of this model and computational tools should enhance the capacity of medical statistics for longitudinal data.

Quality Reporting of Multivariable Regression Models in Observational Studies: Review of a Representative Sample of Articles Published in Biomedical Journals.

PubMed

Real, Jordi; Forné, Carles; Roso-Llorach, Albert; Martínez-Sánchez, Jose M

2016-05-01

Controlling for confounders is a crucial step in analytical observational studies, and multivariable models are widely used as statistical adjustment techniques. However, the validation of the assumptions of the multivariable regression models (MRMs) should be made clear in scientific reporting. The objective of this study is to review the quality of statistical reporting of the most commonly used MRMs (logistic, linear, and Cox regression) that were applied in analytical observational studies published between 2003 and 2014 by journals indexed in MEDLINE.Review of a representative sample of articles indexed in MEDLINE (n = 428) with observational design and use of MRMs (logistic, linear, and Cox regression). We assessed the quality of reporting about: model assumptions and goodness-of-fit, interactions, sensitivity analysis, crude and adjusted effect estimate, and specification of more than 1 adjusted model.The tests of underlying assumptions or goodness-of-fit of the MRMs used were described in 26.2% (95% CI: 22.0-30.3) of the articles and 18.5% (95% CI: 14.8-22.1) reported the interaction analysis. Reporting of all items assessed was higher in articles published in journals with a higher impact factor.A low percentage of articles indexed in MEDLINE that used multivariable techniques provided information demonstrating rigorous application of the model selected as an adjustment method. Given the importance of these methods to the final results and conclusions of observational studies, greater rigor is required in reporting the use of MRMs in the scientific literature.

Estimation of aboveground biomass in Mediterranean forests by statistical modelling of ASTER fraction images

NASA Astrophysics Data System (ADS)

Fernández-Manso, O.; Fernández-Manso, A.; Quintano, C.

2014-09-01

Aboveground biomass (AGB) estimation from optical satellite data is usually based on regression models of original or synthetic bands. To overcome the poor relation between AGB and spectral bands due to mixed-pixels when a medium spatial resolution sensor is considered, we propose to base the AGB estimation on fraction images from Linear Spectral Mixture Analysis (LSMA). Our study area is a managed Mediterranean pine woodland (Pinus pinaster Ait.) in central Spain. A total of 1033 circular field plots were used to estimate AGB from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) optical data. We applied Pearson correlation statistics and stepwise multiple regression to identify suitable predictors from the set of variables of original bands, fraction imagery, Normalized Difference Vegetation Index and Tasselled Cap components. Four linear models and one nonlinear model were tested. A linear combination of ASTER band 2 (red, 0.630-0.690 μm), band 8 (short wave infrared 5, 2.295-2.365 μm) and green vegetation fraction (from LSMA) was the best AGB predictor (Radj2=0.632, the root-mean-squared error of estimated AGB was 13.3 Mg ha-1 (or 37.7%), resulting from cross-validation), rather than other combinations of the above cited independent variables. Results indicated that using ASTER fraction images in regression models improves the AGB estimation in Mediterranean pine forests. The spatial distribution of the estimated AGB, based on a multiple linear regression model, may be used as baseline information for forest managers in future studies, such as quantifying the regional carbon budget, fuel accumulation or monitoring of management practices.

Predictive modeling of hazardous waste landfill total above-ground biomass using passive optical and LIDAR remotely sensed data

NASA Astrophysics Data System (ADS)

Hadley, Brian Christopher

This dissertation assessed remotely sensed data and geospatial modeling technique(s) to map the spatial distribution of total above-ground biomass present on the surface of the Savannah River National Laboratory's (SRNL) Mixed Waste Management Facility (MWMF) hazardous waste landfill. Ordinary least squares (OLS) regression, regression kriging, and tree-structured regression were employed to model the empirical relationship between in-situ measured Bahia (Paspalum notatum Flugge) and Centipede [Eremochloa ophiuroides (Munro) Hack.] grass biomass against an assortment of explanatory variables extracted from fine spatial resolution passive optical and LIDAR remotely sensed data. Explanatory variables included: (1) discrete channels of visible, near-infrared (NIR), and short-wave infrared (SWIR) reflectance, (2) spectral vegetation indices (SVI), (3) spectral mixture analysis (SMA) modeled fractions, (4) narrow-band derivative-based vegetation indices, and (5) LIDAR derived topographic variables (i.e. elevation, slope, and aspect). Results showed that a linear combination of the first- (1DZ_DGVI), second- (2DZ_DGVI), and third-derivative of green vegetation indices (3DZ_DGVI) calculated from hyperspectral data recorded over the 400--960 nm wavelengths of the electromagnetic spectrum explained the largest percentage of statistical variation (R2 = 0.5184) in the total above-ground biomass measurements. In general, the topographic variables did not correlate well with the MWMF biomass data, accounting for less than five percent of the statistical variation. It was concluded that tree-structured regression represented the optimum geospatial modeling technique due to a combination of model performance and efficiency/flexibility factors.

Statistical approaches to account for missing values in accelerometer data: Applications to modeling physical activity.

PubMed

Yue Xu, Selene; Nelson, Sandahl; Kerr, Jacqueline; Godbole, Suneeta; Patterson, Ruth; Merchant, Gina; Abramson, Ian; Staudenmayer, John; Natarajan, Loki

2018-04-01

Physical inactivity is a recognized risk factor for many chronic diseases. Accelerometers are increasingly used as an objective means to measure daily physical activity. One challenge in using these devices is missing data due to device nonwear. We used a well-characterized cohort of 333 overweight postmenopausal breast cancer survivors to examine missing data patterns of accelerometer outputs over the day. Based on these observed missingness patterns, we created psuedo-simulated datasets with realistic missing data patterns. We developed statistical methods to design imputation and variance weighting algorithms to account for missing data effects when fitting regression models. Bias and precision of each method were evaluated and compared. Our results indicated that not accounting for missing data in the analysis yielded unstable estimates in the regression analysis. Incorporating variance weights and/or subject-level imputation improved precision by >50%, compared to ignoring missing data. We recommend that these simple easy-to-implement statistical tools be used to improve analysis of accelerometer data.

An empirical study of statistical properties of variance partition coefficients for multi-level logistic regression models

USGS Publications Warehouse

Li, Ji; Gray, B.R.; Bates, D.M.

2008-01-01

Partitioning the variance of a response by design levels is challenging for binomial and other discrete outcomes. Goldstein (2003) proposed four definitions for variance partitioning coefficients (VPC) under a two-level logistic regression model. In this study, we explicitly derived formulae for multi-level logistic regression model and subsequently studied the distributional properties of the calculated VPCs. Using simulations and a vegetation dataset, we demonstrated associations between different VPC definitions, the importance of methods for estimating VPCs (by comparing VPC obtained using Laplace and penalized quasilikehood methods), and bivariate dependence between VPCs calculated at different levels. Such an empirical study lends an immediate support to wider applications of VPC in scientific data analysis.

Predicting Potential Changes in Suitable Habitat and Distribution by 2100 for Tree Species of the Eastern United States

Treesearch

Louis R Iverson; Anantha M. Prasad; Mark W. Schwartz; Mark W. Schwartz

2005-01-01

We predict current distribution and abundance for tree species present in eastern North America, and subsequently estimate potential suitable habitat for those species under a changed climate with 2 x CO2. We used a series of statistical models (i.e., Regression Tree Analysis (RTA), Multivariate Adaptive Regression Splines (MARS), Bagging Trees (...

Poisson regression models outperform the geometrical model in estimating the peak-to-trough ratio of seasonal variation: a simulation study.

PubMed

Christensen, A L; Lundbye-Christensen, S; Dethlefsen, C

2011-12-01

Several statistical methods of assessing seasonal variation are available. Brookhart and Rothman [3] proposed a second-order moment-based estimator based on the geometrical model derived by Edwards [1], and reported that this estimator is superior in estimating the peak-to-trough ratio of seasonal variation compared with Edwards' estimator with respect to bias and mean squared error. Alternatively, seasonal variation may be modelled using a Poisson regression model, which provides flexibility in modelling the pattern of seasonal variation and adjustments for covariates. Based on a Monte Carlo simulation study three estimators, one based on the geometrical model, and two based on log-linear Poisson regression models, were evaluated in regards to bias and standard deviation (SD). We evaluated the estimators on data simulated according to schemes varying in seasonal variation and presence of a secular trend. All methods and analyses in this paper are available in the R package Peak2Trough[13]. Applying a Poisson regression model resulted in lower absolute bias and SD for data simulated according to the corresponding model assumptions. Poisson regression models had lower bias and SD for data simulated to deviate from the corresponding model assumptions than the geometrical model. This simulation study encourages the use of Poisson regression models in estimating the peak-to-trough ratio of seasonal variation as opposed to the geometrical model. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Statistical methods and regression analysis of stratospheric ozone and meteorological variables in Isfahan

NASA Astrophysics Data System (ADS)

Hassanzadeh, S.; Hosseinibalam, F.; Omidvari, M.

2008-04-01

Data of seven meteorological variables (relative humidity, wet temperature, dry temperature, maximum temperature, minimum temperature, ground temperature and sun radiation time) and ozone values have been used for statistical analysis. Meteorological variables and ozone values were analyzed using both multiple linear regression and principal component methods. Data for the period 1999-2004 are analyzed jointly using both methods. For all periods, temperature dependent variables were highly correlated, but were all negatively correlated with relative humidity. Multiple regression analysis was used to fit the meteorological variables using the meteorological variables as predictors. A variable selection method based on high loading of varimax rotated principal components was used to obtain subsets of the predictor variables to be included in the linear regression model of the meteorological variables. In 1999, 2001 and 2002 one of the meteorological variables was weakly influenced predominantly by the ozone concentrations. However, the model did not predict that the meteorological variables for the year 2000 were not influenced predominantly by the ozone concentrations that point to variation in sun radiation. This could be due to other factors that were not explicitly considered in this study.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Kandler; Shi, Ying; Santhanagopalan, Shriram

Predictive models of Li-ion battery lifetime must consider a multiplicity of electrochemical, thermal, and mechanical degradation modes experienced by batteries in application environments. To complicate matters, Li-ion batteries can experience different degradation trajectories that depend on storage and cycling history of the application environment. Rates of degradation are controlled by factors such as temperature history, electrochemical operating window, and charge/discharge rate. We present a generalized battery life prognostic model framework for battery systems design and control. The model framework consists of trial functions that are statistically regressed to Li-ion cell life datasets wherein the cells have been aged under differentmore » levels of stress. Degradation mechanisms and rate laws dependent on temperature, storage, and cycling condition are regressed to the data, with multiple model hypotheses evaluated and the best model down-selected based on statistics. The resulting life prognostic model, implemented in state variable form, is extensible to arbitrary real-world scenarios. The model is applicable in real-time control algorithms to maximize battery life and performance. We discuss efforts to reduce lifetime prediction error and accommodate its inevitable impact in controller design.« less

qFeature

DOE Office of Scientific and Technical Information (OSTI.GOV)

2015-09-14

This package contains statistical routines for extracting features from multivariate time-series data which can then be used for subsequent multivariate statistical analysis to identify patterns and anomalous behavior. It calculates local linear or quadratic regression model fits to moving windows for each series and then summarizes the model coefficients across user-defined time intervals for each series. These methods are domain agnostic-but they have been successfully applied to a variety of domains, including commercial aviation and electric power grid data.

Improved statistical power with a sparse shape model in detecting an aging effect in the hippocampus and amygdala

NASA Astrophysics Data System (ADS)

Chung, Moo K.; Kim, Seung-Goo; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matthew J.; Davidson, Richard J.

2014-03-01

The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace- Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Tradition- ally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorrectly detecting false negatives. Hence the statistical power improves. The sparse shape model is then applied in investigating the influence of age on amygdala and hippocampus shapes in the normal population. The advantage of the LB sparse framework is demonstrated by showing the increased statistical power.

Assessment and prediction of inter-joint upper limb movement correlations based on kinematic analysis and statistical regression

NASA Astrophysics Data System (ADS)

Toth-Tascau, Mirela; Balanean, Flavia; Krepelka, Mircea

2013-10-01

Musculoskeletal impairment of the upper limb can cause difficulties in performing basic daily activities. Three dimensional motion analyses can provide valuable data of arm movement in order to precisely determine arm movement and inter-joint coordination. The purpose of this study was to develop a method to evaluate the degree of impairment based on the influence of shoulder movements in the amplitude of elbow flexion and extension based on the assumption that a lack of motion of the elbow joint will be compensated by an increased shoulder activity. In order to develop and validate a statistical model, one healthy young volunteer has been involved in the study. The activity of choice simulated blowing the nose, starting from a slight flexion of the elbow and raising the hand until the middle finger touches the tip of the nose and return to the start position. Inter-joint coordination between the elbow and shoulder movements showed significant correlation. Statistical regression was used to fit an equation model describing the influence of shoulder movements on the elbow mobility. The study provides a brief description of the kinematic analysis protocol and statistical models that may be useful in describing the relation between inter-joint movements of daily activities.

Estimating the Probability of Rare Events Occurring Using a Local Model Averaging.

PubMed

Chen, Jin-Hua; Chen, Chun-Shu; Huang, Meng-Fan; Lin, Hung-Chih

2016-10-01

In statistical applications, logistic regression is a popular method for analyzing binary data accompanied by explanatory variables. But when one of the two outcomes is rare, the estimation of model parameters has been shown to be severely biased and hence estimating the probability of rare events occurring based on a logistic regression model would be inaccurate. In this article, we focus on estimating the probability of rare events occurring based on logistic regression models. Instead of selecting a best model, we propose a local model averaging procedure based on a data perturbation technique applied to different information criteria to obtain different probability estimates of rare events occurring. Then an approximately unbiased estimator of Kullback-Leibler loss is used to choose the best one among them. We design complete simulations to show the effectiveness of our approach. For illustration, a necrotizing enterocolitis (NEC) data set is analyzed. © 2016 Society for Risk Analysis.

Application of nonlinear least-squares regression to ground-water flow modeling, west-central Florida

USGS Publications Warehouse

Yobbi, D.K.

2000-01-01

A nonlinear least-squares regression technique for estimation of ground-water flow model parameters was applied to an existing model of the regional aquifer system underlying west-central Florida. The regression technique minimizes the differences between measured and simulated water levels. Regression statistics, including parameter sensitivities and correlations, were calculated for reported parameter values in the existing model. Optimal parameter values for selected hydrologic variables of interest are estimated by nonlinear regression. Optimal estimates of parameter values are about 140 times greater than and about 0.01 times less than reported values. Independently estimating all parameters by nonlinear regression was impossible, given the existing zonation structure and number of observations, because of parameter insensitivity and correlation. Although the model yields parameter values similar to those estimated by other methods and reproduces the measured water levels reasonably accurately, a simpler parameter structure should be considered. Some possible ways of improving model calibration are to: (1) modify the defined parameter-zonation structure by omitting and/or combining parameters to be estimated; (2) carefully eliminate observation data based on evidence that they are likely to be biased; (3) collect additional water-level data; (4) assign values to insensitive parameters, and (5) estimate the most sensitive parameters first, then, using the optimized values for these parameters, estimate the entire data set.

Statistical Validation of Surrogate Endpoints: Another Look at the Prentice Criterion and Other Criteria.

PubMed

Saraf, Sanatan; Mathew, Thomas; Roy, Anindya

2015-01-01

For the statistical validation of surrogate endpoints, an alternative formulation is proposed for testing Prentice's fourth criterion, under a bivariate normal model. In such a setup, the criterion involves inference concerning an appropriate regression parameter, and the criterion holds if the regression parameter is zero. Testing such a null hypothesis has been criticized in the literature since it can only be used to reject a poor surrogate, and not to validate a good surrogate. In order to circumvent this, an equivalence hypothesis is formulated for the regression parameter, namely the hypothesis that the parameter is equivalent to zero. Such an equivalence hypothesis is formulated as an alternative hypothesis, so that the surrogate endpoint is statistically validated when the null hypothesis is rejected. Confidence intervals for the regression parameter and tests for the equivalence hypothesis are proposed using bootstrap methods and small sample asymptotics, and their performances are numerically evaluated and recommendations are made. The choice of the equivalence margin is a regulatory issue that needs to be addressed. The proposed equivalence testing formulation is also adopted for other parameters that have been proposed in the literature on surrogate endpoint validation, namely, the relative effect and proportion explained.

Modified physiologically equivalent temperature—basics and applications for western European climate

NASA Astrophysics Data System (ADS)

Chen, Yung-Chang; Matzarakis, Andreas

2018-05-01

A new thermal index, the modified physiologically equivalent temperature (mPET) has been developed for universal application in different climate zones. The mPET has been improved against the weaknesses of the original physiologically equivalent temperature (PET) by enhancing evaluation of the humidity and clothing variability. The principles of mPET and differences between original PET and mPET are introduced and discussed in this study. Furthermore, this study has also evidenced the usability of mPET with climatic data in Freiburg, which is located in Western Europe. Comparisons of PET, mPET, and Universal Thermal Climate Index (UTCI) have shown that mPET gives a more realistic estimation of human thermal sensation than the other two thermal indices (PET, UTCI) for the thermal conditions in Freiburg. Additionally, a comparison of physiological parameters between mPET model and PET model (Munich Energy Balance Model for Individual, namely MEMI) is proposed. The core temperatures and skin temperatures of PET model vary more violently to a low temperature during cold stress than the mPET model. It can be regarded as that the mPET model gives a more realistic core temperature and mean skin temperature than the PET model. Statistical regression analysis of mPET based on the air temperature, mean radiant temperature, vapor pressure, and wind speed has been carried out. The R square (0.995) has shown a well co-relationship between human biometeorological factors and mPET. The regression coefficient of each factor represents the influence of the each factor on changing mPET (i.e., ±1 °C of T a = ± 0.54 °C of mPET). The first-order regression has been considered predicting a more realistic estimation of mPET at Freiburg during 2003 than the other higher order regression model, because the predicted mPET from the first-order regression has less difference from mPET calculated from measurement data. Statistic tests recognize that mPET can effectively evaluate the influences of all human biometeorological factors on thermal environments. Moreover, a first-order regression function can also predict the thermal evaluations of the mPET by using human biometeorological factors in Freiburg.

Improved estimation of PM2.5 using Lagrangian satellite-measured aerosol optical depth

NASA Astrophysics Data System (ADS)

Olivas Saunders, Rolando

Suspended particulate matter (aerosols) with aerodynamic diameters less than 2.5 mum (PM2.5) has negative effects on human health, plays an important role in climate change and also causes the corrosion of structures by acid deposition. Accurate estimates of PM2.5 concentrations are thus relevant in air quality, epidemiology, cloud microphysics and climate forcing studies. Aerosol optical depth (AOD) retrieved by the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument has been used as an empirical predictor to estimate ground-level concentrations of PM2.5 . These estimates usually have large uncertainties and errors. The main objective of this work is to assess the value of using upwind (Lagrangian) MODIS-AOD as predictors in empirical models of PM2.5. The upwind locations of the Lagrangian AOD were estimated using modeled backward air trajectories. Since the specification of an arrival elevation is somewhat arbitrary, trajectories were calculated to arrive at four different elevations at ten measurement sites within the continental United States. A systematic examination revealed trajectory model calculations to be sensitive to starting elevation. With a 500 m difference in starting elevation, the 48-hr mean horizontal separation of trajectory endpoints was 326 km. When the difference in starting elevation was doubled and tripled to 1000 m and 1500m, the mean horizontal separation of trajectory endpoints approximately doubled and tripled to 627 km and 886 km, respectively. A seasonal dependence of this sensitivity was also found: the smallest mean horizontal separation of trajectory endpoints was exhibited during the summer and the largest separations during the winter. A daily average AOD product was generated and coupled to the trajectory model in order to determine AOD values upwind of the measurement sites during the period 2003-2007. Empirical models that included in situ AOD and upwind AOD as predictors of PM2.5 were generated by multivariate linear regressions using the least squares method. The multivariate models showed improved performance over the single variable regression (PM2.5 and in situ AOD) models. The statistical significance of the improvement of the multivariate models over the single variable regression models was tested using the extra sum of squares principle. In many cases, even when the R-squared was high for the multivariate models, the improvement over the single models was not statistically significant. The R-squared of these multivariate models varied with respect to seasons, with the best performance occurring during the summer months. A set of seasonal categorical variables was included in the regressions to exploit this variability. The multivariate regression models that included these categorical seasonal variables performed better than the models that didn't account for seasonal variability. Furthermore, 71% of these regressions exhibited improvement over the single variable models that was statistically significant at a 95% confidence level.

Improving the long-lead predictability of El Niño using a novel forecasting scheme based on a dynamic components model

NASA Astrophysics Data System (ADS)

Petrova, Desislava; Koopman, Siem Jan; Ballester, Joan; Rodó, Xavier

2017-02-01

El Niño (EN) is a dominant feature of climate variability on inter-annual time scales driving changes in the climate throughout the globe, and having wide-spread natural and socio-economic consequences. In this sense, its forecast is an important task, and predictions are issued on a regular basis by a wide array of prediction schemes and climate centres around the world. This study explores a novel method for EN forecasting. In the state-of-the-art the advantageous statistical technique of unobserved components time series modeling, also known as structural time series modeling, has not been applied. Therefore, we have developed such a model where the statistical analysis, including parameter estimation and forecasting, is based on state space methods, and includes the celebrated Kalman filter. The distinguishing feature of this dynamic model is the decomposition of a time series into a range of stochastically time-varying components such as level (or trend), seasonal, cycles of different frequencies, irregular, and regression effects incorporated as explanatory covariates. These components are modeled separately and ultimately combined in a single forecasting scheme. Customary statistical models for EN prediction essentially use SST and wind stress in the equatorial Pacific. In addition to these, we introduce a new domain of regression variables accounting for the state of the subsurface ocean temperature in the western and central equatorial Pacific, motivated by our analysis, as well as by recent and classical research, showing that subsurface processes and heat accumulation there are fundamental for the genesis of EN. An important feature of the scheme is that different regression predictors are used at different lead months, thus capturing the dynamical evolution of the system and rendering more efficient forecasts. The new model has been tested with the prediction of all warm events that occurred in the period 1996-2015. Retrospective forecasts of these events were made for long lead times of at least two and a half years. Hence, the present study demonstrates that the theoretical limit of ENSO prediction should be sought much longer than the commonly accepted "Spring Barrier". The high correspondence between the forecasts and observations indicates that the proposed model outperforms all current operational statistical models, and behaves comparably to the best dynamical models used for EN prediction. Thus, the novel way in which the modeling scheme has been structured could also be used for improving other statistical and dynamical modeling systems.

The Mantel-Haenszel procedure revisited: models and generalizations.

PubMed

Fidler, Vaclav; Nagelkerke, Nico

2013-01-01

Several statistical methods have been developed for adjusting the Odds Ratio of the relation between two dichotomous variables X and Y for some confounders Z. With the exception of the Mantel-Haenszel method, commonly used methods, notably binary logistic regression, are not symmetrical in X and Y. The classical Mantel-Haenszel method however only works for confounders with a limited number of discrete strata, which limits its utility, and appears to have no basis in statistical models. Here we revisit the Mantel-Haenszel method and propose an extension to continuous and vector valued Z. The idea is to replace the observed cell entries in strata of the Mantel-Haenszel procedure by subject specific classification probabilities for the four possible values of (X,Y) predicted by a suitable statistical model. For situations where X and Y can be treated symmetrically we propose and explore the multinomial logistic model. Under the homogeneity hypothesis, which states that the odds ratio does not depend on Z, the logarithm of the odds ratio estimator can be expressed as a simple linear combination of three parameters of this model. Methods for testing the homogeneity hypothesis are proposed. The relationship between this method and binary logistic regression is explored. A numerical example using survey data is presented.

The Mantel-Haenszel Procedure Revisited: Models and Generalizations

PubMed Central

Fidler, Vaclav; Nagelkerke, Nico

2013-01-01

Several statistical methods have been developed for adjusting the Odds Ratio of the relation between two dichotomous variables X and Y for some confounders Z. With the exception of the Mantel-Haenszel method, commonly used methods, notably binary logistic regression, are not symmetrical in X and Y. The classical Mantel-Haenszel method however only works for confounders with a limited number of discrete strata, which limits its utility, and appears to have no basis in statistical models. Here we revisit the Mantel-Haenszel method and propose an extension to continuous and vector valued Z. The idea is to replace the observed cell entries in strata of the Mantel-Haenszel procedure by subject specific classification probabilities for the four possible values of (X,Y) predicted by a suitable statistical model. For situations where X and Y can be treated symmetrically we propose and explore the multinomial logistic model. Under the homogeneity hypothesis, which states that the odds ratio does not depend on Z, the logarithm of the odds ratio estimator can be expressed as a simple linear combination of three parameters of this model. Methods for testing the homogeneity hypothesis are proposed. The relationship between this method and binary logistic regression is explored. A numerical example using survey data is presented. PMID:23516463

Analytic Methods for Adjusting Subjective Rating Schemes.

ERIC Educational Resources Information Center

Cooper, Richard V. L.; Nelson, Gary R.

Statistical and econometric techniques of correcting for supervisor bias in models of individual performance appraisal were developed, using a variant of the classical linear regression model. Location bias occurs when individual performance is systematically overestimated or underestimated, while scale bias results when raters either exaggerate…

Trends in Mortality After Primary Cytoreductive Surgery for Ovarian Cancer: A Systematic Review and Metaregression of Randomized Clinical Trials and Observational Studies.

PubMed

Di Donato, Violante; Kontopantelis, Evangelos; Aletti, Giovanni; Casorelli, Assunta; Piacenti, Ilaria; Bogani, Giorgio; Lecce, Francesca; Benedetti Panici, Pierluigi

2017-06-01

Primary cytoreductive surgery (PDS) followed by platinum-based chemotherapy is the cornerstone of treatment and the absence of residual tumor after PDS is universally considered the most important prognostic factor. The aim of the present analysis was to evaluate trend and predictors of 30-day mortality in patients undergoing primary cytoreduction for ovarian cancer. Literature was searched for records reporting 30-day mortality after PDS. All cohorts were rated for quality. Simple and multiple Poisson regression models were used to quantify the association between 30-day mortality and the following: overall or severe complications, proportion of patients with stage IV disease, median age, year of publication, and weighted surgical complexity index. Using the multiple regression model, we calculated the risk of perioperative mortality at different levels for statistically significant covariates of interest. Simple regression identified median age and proportion of patients with stage IV disease as statistically significant predictors of 30-day mortality. When included in the multiple Poisson regression model, both remained statistically significant, with an incidence rate ratio of 1.087 for median age and 1.017 for stage IV disease. Disease stage was a strong predictor, with the risk estimated to increase from 2.8% (95% confidence interval 2.02-3.66) for stage III to 16.1% (95% confidence interval 6.18-25.93) for stage IV, for a cohort with a median age of 65 years. Metaregression demonstrated that increased age and advanced clinical stage were independently associated with an increased risk of mortality, and the combined effects of both factors greatly increased the risk.

Guidelines and Procedures for Computing Time-Series Suspended-Sediment Concentrations and Loads from In-Stream Turbidity-Sensor and Streamflow Data

USGS Publications Warehouse

Rasmussen, Patrick P.; Gray, John R.; Glysson, G. Douglas; Ziegler, Andrew C.

2009-01-01

In-stream continuous turbidity and streamflow data, calibrated with measured suspended-sediment concentration data, can be used to compute a time series of suspended-sediment concentration and load at a stream site. Development of a simple linear (ordinary least squares) regression model for computing suspended-sediment concentrations from instantaneous turbidity data is the first step in the computation process. If the model standard percentage error (MSPE) of the simple linear regression model meets a minimum criterion, this model should be used to compute a time series of suspended-sediment concentrations. Otherwise, a multiple linear regression model using paired instantaneous turbidity and streamflow data is developed and compared to the simple regression model. If the inclusion of the streamflow variable proves to be statistically significant and the uncertainty associated with the multiple regression model results in an improvement over that for the simple linear model, the turbidity-streamflow multiple linear regression model should be used to compute a suspended-sediment concentration time series. The computed concentration time series is subsequently used with its paired streamflow time series to compute suspended-sediment loads by standard U.S. Geological Survey techniques. Once an acceptable regression model is developed, it can be used to compute suspended-sediment concentration beyond the period of record used in model development with proper ongoing collection and analysis of calibration samples. Regression models to compute suspended-sediment concentrations are generally site specific and should never be considered static, but they represent a set period in a continually dynamic system in which additional data will help verify any change in sediment load, type, and source.

Valid Statistical Analysis for Logistic Regression with Multiple Sources

NASA Astrophysics Data System (ADS)

Fienberg, Stephen E.; Nardi, Yuval; Slavković, Aleksandra B.

Considerable effort has gone into understanding issues of privacy protection of individual information in single databases, and various solutions have been proposed depending on the nature of the data, the ways in which the database will be used and the precise nature of the privacy protection being offered. Once data are merged across sources, however, the nature of the problem becomes far more complex and a number of privacy issues arise for the linked individual files that go well beyond those that are considered with regard to the data within individual sources. In the paper, we propose an approach that gives full statistical analysis on the combined database without actually combining it. We focus mainly on logistic regression, but the method and tools described may be applied essentially to other statistical models as well.

Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology

NASA Astrophysics Data System (ADS)

Kang, Pilsang; Koo, Changhoi; Roh, Hokyu

2017-11-01

Since simple linear regression theory was established at the beginning of the 1900s, it has been used in a variety of fields. Unfortunately, it cannot be used directly for calibration. In practical calibrations, the observed measurements (the inputs) are subject to errors, and hence they vary, thus violating the assumption that the inputs are fixed. Therefore, in the case of calibration, the regression line fitted using the method of least squares is not consistent with the statistical properties of simple linear regression as already established based on this assumption. To resolve this problem, "classical regression" and "inverse regression" have been proposed. However, they do not completely resolve the problem. As a fundamental solution, we introduce "reversed inverse regression" along with a new methodology for deriving its statistical properties. In this study, the statistical properties of this regression are derived using the "error propagation rule" and the "method of simultaneous error equations" and are compared with those of the existing regression approaches. The accuracy of the statistical properties thus derived is investigated in a simulation study. We conclude that the newly proposed regression and methodology constitute the complete regression approach for univariate linear calibrations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gissi, Andrea; Dipartimento di Farmacia – Scienze del Farmaco, Università degli Studi di Bari “Aldo Moro”, Via E. Orabona 4, 70125 Bari; Lombardo, Anna

The bioconcentration factor (BCF) is an important bioaccumulation hazard assessment metric in many regulatory contexts. Its assessment is required by the REACH regulation (Registration, Evaluation, Authorization and Restriction of Chemicals) and by CLP (Classification, Labeling and Packaging). We challenged nine well-known and widely used BCF QSAR models against 851 compounds stored in an ad-hoc created database. The goodness of the regression analysis was assessed by considering the determination coefficient (R{sup 2}) and the Root Mean Square Error (RMSE); Cooper's statistics and Matthew's Correlation Coefficient (MCC) were calculated for all the thresholds relevant for regulatory purposes (i.e. 100 L/kg for Chemicalmore » Safety Assessment; 500 L/kg for Classification and Labeling; 2000 and 5000 L/kg for Persistent, Bioaccumulative and Toxic (PBT) and very Persistent, very Bioaccumulative (vPvB) assessment) to assess the classification, with particular attention to the models' ability to control the occurrence of false negatives. As a first step, statistical analysis was performed for the predictions of the entire dataset; R{sup 2}>0.70 was obtained using CORAL, T.E.S.T. and EPISuite Arnot–Gobas models. As classifiers, ACD and log P-based equations were the best in terms of sensitivity, ranging from 0.75 to 0.94. External compound predictions were carried out for the models that had their own training sets. CORAL model returned the best performance (R{sup 2}{sub ext}=0.59), followed by the EPISuite Meylan model (R{sup 2}{sub ext}=0.58). The latter gave also the highest sensitivity on external compounds with values from 0.55 to 0.85, depending on the thresholds. Statistics were also compiled for compounds falling into the models Applicability Domain (AD), giving better performances. In this respect, VEGA CAESAR was the best model in terms of regression (R{sup 2}=0.94) and classification (average sensitivity>0.80). This model also showed the best regression (R{sup 2}=0.85) and sensitivity (average>0.70) for new compounds in the AD but not present in the training set. However, no single optimal model exists and, thus, it would be wise a case-by-case assessment. Yet, integrating the wealth of information from multiple models remains the winner approach. - Highlights: • REACH encourages the use of in silico methods in the assessment of chemicals safety. • The performances of nine BCF models were evaluated on a benchmark database of 851 chemicals. • We compared the models on the basis of both regression and classification performance. • Statistics on chemicals out of the training set and/or within the applicability domain were compiled. • The results show that QSAR models are useful as weight-of-evidence in support to other methods.« less

Remote sensing estimation of the total phosphorus concentration in a large lake using band combinations and regional multivariate statistical modeling techniques.

PubMed

Gao, Yongnian; Gao, Junfeng; Yin, Hongbin; Liu, Chuansheng; Xia, Ting; Wang, Jing; Huang, Qi

2015-03-15

Remote sensing has been widely used for ater quality monitoring, but most of these monitoring studies have only focused on a few water quality variables, such as chlorophyll-a, turbidity, and total suspended solids, which have typically been considered optically active variables. Remote sensing presents a challenge in estimating the phosphorus concentration in water. The total phosphorus (TP) in lakes has been estimated from remotely sensed observations, primarily using the simple individual band ratio or their natural logarithm and the statistical regression method based on the field TP data and the spectral reflectance. In this study, we investigated the possibility of establishing a spatial modeling scheme to estimate the TP concentration of a large lake from multi-spectral satellite imagery using band combinations and regional multivariate statistical modeling techniques, and we tested the applicability of the spatial modeling scheme. The results showed that HJ-1A CCD multi-spectral satellite imagery can be used to estimate the TP concentration in a lake. The correlation and regression analysis showed a highly significant positive relationship between the TP concentration and certain remotely sensed combination variables. The proposed modeling scheme had a higher accuracy for the TP concentration estimation in the large lake compared with the traditional individual band ratio method and the whole-lake scale regression-modeling scheme. The TP concentration values showed a clear spatial variability and were high in western Lake Chaohu and relatively low in eastern Lake Chaohu. The northernmost portion, the northeastern coastal zone and the southeastern portion of western Lake Chaohu had the highest TP concentrations, and the other regions had the lowest TP concentration values, except for the coastal zone of eastern Lake Chaohu. These results strongly suggested that the proposed modeling scheme, i.e., the band combinations and the regional multivariate statistical modeling techniques, demonstrated advantages for estimating the TP concentration in a large lake and had a strong potential for universal application for the TP concentration estimation in large lake waters worldwide. Copyright © 2014 Elsevier Ltd. All rights reserved.

Machine learning modeling of plant phenology based on coupling satellite and gridded meteorological dataset

NASA Astrophysics Data System (ADS)

Czernecki, Bartosz; Nowosad, Jakub; Jabłońska, Katarzyna

2018-04-01

Changes in the timing of plant phenological phases are important proxies in contemporary climate research. However, most of the commonly used traditional phenological observations do not give any coherent spatial information. While consistent spatial data can be obtained from airborne sensors and preprocessed gridded meteorological data, not many studies robustly benefit from these data sources. Therefore, the main aim of this study is to create and evaluate different statistical models for reconstructing, predicting, and improving quality of phenological phases monitoring with the use of satellite and meteorological products. A quality-controlled dataset of the 13 BBCH plant phenophases in Poland was collected for the period 2007-2014. For each phenophase, statistical models were built using the most commonly applied regression-based machine learning techniques, such as multiple linear regression, lasso, principal component regression, generalized boosted models, and random forest. The quality of the models was estimated using a k-fold cross-validation. The obtained results showed varying potential for coupling meteorological derived indices with remote sensing products in terms of phenological modeling; however, application of both data sources improves models' accuracy from 0.6 to 4.6 day in terms of obtained RMSE. It is shown that a robust prediction of early phenological phases is mostly related to meteorological indices, whereas for autumn phenophases, there is a stronger information signal provided by satellite-derived vegetation metrics. Choosing a specific set of predictors and applying a robust preprocessing procedures is more important for final results than the selection of a particular statistical model. The average RMSE for the best models of all phenophases is 6.3, while the individual RMSE vary seasonally from 3.5 to 10 days. Models give reliable proxy for ground observations with RMSE below 5 days for early spring and late spring phenophases. For other phenophases, RMSE are higher and rise up to 9-10 days in the case of the earliest spring phenophases.

Analysis of Sting Balance Calibration Data Using Optimized Regression Models

NASA Technical Reports Server (NTRS)

Ulbrich, N.; Bader, Jon B.

2010-01-01

Calibration data of a wind tunnel sting balance was processed using a candidate math model search algorithm that recommends an optimized regression model for the data analysis. During the calibration the normal force and the moment at the balance moment center were selected as independent calibration variables. The sting balance itself had two moment gages. Therefore, after analyzing the connection between calibration loads and gage outputs, it was decided to choose the difference and the sum of the gage outputs as the two responses that best describe the behavior of the balance. The math model search algorithm was applied to these two responses. An optimized regression model was obtained for each response. Classical strain gage balance load transformations and the equations of the deflection of a cantilever beam under load are used to show that the search algorithm s two optimized regression models are supported by a theoretical analysis of the relationship between the applied calibration loads and the measured gage outputs. The analysis of the sting balance calibration data set is a rare example of a situation when terms of a regression model of a balance can directly be derived from first principles of physics. In addition, it is interesting to note that the search algorithm recommended the correct regression model term combinations using only a set of statistical quality metrics that were applied to the experimental data during the algorithm s term selection process.

Modeling Success: Using Preenrollment Data to Identify Academically At-Risk Students

ERIC Educational Resources Information Center

Gansemer-Topf, Ann M.; Compton, Jonathan; Wohlgemuth, Darin; Forbes, Greg; Ralston, Ekaterina

2015-01-01

Improving student success and degree completion is one of the core principles of strategic enrollment management. To address this principle, institutional data were used to develop a statistical model to identify academically at-risk students. The model employs multiple linear regression techniques to predict students at risk of earning below a…

Post-Modeling Histogram Matching of Maps Produced Using Regression Trees

Treesearch

Andrew J. Lister; Tonya W. Lister

2006-01-01

Spatial predictive models often use statistical techniques that in some way rely on averaging of values. Estimates from linear modeling are known to be susceptible to truncation of variance when the independent (predictor) variables are measured with error. A straightforward post-processing technique (histogram matching) for attempting to mitigate this effect is...

Large-area forest inventory regression modeling: spatial scale considerations

Treesearch

James A. Westfall

2015-01-01

In many forest inventories, statistical models are employed to predict values for attributes that are difficult and/or time-consuming to measure. In some applications, models are applied across a large geographic area, which assumes the relationship between the response variable and predictors is ubiquitously invariable within the area. The extent to which this...

The PIT-trap-A "model-free" bootstrap procedure for inference about regression models with discrete, multivariate responses.

PubMed

Warton, David I; Thibaut, Loïc; Wang, Yi Alice

2017-01-01

Bootstrap methods are widely used in statistics, and bootstrapping of residuals can be especially useful in the regression context. However, difficulties are encountered extending residual resampling to regression settings where residuals are not identically distributed (thus not amenable to bootstrapping)-common examples including logistic or Poisson regression and generalizations to handle clustered or multivariate data, such as generalised estimating equations. We propose a bootstrap method based on probability integral transform (PIT-) residuals, which we call the PIT-trap, which assumes data come from some marginal distribution F of known parametric form. This method can be understood as a type of "model-free bootstrap", adapted to the problem of discrete and highly multivariate data. PIT-residuals have the key property that they are (asymptotically) pivotal. The PIT-trap thus inherits the key property, not afforded by any other residual resampling approach, that the marginal distribution of data can be preserved under PIT-trapping. This in turn enables the derivation of some standard bootstrap properties, including second-order correctness of pivotal PIT-trap test statistics. In multivariate data, bootstrapping rows of PIT-residuals affords the property that it preserves correlation in data without the need for it to be modelled, a key point of difference as compared to a parametric bootstrap. The proposed method is illustrated on an example involving multivariate abundance data in ecology, and demonstrated via simulation to have improved properties as compared to competing resampling methods.

The PIT-trap—A “model-free” bootstrap procedure for inference about regression models with discrete, multivariate responses

PubMed Central

Thibaut, Loïc; Wang, Yi Alice

2017-01-01

Bootstrap methods are widely used in statistics, and bootstrapping of residuals can be especially useful in the regression context. However, difficulties are encountered extending residual resampling to regression settings where residuals are not identically distributed (thus not amenable to bootstrapping)—common examples including logistic or Poisson regression and generalizations to handle clustered or multivariate data, such as generalised estimating equations. We propose a bootstrap method based on probability integral transform (PIT-) residuals, which we call the PIT-trap, which assumes data come from some marginal distribution F of known parametric form. This method can be understood as a type of “model-free bootstrap”, adapted to the problem of discrete and highly multivariate data. PIT-residuals have the key property that they are (asymptotically) pivotal. The PIT-trap thus inherits the key property, not afforded by any other residual resampling approach, that the marginal distribution of data can be preserved under PIT-trapping. This in turn enables the derivation of some standard bootstrap properties, including second-order correctness of pivotal PIT-trap test statistics. In multivariate data, bootstrapping rows of PIT-residuals affords the property that it preserves correlation in data without the need for it to be modelled, a key point of difference as compared to a parametric bootstrap. The proposed method is illustrated on an example involving multivariate abundance data in ecology, and demonstrated via simulation to have improved properties as compared to competing resampling methods. PMID:28738071

Probabilistic Forecasting of Surface Ozone with a Novel Statistical Approach

NASA Technical Reports Server (NTRS)

Balashov, Nikolay V.; Thompson, Anne M.; Young, George S.

2017-01-01

The recent change in the Environmental Protection Agency's surface ozone regulation, lowering the surface ozone daily maximum 8-h average (MDA8) exceedance threshold from 75 to 70 ppbv, poses significant challenges to U.S. air quality (AQ) forecasters responsible for ozone MDA8 forecasts. The forecasters, supplied by only a few AQ model products, end up relying heavily on self-developed tools. To help U.S. AQ forecasters, this study explores a surface ozone MDA8 forecasting tool that is based solely on statistical methods and standard meteorological variables from the numerical weather prediction (NWP) models. The model combines the self-organizing map (SOM), which is a clustering technique, with a step wise weighted quadratic regression using meteorological variables as predictors for ozone MDA8. The SOM method identifies different weather regimes, to distinguish between various modes of ozone variability, and groups them according to similarity. In this way, when a regression is developed for a specific regime, data from the other regimes are also used, with weights that are based on their similarity to this specific regime. This approach, regression in SOM (REGiS), yields a distinct model for each regime taking into account both the training cases for that regime and other similar training cases. To produce probabilistic MDA8 ozone forecasts, REGiS weighs and combines all of the developed regression models on the basis of the weather patterns predicted by an NWP model. REGiS is evaluated over the San Joaquin Valley in California and the northeastern plains of Colorado. The results suggest that the model performs best when trained and adjusted separately for an individual AQ station and its corresponding meteorological site.

A critical re-evaluation of the regression model specification in the US D1 EQ-5D value function

PubMed Central

2012-01-01

Background The EQ-5D is a generic health-related quality of life instrument (five dimensions with three levels, 243 health states), used extensively in cost-utility/cost-effectiveness analyses. EQ-5D health states are assigned values on a scale anchored in perfect health (1) and death (0). The dominant procedure for defining values for EQ-5D health states involves regression modeling. These regression models have typically included a constant term, interpreted as the utility loss associated with any movement away from perfect health. The authors of the United States EQ-5D valuation study replaced this constant with a variable, D1, which corresponds to the number of impaired dimensions beyond the first. The aim of this study was to illustrate how the use of the D1 variable in place of a constant is problematic. Methods We compared the original D1 regression model with a mathematically equivalent model with a constant term. Comparisons included implications for the magnitude and statistical significance of the coefficients, multicollinearity (variance inflation factors, or VIFs), number of calculation steps needed to determine tariff values, and consequences for tariff interpretation. Results Using the D1 variable in place of a constant shifted all dummy variable coefficients away from zero by the value of the constant, greatly increased the multicollinearity of the model (maximum VIF of 113.2 vs. 21.2), and increased the mean number of calculation steps required to determine health state values. Discussion Using the D1 variable in place of a constant constitutes an unnecessary complication of the model, obscures the fact that at least two of the main effect dummy variables are statistically nonsignificant, and complicates and biases interpretation of the tariff algorithm. PMID:22244261

A critical re-evaluation of the regression model specification in the US D1 EQ-5D value function.

PubMed

Rand-Hendriksen, Kim; Augestad, Liv A; Dahl, Fredrik A

2012-01-13

The EQ-5D is a generic health-related quality of life instrument (five dimensions with three levels, 243 health states), used extensively in cost-utility/cost-effectiveness analyses. EQ-5D health states are assigned values on a scale anchored in perfect health (1) and death (0).The dominant procedure for defining values for EQ-5D health states involves regression modeling. These regression models have typically included a constant term, interpreted as the utility loss associated with any movement away from perfect health. The authors of the United States EQ-5D valuation study replaced this constant with a variable, D1, which corresponds to the number of impaired dimensions beyond the first. The aim of this study was to illustrate how the use of the D1 variable in place of a constant is problematic. We compared the original D1 regression model with a mathematically equivalent model with a constant term. Comparisons included implications for the magnitude and statistical significance of the coefficients, multicollinearity (variance inflation factors, or VIFs), number of calculation steps needed to determine tariff values, and consequences for tariff interpretation. Using the D1 variable in place of a constant shifted all dummy variable coefficients away from zero by the value of the constant, greatly increased the multicollinearity of the model (maximum VIF of 113.2 vs. 21.2), and increased the mean number of calculation steps required to determine health state values. Using the D1 variable in place of a constant constitutes an unnecessary complication of the model, obscures the fact that at least two of the main effect dummy variables are statistically nonsignificant, and complicates and biases interpretation of the tariff algorithm.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butler, W.J.; Kalasinski, L.A.

In this paper, a generalized logistic regression model for correlated observations is used to analyze epidemiologic data on the frequency of spontaneous abortion among a group of women office workers. The results are compared to those obtained from the use of the standard logistic regression model that assumes statistical independence among all the pregnancies contributed by one woman. In this example, the correlation among pregnancies from the same woman is fairly small and did not have a substantial impact on the magnitude of estimates of parameters of the model. This is due at least partly to the small average numbermore » of pregnancies contributed by each woman.« less

Multicollinearity and Regression Analysis

NASA Astrophysics Data System (ADS)

Daoud, Jamal I.

2017-12-01

In regression analysis it is obvious to have a correlation between the response and predictor(s), but having correlation among predictors is something undesired. The number of predictors included in the regression model depends on many factors among which, historical data, experience, etc. At the end selection of most important predictors is something objective due to the researcher. Multicollinearity is a phenomena when two or more predictors are correlated, if this happens, the standard error of the coefficients will increase [8]. Increased standard errors means that the coefficients for some or all independent variables may be found to be significantly different from In other words, by overinflating the standard errors, multicollinearity makes some variables statistically insignificant when they should be significant. In this paper we focus on the multicollinearity, reasons and consequences on the reliability of the regression model.

Statistical Learning Theory for High Dimensional Prediction: Application to Criterion-Keyed Scale Development

PubMed Central

Chapman, Benjamin P.; Weiss, Alexander; Duberstein, Paul

2016-01-01

Statistical learning theory (SLT) is the statistical formulation of machine learning theory, a body of analytic methods common in “big data” problems. Regression-based SLT algorithms seek to maximize predictive accuracy for some outcome, given a large pool of potential predictors, without overfitting the sample. Research goals in psychology may sometimes call for high dimensional regression. One example is criterion-keyed scale construction, where a scale with maximal predictive validity must be built from a large item pool. Using this as a working example, we first introduce a core principle of SLT methods: minimization of expected prediction error (EPE). Minimizing EPE is fundamentally different than maximizing the within-sample likelihood, and hinges on building a predictive model of sufficient complexity to predict the outcome well, without undue complexity leading to overfitting. We describe how such models are built and refined via cross-validation. We then illustrate how three common SLT algorithms–Supervised Principal Components, Regularization, and Boosting—can be used to construct a criterion-keyed scale predicting all-cause mortality, using a large personality item pool within a population cohort. Each algorithm illustrates a different approach to minimizing EPE. Finally, we consider broader applications of SLT predictive algorithms, both as supportive analytic tools for conventional methods, and as primary analytic tools in discovery phase research. We conclude that despite their differences from the classic null-hypothesis testing approach—or perhaps because of them–SLT methods may hold value as a statistically rigorous approach to exploratory regression. PMID:27454257

Spatial analysis of relative humidity during ungauged periods in a mountainous region

NASA Astrophysics Data System (ADS)

Um, Myoung-Jin; Kim, Yeonjoo

2017-08-01

Although atmospheric humidity influences environmental and agricultural conditions, thereby influencing plant growth, human health, and air pollution, efforts to develop spatial maps of atmospheric humidity using statistical approaches have thus far been limited. This study therefore aims to develop statistical approaches for inferring the spatial distribution of relative humidity (RH) for a mountainous island, for which data are not uniformly available across the region. A multiple regression analysis based on various mathematical models was used to identify the optimal model for estimating monthly RH by incorporating not only temperature but also location and elevation. Based on the regression analysis, we extended the monthly RH data from weather stations to cover the ungauged periods when no RH observations were available. Then, two different types of station-based data, the observational data and the data extended via the regression model, were used to form grid-based data with a resolution of 100 m. The grid-based data that used the extended station-based data captured the increasing RH trend along an elevation gradient. Furthermore, annual RH values averaged over the regions were examined. Decreasing temporal trends were found in most cases, with magnitudes varying based on the season and region.

Estimation Methods for Non-Homogeneous Regression - Minimum CRPS vs Maximum Likelihood

NASA Astrophysics Data System (ADS)

Gebetsberger, Manuel; Messner, Jakob W.; Mayr, Georg J.; Zeileis, Achim

2017-04-01

Non-homogeneous regression models are widely used to statistically post-process numerical weather prediction models. Such regression models correct for errors in mean and variance and are capable to forecast a full probability distribution. In order to estimate the corresponding regression coefficients, CRPS minimization is performed in many meteorological post-processing studies since the last decade. In contrast to maximum likelihood estimation, CRPS minimization is claimed to yield more calibrated forecasts. Theoretically, both scoring rules used as an optimization score should be able to locate a similar and unknown optimum. Discrepancies might result from a wrong distributional assumption of the observed quantity. To address this theoretical concept, this study compares maximum likelihood and minimum CRPS estimation for different distributional assumptions. First, a synthetic case study shows that, for an appropriate distributional assumption, both estimation methods yield to similar regression coefficients. The log-likelihood estimator is slightly more efficient. A real world case study for surface temperature forecasts at different sites in Europe confirms these results but shows that surface temperature does not always follow the classical assumption of a Gaussian distribution. KEYWORDS: ensemble post-processing, maximum likelihood estimation, CRPS minimization, probabilistic temperature forecasting, distributional regression models

Censored quantile regression with recursive partitioning-based weights

PubMed Central

Wey, Andrew; Wang, Lan; Rudser, Kyle

2014-01-01

Censored quantile regression provides a useful alternative to the Cox proportional hazards model for analyzing survival data. It directly models the conditional quantile of the survival time and hence is easy to interpret. Moreover, it relaxes the proportionality constraint on the hazard function associated with the popular Cox model and is natural for modeling heterogeneity of the data. Recently, Wang and Wang (2009. Locally weighted censored quantile regression. Journal of the American Statistical Association 103, 1117–1128) proposed a locally weighted censored quantile regression approach that allows for covariate-dependent censoring and is less restrictive than other censored quantile regression methods. However, their kernel smoothing-based weighting scheme requires all covariates to be continuous and encounters practical difficulty with even a moderate number of covariates. We propose a new weighting approach that uses recursive partitioning, e.g. survival trees, that offers greater flexibility in handling covariate-dependent censoring in moderately high dimensions and can incorporate both continuous and discrete covariates. We prove that this new weighting scheme leads to consistent estimation of the quantile regression coefficients and demonstrate its effectiveness via Monte Carlo simulations. We also illustrate the new method using a widely recognized data set from a clinical trial on primary biliary cirrhosis. PMID:23975800

Effect of folic acid on appetite in children: ordinal logistic and fuzzy logistic regressions.

PubMed

Namdari, Mahshid; Abadi, Alireza; Taheri, S Mahmoud; Rezaei, Mansour; Kalantari, Naser; Omidvar, Nasrin

2014-03-01

Reduced appetite and low food intake are often a concern in preschool children, since it can lead to malnutrition, a leading cause of impaired growth and mortality in childhood. It is occasionally considered that folic acid has a positive effect on appetite enhancement and consequently growth in children. The aim of this study was to assess the effect of folic acid on the appetite of preschool children 3 to 6 y old. The study sample included 127 children ages 3 to 6 who were randomly selected from 20 preschools in the city of Tehran in 2011. Since appetite was measured by linguistic terms, a fuzzy logistic regression was applied for modeling. The obtained results were compared with a statistical ordinal logistic model. After controlling for the potential confounders, in a statistical ordinal logistic model, serum folate showed a significantly positive effect on appetite. A small but positive effect of folate was detected by fuzzy logistic regression. Based on fuzzy regression, the risk for poor appetite in preschool children was related to the employment status of their mothers. In this study, a positive association was detected between the levels of serum folate and improved appetite. For further investigation, a randomized controlled, double-blind clinical trial could be helpful to address causality. Copyright © 2014 Elsevier Inc. All rights reserved.

Waste generated in high-rise buildings construction: a quantification model based on statistical multiple regression.

PubMed

Parisi Kern, Andrea; Ferreira Dias, Michele; Piva Kulakowski, Marlova; Paulo Gomes, Luciana

2015-05-01

Reducing construction waste is becoming a key environmental issue in the construction industry. The quantification of waste generation rates in the construction sector is an invaluable management tool in supporting mitigation actions. However, the quantification of waste can be a difficult process because of the specific characteristics and the wide range of materials used in different construction projects. Large variations are observed in the methods used to predict the amount of waste generated because of the range of variables involved in construction processes and the different contexts in which these methods are employed. This paper proposes a statistical model to determine the amount of waste generated in the construction of high-rise buildings by assessing the influence of design process and production system, often mentioned as the major culprits behind the generation of waste in construction. Multiple regression was used to conduct a case study based on multiple sources of data of eighteen residential buildings. The resulting statistical model produced dependent (i.e. amount of waste generated) and independent variables associated with the design and the production system used. The best regression model obtained from the sample data resulted in an adjusted R(2) value of 0.694, which means that it predicts approximately 69% of the factors involved in the generation of waste in similar constructions. Most independent variables showed a low determination coefficient when assessed in isolation, which emphasizes the importance of assessing their joint influence on the response (dependent) variable. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analyzing Seasonal Variations in Suicide With Fourier Poisson Time-Series Regression: A Registry-Based Study From Norway, 1969-2007.

PubMed

Bramness, Jørgen G; Walby, Fredrik A; Morken, Gunnar; Røislien, Jo

2015-08-01

Seasonal variation in the number of suicides has long been acknowledged. It has been suggested that this seasonality has declined in recent years, but studies have generally used statistical methods incapable of confirming this. We examined all suicides occurring in Norway during 1969-2007 (more than 20,000 suicides in total) to establish whether seasonality decreased over time. Fitting of additive Fourier Poisson time-series regression models allowed for formal testing of a possible linear decrease in seasonality, or a reduction at a specific point in time, while adjusting for a possible smooth nonlinear long-term change without having to categorize time into discrete yearly units. The models were compared using Akaike's Information Criterion and analysis of variance. A model with a seasonal pattern was significantly superior to a model without one. There was a reduction in seasonality during the period. Both the model assuming a linear decrease in seasonality and the model assuming a change at a specific point in time were both superior to a model assuming constant seasonality, thus confirming by formal statistical testing that the magnitude of the seasonality in suicides has diminished. The additive Fourier Poisson time-series regression model would also be useful for studying other temporal phenomena with seasonal components. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Periodicity analysis of tourist arrivals to Banda Aceh using smoothing SARIMA approach

NASA Astrophysics Data System (ADS)

Miftahuddin, Helida, Desri; Sofyan, Hizir

2017-11-01

Forecasting the number of tourist arrivals who enters a region is needed for tourism businesses, economic and industrial policies, so that the statistical modeling needs to be conducted. Banda Aceh is the capital of Aceh province more economic activity is driven by the services sector, one of which is the tourism sector. Therefore, the prediction of the number of tourist arrivals is needed to develop further policies. The identification results indicate that the data arrival of foreign tourists to Banda Aceh to contain the trend and seasonal nature. Allegedly, the number of arrivals is influenced by external factors, such as economics, politics, and the holiday season caused the structural break in the data. Trend patterns are detected by using polynomial regression with quadratic and cubic approaches, while seasonal is detected by a periodic regression polynomial with quadratic and cubic approach. To model the data that has seasonal effects, one of the statistical methods that can be used is SARIMA (Seasonal Autoregressive Integrated Moving Average). The results showed that the smoothing, a method to detect the trend pattern is cubic polynomial regression approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 70.52. While the method for detecting the seasonal pattern is a periodic regression polynomial cubic approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 73.37. Furthermore, the best model to predict the number of foreign tourist arrivals to Banda Aceh in 2017 to 2018 is SARIMA (0,1,1)(1,1,0) with MAPE is 26%.

New machine learning tools for predictive vegetation mapping after climate change: Bagging and Random Forest perform better than Regression Tree Analysis

Treesearch

L.R. Iverson; A.M. Prasad; A. Liaw

2004-01-01

More and better machine learning tools are becoming available for landscape ecologists to aid in understanding species-environment relationships and to map probable species occurrence now and potentially into the future. To thal end, we evaluated three statistical models: Regression Tree Analybib (RTA), Bagging Trees (BT) and Random Forest (RF) for their utility in...

Understanding poisson regression.

PubMed

Hayat, Matthew J; Higgins, Melinda

2014-04-01

Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes. Copyright 2014, SLACK Incorporated.

DEVELOPMENT OF RESIDENTIAL WOOD COMSUMPTION ESTIMATION MODELS

EPA Science Inventory

The report gives data on the distribution and usage of firewood, obtained from a pool of household wood use surveys. ased on a series of regression models developed using the STEPWISE procedure in the SAS statistical package, two variables appear to be most predictive of wood use...

Survival Regression Modeling Strategies in CVD Prediction.

PubMed

Barkhordari, Mahnaz; Padyab, Mojgan; Sardarinia, Mahsa; Hadaegh, Farzad; Azizi, Fereidoun; Bozorgmanesh, Mohammadreza

2016-04-01

A fundamental part of prevention is prediction. Potential predictors are the sine qua non of prediction models. However, whether incorporating novel predictors to prediction models could be directly translated to added predictive value remains an area of dispute. The difference between the predictive power of a predictive model with (enhanced model) and without (baseline model) a certain predictor is generally regarded as an indicator of the predictive value added by that predictor. Indices such as discrimination and calibration have long been used in this regard. Recently, the use of added predictive value has been suggested while comparing the predictive performances of the predictive models with and without novel biomarkers. User-friendly statistical software capable of implementing novel statistical procedures is conspicuously lacking. This shortcoming has restricted implementation of such novel model assessment methods. We aimed to construct Stata commands to help researchers obtain the aforementioned statistical indices. We have written Stata commands that are intended to help researchers obtain the following. 1, Nam-D'Agostino X 2 goodness of fit test; 2, Cut point-free and cut point-based net reclassification improvement index (NRI), relative absolute integrated discriminatory improvement index (IDI), and survival-based regression analyses. We applied the commands to real data on women participating in the Tehran lipid and glucose study (TLGS) to examine if information relating to a family history of premature cardiovascular disease (CVD), waist circumference, and fasting plasma glucose can improve predictive performance of Framingham's general CVD risk algorithm. The command is adpredsurv for survival models. Herein we have described the Stata package "adpredsurv" for calculation of the Nam-D'Agostino X 2 goodness of fit test as well as cut point-free and cut point-based NRI, relative and absolute IDI, and survival-based regression analyses. We hope this work encourages the use of novel methods in examining predictive capacity of the emerging plethora of novel biomarkers.

Genomic-Enabled Prediction of Ordinal Data with Bayesian Logistic Ordinal Regression.

PubMed

Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Burgueño, Juan; Eskridge, Kent

2015-08-18

Most genomic-enabled prediction models developed so far assume that the response variable is continuous and normally distributed. The exception is the probit model, developed for ordered categorical phenotypes. In statistical applications, because of the easy implementation of the Bayesian probit ordinal regression (BPOR) model, Bayesian logistic ordinal regression (BLOR) is implemented rarely in the context of genomic-enabled prediction [sample size (n) is much smaller than the number of parameters (p)]. For this reason, in this paper we propose a BLOR model using the Pólya-Gamma data augmentation approach that produces a Gibbs sampler with similar full conditional distributions of the BPOR model and with the advantage that the BPOR model is a particular case of the BLOR model. We evaluated the proposed model by using simulation and two real data sets. Results indicate that our BLOR model is a good alternative for analyzing ordinal data in the context of genomic-enabled prediction with the probit or logit link. Copyright © 2015 Montesinos-López et al.

Using Bayesian regression to test hypotheses about relationships between parameters and covariates in cognitive models.

PubMed

Boehm, Udo; Steingroever, Helen; Wagenmakers, Eric-Jan

2018-06-01

An important tool in the advancement of cognitive science are quantitative models that represent different cognitive variables in terms of model parameters. To evaluate such models, their parameters are typically tested for relationships with behavioral and physiological variables that are thought to reflect specific cognitive processes. However, many models do not come equipped with the statistical framework needed to relate model parameters to covariates. Instead, researchers often revert to classifying participants into groups depending on their values on the covariates, and subsequently comparing the estimated model parameters between these groups. Here we develop a comprehensive solution to the covariate problem in the form of a Bayesian regression framework. Our framework can be easily added to existing cognitive models and allows researchers to quantify the evidential support for relationships between covariates and model parameters using Bayes factors. Moreover, we present a simulation study that demonstrates the superiority of the Bayesian regression framework to the conventional classification-based approach.

The statistical analysis of multi-environment data: modeling genotype-by-environment interaction and its genetic basis

PubMed Central

Malosetti, Marcos; Ribaut, Jean-Marcel; van Eeuwijk, Fred A.

2013-01-01

Genotype-by-environment interaction (GEI) is an important phenomenon in plant breeding. This paper presents a series of models for describing, exploring, understanding, and predicting GEI. All models depart from a two-way table of genotype by environment means. First, a series of descriptive and explorative models/approaches are presented: Finlay–Wilkinson model, AMMI model, GGE biplot. All of these approaches have in common that they merely try to group genotypes and environments and do not use other information than the two-way table of means. Next, factorial regression is introduced as an approach to explicitly introduce genotypic and environmental covariates for describing and explaining GEI. Finally, QTL modeling is presented as a natural extension of factorial regression, where marker information is translated into genetic predictors. Tests for regression coefficients corresponding to these genetic predictors are tests for main effect QTL expression and QTL by environment interaction (QEI). QTL models for which QEI depends on environmental covariables form an interesting model class for predicting GEI for new genotypes and new environments. For realistic modeling of genotypic differences across multiple environments, sophisticated mixed models are necessary to allow for heterogeneity of genetic variances and correlations across environments. The use and interpretation of all models is illustrated by an example data set from the CIMMYT maize breeding program, containing environments differing in drought and nitrogen stress. To help readers to carry out the statistical analyses, GenStat® programs, 15th Edition and Discovery® version, are presented as “Appendix.” PMID:23487515

Statistical experiments using the multiple regression research for prediction of proper hardness in areas of phosphorus cast-iron brake shoes manufacturing

NASA Astrophysics Data System (ADS)

Kiss, I.; Cioată, V. G.; Ratiu, S. A.; Rackov, M.; Penčić, M.

2018-01-01

Multivariate research is important in areas of cast-iron brake shoes manufacturing, because many variables interact with each other simultaneously. This article focuses on expressing the multiple linear regression model related to the hardness assurance by the chemical composition of the phosphorous cast irons destined to the brake shoes, having in view that the regression coefficients will illustrate the unrelated contributions of each independent variable towards predicting the dependent variable. In order to settle the multiple correlations between the hardness of the cast-iron brake shoes, and their chemical compositions several regression equations has been proposed. Is searched a mathematical solution which can determine the optimum chemical composition for the hardness desirable values. Starting from the above-mentioned affirmations two new statistical experiments are effectuated related to the values of Phosphorus [P], Manganese [Mn] and Silicon [Si]. Therefore, the regression equations, which describe the mathematical dependency between the above-mentioned elements and the hardness, are determined. As result, several correlation charts will be revealed.

Genome-wide regression and prediction with the BGLR statistical package.

PubMed

Pérez, Paulino; de los Campos, Gustavo

2014-10-01

Many modern genomic data analyses require implementing regressions where the number of parameters (p, e.g., the number of marker effects) exceeds sample size (n). Implementing these large-p-with-small-n regressions poses several statistical and computational challenges, some of which can be confronted using Bayesian methods. This approach allows integrating various parametric and nonparametric shrinkage and variable selection procedures in a unified and consistent manner. The BGLR R-package implements a large collection of Bayesian regression models, including parametric variable selection and shrinkage methods and semiparametric procedures (Bayesian reproducing kernel Hilbert spaces regressions, RKHS). The software was originally developed for genomic applications; however, the methods implemented are useful for many nongenomic applications as well. The response can be continuous (censored or not) or categorical (either binary or ordinal). The algorithm is based on a Gibbs sampler with scalar updates and the implementation takes advantage of efficient compiled C and Fortran routines. In this article we describe the methods implemented in BGLR, present examples of the use of the package, and discuss practical issues emerging in real-data analysis. Copyright © 2014 by the Genetics Society of America.

Synthesis of linear regression coefficients by recovering the within-study covariance matrix from summary statistics.

PubMed

Yoneoka, Daisuke; Henmi, Masayuki

2017-06-01

Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data.

PubMed

Spelman, Tim; Gray, Orla; Lucas, Robyn; Butzkueven, Helmut

2015-12-09

This report describes a novel Stata-based application of trigonometric regression modelling to 55 years of multiple sclerosis relapse data from 46 clinical centers across 20 countries located in both hemispheres. Central to the success of this method was the strategic use of plot analysis to guide and corroborate the statistical regression modelling. Initial plot analysis was necessary for establishing realistic hypotheses regarding the presence and structural form of seasonal and latitudinal influences on relapse probability and then testing the performance of the resultant models. Trigonometric regression was then necessary to quantify these relationships, adjust for important confounders and provide a measure of certainty as to how plausible these associations were. Synchronization of graphing techniques with regression modelling permitted a systematic refinement of models until best-fit convergence was achieved, enabling novel inferences to be made regarding the independent influence of both season and latitude in predicting relapse onset timing in MS. These methods have the potential for application across other complex disease and epidemiological phenomena suspected or known to vary systematically with season and/or geographic location.

A Regression Framework for Effect Size Assessments in Longitudinal Modeling of Group Differences

PubMed Central

Feingold, Alan

2013-01-01

The use of growth modeling analysis (GMA)--particularly multilevel analysis and latent growth modeling--to test the significance of intervention effects has increased exponentially in prevention science, clinical psychology, and psychiatry over the past 15 years. Model-based effect sizes for differences in means between two independent groups in GMA can be expressed in the same metric (Cohen’s d) commonly used in classical analysis and meta-analysis. This article first reviews conceptual issues regarding calculation of d for findings from GMA and then introduces an integrative framework for effect size assessments that subsumes GMA. The new approach uses the structure of the linear regression model, from which effect sizes for findings from diverse cross-sectional and longitudinal analyses can be calculated with familiar statistics, such as the regression coefficient, the standard deviation of the dependent measure, and study duration. PMID:23956615

Estimates of Flow Duration, Mean Flow, and Peak-Discharge Frequency Values for Kansas Stream Locations

USGS Publications Warehouse

Perry, Charles A.; Wolock, David M.; Artman, Joshua C.

2004-01-01

Streamflow statistics of flow duration and peak-discharge frequency were estimated for 4,771 individual locations on streams listed on the 1999 Kansas Surface Water Register. These statistics included the flow-duration values of 90, 75, 50, 25, and 10 percent, as well as the mean flow value. Peak-discharge frequency values were estimated for the 2-, 5-, 10-, 25-, 50-, and 100-year floods. Least-squares multiple regression techniques were used, along with Tobit analyses, to develop equations for estimating flow-duration values of 90, 75, 50, 25, and 10 percent and the mean flow for uncontrolled flow stream locations. The contributing-drainage areas of 149 U.S. Geological Survey streamflow-gaging stations in Kansas and parts of surrounding States that had flow uncontrolled by Federal reservoirs and used in the regression analyses ranged from 2.06 to 12,004 square miles. Logarithmic transformations of climatic and basin data were performed to yield the best linear relation for developing equations to compute flow durations and mean flow. In the regression analyses, the significant climatic and basin characteristics, in order of importance, were contributing-drainage area, mean annual precipitation, mean basin permeability, and mean basin slope. The analyses yielded a model standard error of prediction range of 0.43 logarithmic units for the 90-percent duration analysis to 0.15 logarithmic units for the 10-percent duration analysis. The model standard error of prediction was 0.14 logarithmic units for the mean flow. Regression equations used to estimate peak-discharge frequency values were obtained from a previous report, and estimates for the 2-, 5-, 10-, 25-, 50-, and 100-year floods were determined for this report. The regression equations and an interpolation procedure were used to compute flow durations, mean flow, and estimates of peak-discharge frequency for locations along uncontrolled flow streams on the 1999 Kansas Surface Water Register. Flow durations, mean flow, and peak-discharge frequency values determined at available gaging stations were used to interpolate the regression-estimated flows for the stream locations where available. Streamflow statistics for locations that had uncontrolled flow were interpolated using data from gaging stations weighted according to the drainage area and the bias between the regression-estimated and gaged flow information. On controlled reaches of Kansas streams, the streamflow statistics were interpolated between gaging stations using only gaged data weighted by drainage area.

Weather variability and the incidence of cryptosporidiosis: comparison of time series poisson regression and SARIMA models.

PubMed

Hu, Wenbiao; Tong, Shilu; Mengersen, Kerrie; Connell, Des

2007-09-01

Few studies have examined the relationship between weather variables and cryptosporidiosis in Australia. This paper examines the potential impact of weather variability on the transmission of cryptosporidiosis and explores the possibility of developing an empirical forecast system. Data on weather variables, notified cryptosporidiosis cases, and population size in Brisbane were supplied by the Australian Bureau of Meteorology, Queensland Department of Health, and Australian Bureau of Statistics for the period of January 1, 1996-December 31, 2004, respectively. Time series Poisson regression and seasonal auto-regression integrated moving average (SARIMA) models were performed to examine the potential impact of weather variability on the transmission of cryptosporidiosis. Both the time series Poisson regression and SARIMA models show that seasonal and monthly maximum temperature at a prior moving average of 1 and 3 months were significantly associated with cryptosporidiosis disease. It suggests that there may be 50 more cases a year for an increase of 1 degrees C maximum temperature on average in Brisbane. Model assessments indicated that the SARIMA model had better predictive ability than the Poisson regression model (SARIMA: root mean square error (RMSE): 0.40, Akaike information criterion (AIC): -12.53; Poisson regression: RMSE: 0.54, AIC: -2.84). Furthermore, the analysis of residuals shows that the time series Poisson regression appeared to violate a modeling assumption, in that residual autocorrelation persisted. The results of this study suggest that weather variability (particularly maximum temperature) may have played a significant role in the transmission of cryptosporidiosis. A SARIMA model may be a better predictive model than a Poisson regression model in the assessment of the relationship between weather variability and the incidence of cryptosporidiosis.

Use of genetic programming, logistic regression, and artificial neural nets to predict readmission after coronary artery bypass surgery.

PubMed

Engoren, Milo; Habib, Robert H; Dooner, John J; Schwann, Thomas A

2013-08-01

As many as 14 % of patients undergoing coronary artery bypass surgery are readmitted within 30 days. Readmission is usually the result of morbidity and may lead to death. The purpose of this study is to develop and compare statistical and genetic programming models to predict readmission. Patients were divided into separate Construction and Validation populations. Using 88 variables, logistic regression, genetic programs, and artificial neural nets were used to develop predictive models. Models were first constructed and tested on the Construction populations, then validated on the Validation population. Areas under the receiver operator characteristic curves (AU ROC) were used to compare the models. Two hundred and two patients (7.6 %) in the 2,644 patient Construction group and 216 (8.0 %) of the 2,711 patient Validation group were re-admitted within 30 days of CABG surgery. Logistic regression predicted readmission with AU ROC = .675 ± .021 in the Construction group. Genetic programs significantly improved the accuracy, AU ROC = .767 ± .001, p < .001). Artificial neural nets were less accurate with AU ROC = 0.597 ± .001 in the Construction group. Predictive accuracy of all three techniques fell in the Validation group. However, the accuracy of genetic programming (AU ROC = .654 ± .001) was still trivially but statistically non-significantly better than that of the logistic regression (AU ROC = .644 ± .020, p = .61). Genetic programming and logistic regression provide alternative methods to predict readmission that are similarly accurate.

An Analysis of San Diego's Housing Market Using a Geographically Weighted Regression Approach

NASA Astrophysics Data System (ADS)

Grant, Christina P.

San Diego County real estate transaction data was evaluated with a set of linear models calibrated by ordinary least squares and geographically weighted regression (GWR). The goal of the analysis was to determine whether the spatial effects assumed to be in the data are best studied globally with no spatial terms, globally with a fixed effects submarket variable, or locally with GWR. 18,050 single-family residential sales which closed in the six months between April 2014 and September 2014 were used in the analysis. Diagnostic statistics including AICc, R2, Global Moran's I, and visual inspection of diagnostic plots and maps indicate superior model performance by GWR as compared to both global regressions.

Using Gamma and Quantile Regressions to Explore the Association between Job Strain and Adiposity in the ELSA-Brasil Study: Does Gender Matter?

PubMed

Fonseca, Maria de Jesus Mendes da; Juvanhol, Leidjaira Lopes; Rotenberg, Lúcia; Nobre, Aline Araújo; Griep, Rosane Härter; Alves, Márcia Guimarães de Mello; Cardoso, Letícia de Oliveira; Giatti, Luana; Nunes, Maria Angélica; Aquino, Estela M L; Chor, Dóra

2017-11-17

This paper explores the association between job strain and adiposity, using two statistical analysis approaches and considering the role of gender. The research evaluated 11,960 active baseline participants (2008-2010) in the ELSA-Brasil study. Job strain was evaluated through a demand-control questionnaire, while body mass index (BMI) and waist circumference (WC) were evaluated in continuous form. The associations were estimated using gamma regression models with an identity link function. Quantile regression models were also estimated from the final set of co-variables established by gamma regression. The relationship that was found varied by analytical approach and gender. Among the women, no association was observed between job strain and adiposity in the fitted gamma models. In the quantile models, a pattern of increasing effects of high strain was observed at higher BMI and WC distribution quantiles. Among the men, high strain was associated with adiposity in the gamma regression models. However, when quantile regression was used, that association was found not to be homogeneous across outcome distributions. In addition, in the quantile models an association was observed between active jobs and BMI. Our results point to an association between job strain and adiposity, which follows a heterogeneous pattern. Modelling strategies can produce different results and should, accordingly, be used to complement one another.

Validation of statistical predictive models meant to select melanoma patients for sentinel lymph node biopsy.

PubMed

Sabel, Michael S; Rice, John D; Griffith, Kent A; Lowe, Lori; Wong, Sandra L; Chang, Alfred E; Johnson, Timothy M; Taylor, Jeremy M G

2012-01-01

To identify melanoma patients at sufficiently low risk of nodal metastases who could avoid sentinel lymph node biopsy (SLNB), several statistical models have been proposed based upon patient/tumor characteristics, including logistic regression, classification trees, random forests, and support vector machines. We sought to validate recently published models meant to predict sentinel node status. We queried our comprehensive, prospectively collected melanoma database for consecutive melanoma patients undergoing SLNB. Prediction values were estimated based upon four published models, calculating the same reported metrics: negative predictive value (NPV), rate of negative predictions (RNP), and false-negative rate (FNR). Logistic regression performed comparably with our data when considering NPV (89.4 versus 93.6%); however, the model's specificity was not high enough to significantly reduce the rate of biopsies (SLN reduction rate of 2.9%). When applied to our data, the classification tree produced NPV and reduction in biopsy rates that were lower (87.7 versus 94.1 and 29.8 versus 14.3, respectively). Two published models could not be applied to our data due to model complexity and the use of proprietary software. Published models meant to reduce the SLNB rate among patients with melanoma either underperformed when applied to our larger dataset, or could not be validated. Differences in selection criteria and histopathologic interpretation likely resulted in underperformance. Statistical predictive models must be developed in a clinically applicable manner to allow for both validation and ultimately clinical utility.

Inferring general relations between network characteristics from specific network ensembles.

PubMed

Cardanobile, Stefano; Pernice, Volker; Deger, Moritz; Rotter, Stefan

2012-01-01

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their ability to generate networks with large structural variability. In particular, we consider the statistical constraints which the respective construction scheme imposes on the generated networks. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This makes it possible to infer global features from local ones using regression models trained on networks with high generalization power. Our results confirm and extend previous findings regarding the synchronization properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks in good approximation. Finally, we demonstrate on three different data sets (C. elegans neuronal network, R. prowazekii metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models.

Epidemiologic programs for computers and calculators. A microcomputer program for multiple logistic regression by unconditional and conditional maximum likelihood methods.

PubMed

Campos-Filho, N; Franco, E L

1989-02-01

A frequent procedure in matched case-control studies is to report results from the multivariate unmatched analyses if they do not differ substantially from the ones obtained after conditioning on the matching variables. Although conceptually simple, this rule requires that an extensive series of logistic regression models be evaluated by both the conditional and unconditional maximum likelihood methods. Most computer programs for logistic regression employ only one maximum likelihood method, which requires that the analyses be performed in separate steps. This paper describes a Pascal microcomputer (IBM PC) program that performs multiple logistic regression by both maximum likelihood estimation methods, which obviates the need for switching between programs to obtain relative risk estimates from both matched and unmatched analyses. The program calculates most standard statistics and allows factoring of categorical or continuous variables by two distinct methods of contrast. A built-in, descriptive statistics option allows the user to inspect the distribution of cases and controls across categories of any given variable.

Censored Hurdle Negative Binomial Regression (Case Study: Neonatorum Tetanus Case in Indonesia)

NASA Astrophysics Data System (ADS)

Yuli Rusdiana, Riza; Zain, Ismaini; Wulan Purnami, Santi

2017-06-01

Hurdle negative binomial model regression is a method that can be used for discreate dependent variable, excess zero and under- and overdispersion. It uses two parts approach. The first part estimates zero elements from dependent variable is zero hurdle model and the second part estimates not zero elements (non-negative integer) from dependent variable is called truncated negative binomial models. The discrete dependent variable in such cases is censored for some values. The type of censor that will be studied in this research is right censored. This study aims to obtain the parameter estimator hurdle negative binomial regression for right censored dependent variable. In the assessment of parameter estimation methods used Maximum Likelihood Estimator (MLE). Hurdle negative binomial model regression for right censored dependent variable is applied on the number of neonatorum tetanus cases in Indonesia. The type data is count data which contains zero values in some observations and other variety value. This study also aims to obtain the parameter estimator and test statistic censored hurdle negative binomial model. Based on the regression results, the factors that influence neonatorum tetanus case in Indonesia is the percentage of baby health care coverage and neonatal visits.

Robust regression for large-scale neuroimaging studies.

PubMed

Fritsch, Virgile; Da Mota, Benoit; Loth, Eva; Varoquaux, Gaël; Banaschewski, Tobias; Barker, Gareth J; Bokde, Arun L W; Brühl, Rüdiger; Butzek, Brigitte; Conrod, Patricia; Flor, Herta; Garavan, Hugh; Lemaitre, Hervé; Mann, Karl; Nees, Frauke; Paus, Tomas; Schad, Daniel J; Schümann, Gunter; Frouin, Vincent; Poline, Jean-Baptiste; Thirion, Bertrand

2015-05-01

Multi-subject datasets used in neuroimaging group studies have a complex structure, as they exhibit non-stationary statistical properties across regions and display various artifacts. While studies with small sample sizes can rarely be shown to deviate from standard hypotheses (such as the normality of the residuals) due to the poor sensitivity of normality tests with low degrees of freedom, large-scale studies (e.g. >100 subjects) exhibit more obvious deviations from these hypotheses and call for more refined models for statistical inference. Here, we demonstrate the benefits of robust regression as a tool for analyzing large neuroimaging cohorts. First, we use an analytic test based on robust parameter estimates; based on simulations, this procedure is shown to provide an accurate statistical control without resorting to permutations. Second, we show that robust regression yields more detections than standard algorithms using as an example an imaging genetics study with 392 subjects. Third, we show that robust regression can avoid false positives in a large-scale analysis of brain-behavior relationships with over 1500 subjects. Finally we embed robust regression in the Randomized Parcellation Based Inference (RPBI) method and demonstrate that this combination further improves the sensitivity of tests carried out across the whole brain. Altogether, our results show that robust procedures provide important advantages in large-scale neuroimaging group studies. Copyright © 2015 Elsevier Inc. All rights reserved.

What are hierarchical models and how do we analyze them?

USGS Publications Warehouse

Royle, Andy

2016-01-01

In this chapter we provide a basic definition of hierarchical models and introduce the two canonical hierarchical models in this book: site occupancy and N-mixture models. The former is a hierarchical extension of logistic regression and the latter is a hierarchical extension of Poisson regression. We introduce basic concepts of probability modeling and statistical inference including likelihood and Bayesian perspectives. We go through the mechanics of maximizing the likelihood and characterizing the posterior distribution by Markov chain Monte Carlo (MCMC) methods. We give a general perspective on topics such as model selection and assessment of model fit, although we demonstrate these topics in practice in later chapters (especially Chapters 5, 6, 7, and 10 Chapter 5 Chapter 6 Chapter 7 Chapter 10)

A metabolism-based whole lake eutrophication model to estimate the magnitude and time scales of the effects of restoration in Upper Klamath Lake, south-central Oregon

USGS Publications Warehouse

Wherry, Susan A.; Wood, Tamara M.

2018-04-27

A whole lake eutrophication (WLE) model approach for phosphorus and cyanobacterial biomass in Upper Klamath Lake, south-central Oregon, is presented here. The model is a successor to a previous model developed to inform a Total Maximum Daily Load (TMDL) for phosphorus in the lake, but is based on net primary production (NPP), which can be calculated from dissolved oxygen, rather than scaling up a small-scale description of cyanobacterial growth and respiration rates. This phase 3 WLE model is a refinement of the proof-of-concept developed in phase 2, which was the first attempt to use NPP to simulate cyanobacteria in the TMDL model. The calibration of the calculated NPP WLE model was successful, with performance metrics indicating a good fit to calibration data, and the calculated NPP WLE model was able to simulate mid-season bloom decreases, a feature that previous models could not reproduce.In order to use the model to simulate future scenarios based on phosphorus load reduction, a multivariate regression model was created to simulate NPP as a function of the model state variables (phosphorus and chlorophyll a) and measured meteorological and temperature model inputs. The NPP time series was split into a low- and high-frequency component using wavelet analysis, and regression models were fit to the components separately, with moderate success.The regression models for NPP were incorporated in the WLE model, referred to as the “scenario” WLE (SWLE), and the fit statistics for phosphorus during the calibration period were mostly unchanged. The fit statistics for chlorophyll a, however, were degraded. These statistics are still an improvement over prior models, and indicate that the SWLE is appropriate for long-term predictions even though it misses some of the seasonal variations in chlorophyll a.The complete whole lake SWLE model, with multivariate regression to predict NPP, was used to make long-term simulations of the response to 10-, 20-, and 40-percent reductions in tributary nutrient loads. The long-term mean water column concentration of total phosphorus was reduced by 9, 18, and 36 percent, respectively, in response to these load reductions. The long-term water column chlorophyll a concentration was reduced by 4, 13, and 44 percent, respectively. The adjustment to a new equilibrium between the water column and sediments occurred over about 30 years.

Vector autoregressive models: A Gini approach

NASA Astrophysics Data System (ADS)

Mussard, Stéphane; Ndiaye, Oumar Hamady

2018-02-01

In this paper, it is proven that the usual VAR models may be performed in the Gini sense, that is, on a ℓ1 metric space. The Gini regression is robust to outliers. As a consequence, when data are contaminated by extreme values, we show that semi-parametric VAR-Gini regressions may be used to obtain robust estimators. The inference about the estimators is made with the ℓ1 norm. Also, impulse response functions and Gini decompositions for prevision errors are introduced. Finally, Granger's causality tests are properly derived based on U-statistics.

Water resources management: Hydrologic characterization through hydrograph simulation may bias streamflow statistics

NASA Astrophysics Data System (ADS)

Farmer, W. H.; Kiang, J. E.

2017-12-01

The development, deployment and maintenance of water resources management infrastructure and practices rely on hydrologic characterization, which requires an understanding of local hydrology. With regards to streamflow, this understanding is typically quantified with statistics derived from long-term streamgage records. However, a fundamental problem is how to characterize local hydrology without the luxury of streamgage records, a problem that complicates water resources management at ungaged locations and for long-term future projections. This problem has typically been addressed through the development of point estimators, such as regression equations, to estimate particular statistics. Physically-based precipitation-runoff models, which are capable of producing simulated hydrographs, offer an alternative to point estimators. The advantage of simulated hydrographs is that they can be used to compute any number of streamflow statistics from a single source (the simulated hydrograph) rather than relying on a diverse set of point estimators. However, the use of simulated hydrographs introduces a degree of model uncertainty that is propagated through to estimated streamflow statistics and may have drastic effects on management decisions. We compare the accuracy and precision of streamflow statistics (e.g. the mean annual streamflow, the annual maximum streamflow exceeded in 10% of years, and the minimum seven-day average streamflow exceeded in 90% of years, among others) derived from point estimators (e.g. regressions, kriging, machine learning) to that of statistics derived from simulated hydrographs across the continental United States. Initial results suggest that the error introduced through hydrograph simulation may substantially bias the resulting hydrologic characterization.

Egg production forecasting: Determining efficient modeling approaches.

PubMed

Ahmad, H A

2011-12-01

Several mathematical or statistical and artificial intelligence models were developed to compare egg production forecasts in commercial layers. Initial data for these models were collected from a comparative layer trial on commercial strains conducted at the Poultry Research Farms, Auburn University. Simulated data were produced to represent new scenarios by using means and SD of egg production of the 22 commercial strains. From the simulated data, random examples were generated for neural network training and testing for the weekly egg production prediction from wk 22 to 36. Three neural network architectures-back-propagation-3, Ward-5, and the general regression neural network-were compared for their efficiency to forecast egg production, along with other traditional models. The general regression neural network gave the best-fitting line, which almost overlapped with the commercial egg production data, with an R(2) of 0.71. The general regression neural network-predicted curve was compared with original egg production data, the average curves of white-shelled and brown-shelled strains, linear regression predictions, and the Gompertz nonlinear model. The general regression neural network was superior in all these comparisons and may be the model of choice if the initial overprediction is managed efficiently. In general, neural network models are efficient, are easy to use, require fewer data, and are practical under farm management conditions to forecast egg production.

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred

2013-01-01

A new regression model search algorithm was developed in 2011 that may be used to analyze both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The new algorithm is a simplified version of a more complex search algorithm that was originally developed at the NASA Ames Balance Calibration Laboratory. The new algorithm has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression models. Therefore, the simplified search algorithm is not intended to replace the original search algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm either fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new regression model search algorithm.

The impact of meteorology on the occurrence of waterborne outbreaks of vero cytotoxin-producing Escherichia coli (VTEC): a logistic regression approach.

PubMed

O'Dwyer, Jean; Morris Downes, Margaret; Adley, Catherine C

2016-02-01

This study analyses the relationship between meteorological phenomena and outbreaks of waterborne-transmitted vero cytotoxin-producing Escherichia coli (VTEC) in the Republic of Ireland over an 8-year period (2005-2012). Data pertaining to the notification of waterborne VTEC outbreaks were extracted from the Computerised Infectious Disease Reporting system, which is administered through the national Health Protection Surveillance Centre as part of the Health Service Executive. Rainfall and temperature data were obtained from the national meteorological office and categorised as cumulative rainfall, heavy rainfall events in the previous 7 days, and mean temperature. Regression analysis was performed using logistic regression (LR) analysis. The LR model was significant (p < 0.001), with all independent variables: cumulative rainfall, heavy rainfall and mean temperature making a statistically significant contribution to the model. The study has found that rainfall, particularly heavy rainfall in the preceding 7 days of an outbreak, is a strong statistical indicator of a waterborne outbreak and that temperature also impacts waterborne VTEC outbreak occurrence.

Predictors of effects of lifestyle intervention on diabetes mellitus type 2 patients.

PubMed

Jacobsen, Ramune; Vadstrup, Eva; Røder, Michael; Frølich, Anne

2012-01-01

The main aim of the study was to identify predictors of the effects of lifestyle intervention on diabetes mellitus type 2 patients by means of multivariate analysis. Data from a previously published randomised clinical trial, which compared the effects of a rehabilitation programme including standardised education and physical training sessions in the municipality's health care centre with the same duration of individual counseling in the diabetes outpatient clinic, were used. Data from 143 diabetes patients were analysed. The merged lifestyle intervention resulted in statistically significant improvements in patients' systolic blood pressure, waist circumference, exercise capacity, glycaemic control, and some aspects of general health-related quality of life. The linear multivariate regression models explained 45% to 80% of the variance in these improvements. The baseline outcomes in accordance to the logic of the regression to the mean phenomenon were the only statistically significant and robust predictors in all regression models. These results are important from a clinical point of view as they highlight the more urgent need for and better outcomes following lifestyle intervention for those patients who have worse general and disease-specific health.

VARIABLE SELECTION FOR REGRESSION MODELS WITH MISSING DATA

PubMed Central

Garcia, Ramon I.; Ibrahim, Joseph G.; Zhu, Hongtu

2009-01-01

We consider the variable selection problem for a class of statistical models with missing data, including missing covariate and/or response data. We investigate the smoothly clipped absolute deviation penalty (SCAD) and adaptive LASSO and propose a unified model selection and estimation procedure for use in the presence of missing data. We develop a computationally attractive algorithm for simultaneously optimizing the penalized likelihood function and estimating the penalty parameters. Particularly, we propose to use a model selection criterion, called the ICQ statistic, for selecting the penalty parameters. We show that the variable selection procedure based on ICQ automatically and consistently selects the important covariates and leads to efficient estimates with oracle properties. The methodology is very general and can be applied to numerous situations involving missing data, from covariates missing at random in arbitrary regression models to nonignorably missing longitudinal responses and/or covariates. Simulations are given to demonstrate the methodology and examine the finite sample performance of the variable selection procedures. Melanoma data from a cancer clinical trial is presented to illustrate the proposed methodology. PMID:20336190

Statistical modeling of landslide hazard using GIS

Treesearch

Peter V. Gorsevski; Randy B. Foltz; Paul E. Gessler; Terrance W. Cundy

2001-01-01

A model for spatial prediction of landslide hazard was applied to a watershed affected by landslide events that occurred during the winter of 1995-96, following heavy rains, and snowmelt. Digital elevation data with 22.86 m x 22.86 m resolution was used for deriving topographic attributes used for modeling. The model is based on the combination of logistic regression...

Key Results of Interaction Models with Centering

ERIC Educational Resources Information Center

Afshartous, David; Preston, Richard A.

2011-01-01

We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we…

Assessing the sensitivity and robustness of prediction models for apple firmness using spectral scattering technique

USDA-ARS?s Scientific Manuscript database

Spectral scattering is useful for nondestructive sensing of fruit firmness. Prediction models, however, are typically built using multivariate statistical methods such as partial least squares regression (PLSR), whose performance generally depends on the characteristics of the data. The aim of this ...

Assessing landslide susceptibility by statistical data analysis and GIS: the case of Daunia (Apulian Apennines, Italy)

NASA Astrophysics Data System (ADS)

Ceppi, C.; Mancini, F.; Ritrovato, G.

2009-04-01

This study aim at the landslide susceptibility mapping within an area of the Daunia (Apulian Apennines, Italy) by a multivariate statistical method and data manipulation in a Geographical Information System (GIS) environment. Among the variety of existing statistical data analysis techniques, the logistic regression was chosen to produce a susceptibility map all over an area where small settlements are historically threatened by landslide phenomena. By logistic regression a best fitting between the presence or absence of landslide (dependent variable) and the set of independent variables is performed on the basis of a maximum likelihood criterion, bringing to the estimation of regression coefficients. The reliability of such analysis is therefore due to the ability to quantify the proneness to landslide occurrences by the probability level produced by the analysis. The inventory of dependent and independent variables were managed in a GIS, where geometric properties and attributes have been translated into raster cells in order to proceed with the logistic regression by means of SPSS (Statistical Package for the Social Sciences) package. A landslide inventory was used to produce the bivariate dependent variable whereas the independent set of variable concerned with slope, aspect, elevation, curvature, drained area, lithology and land use after their reductions to dummy variables. The effect of independent parameters on landslide occurrence was assessed by the corresponding coefficient in the logistic regression function, highlighting a major role played by the land use variable in determining occurrence and distribution of phenomena. Once the outcomes of the logistic regression are determined, data are re-introduced in the GIS to produce a map reporting the proneness to landslide as predicted level of probability. As validation of results and regression model a cell-by-cell comparison between the susceptibility map and the initial inventory of landslide events was performed and an agreement at 75% level achieved.

Segmented regression analysis of interrupted time series data to assess outcomes of a South American road traffic alcohol policy change.

PubMed

Nistal-Nuño, Beatriz

2017-09-01

In Chile, a new law introduced in March 2012 decreased the legal blood alcohol concentration (BAC) limit for driving while impaired from 1 to 0.8 g/l and the legal BAC limit for driving under the influence of alcohol from 0.5 to 0.3 g/l. The goal is to assess the impact of this new law on mortality and morbidity outcomes in Chile. A review of national databases in Chile was conducted from January 2003 to December 2014. Segmented regression analysis of interrupted time series was used for analyzing the data. In a series of multivariable linear regression models, the change in intercept and slope in the monthly incidence rate of traffic deaths and injuries and association with alcohol per 100,000 inhabitants was estimated from pre-intervention to postintervention, while controlling for secular changes. In nested regression models, potential confounding seasonal effects were accounted for. All analyses were performed at a two-sided significance level of 0.05. Immediate level drops in all the monthly rates were observed after the law from the end of the prelaw period in the majority of models and in all the de-seasonalized models, although statistical significance was reached only in the model for injures related to alcohol. After the law, the estimated monthly rate dropped abruptly by -0.869 for injuries related to alcohol and by -0.859 adjusting for seasonality (P < 0.001). Regarding the postlaw long-term trends, it was evidenced a steeper decreasing trend after the law in the models for deaths related to alcohol, although these differences were not statistically significant. A strong evidence of a reduction in traffic injuries related to alcohol was found following the law in Chile. Although insufficient evidence was found of a statistically significant effect for the beneficial effects seen on deaths and overall injuries, potential clinically important effects cannot be ruled out. Copyright © 2017 The Royal Society for Public Health. Published by Elsevier Ltd. All rights reserved.

Pitfalls in statistical landslide susceptibility modelling

NASA Astrophysics Data System (ADS)

Schröder, Boris; Vorpahl, Peter; Märker, Michael; Elsenbeer, Helmut

2010-05-01

The use of statistical methods is a well-established approach to predict landslide occurrence probabilities and to assess landslide susceptibility. This is achieved by applying statistical methods relating historical landslide inventories to topographic indices as predictor variables. In our contribution, we compare several new and powerful methods developed in machine learning and well-established in landscape ecology and macroecology for predicting the distribution of shallow landslides in tropical mountain rainforests in southern Ecuador (among others: boosted regression trees, multivariate adaptive regression splines, maximum entropy). Although these methods are powerful, we think it is necessary to follow a basic set of guidelines to avoid some pitfalls regarding data sampling, predictor selection, and model quality assessment, especially if a comparison of different models is contemplated. We therefore suggest to apply a novel toolbox to evaluate approaches to the statistical modelling of landslide susceptibility. Additionally, we propose some methods to open the "black box" as an inherent part of machine learning methods in order to achieve further explanatory insights into preparatory factors that control landslides. Sampling of training data should be guided by hypotheses regarding processes that lead to slope failure taking into account their respective spatial scales. This approach leads to the selection of a set of candidate predictor variables considered on adequate spatial scales. This set should be checked for multicollinearity in order to facilitate model response curve interpretation. Model quality assesses how well a model is able to reproduce independent observations of its response variable. This includes criteria to evaluate different aspects of model performance, i.e. model discrimination, model calibration, and model refinement. In order to assess a possible violation of the assumption of independency in the training samples or a possible lack of explanatory information in the chosen set of predictor variables, the model residuals need to be checked for spatial auto¬correlation. Therefore, we calculate spline correlograms. In addition to this, we investigate partial dependency plots and bivariate interactions plots considering possible interactions between predictors to improve model interpretation. Aiming at presenting this toolbox for model quality assessment, we investigate the influence of strategies in the construction of training datasets for statistical models on model quality.

Predicting Energy Performance of a Net-Zero Energy Building: A Statistical Approach

PubMed Central

Kneifel, Joshua; Webb, David

2016-01-01

Performance-based building requirements have become more prevalent because it gives freedom in building design while still maintaining or exceeding the energy performance required by prescriptive-based requirements. In order to determine if building designs reach target energy efficiency improvements, it is necessary to estimate the energy performance of a building using predictive models and different weather conditions. Physics-based whole building energy simulation modeling is the most common approach. However, these physics-based models include underlying assumptions and require significant amounts of information in order to specify the input parameter values. An alternative approach to test the performance of a building is to develop a statistically derived predictive regression model using post-occupancy data that can accurately predict energy consumption and production based on a few common weather-based factors, thus requiring less information than simulation models. A regression model based on measured data should be able to predict energy performance of a building for a given day as long as the weather conditions are similar to those during the data collection time frame. This article uses data from the National Institute of Standards and Technology (NIST) Net-Zero Energy Residential Test Facility (NZERTF) to develop and validate a regression model to predict the energy performance of the NZERTF using two weather variables aggregated to the daily level, applies the model to estimate the energy performance of hypothetical NZERTFs located in different cities in the Mixed-Humid climate zone, and compares these estimates to the results from already existing EnergyPlus whole building energy simulations. This regression model exhibits agreement with EnergyPlus predictive trends in energy production and net consumption, but differs greatly in energy consumption. The model can be used as a framework for alternative and more complex models based on the experimental data collected from the NZERTF. PMID:27956756

Predicting Energy Performance of a Net-Zero Energy Building: A Statistical Approach.

PubMed

Kneifel, Joshua; Webb, David

2016-09-01

Performance-based building requirements have become more prevalent because it gives freedom in building design while still maintaining or exceeding the energy performance required by prescriptive-based requirements. In order to determine if building designs reach target energy efficiency improvements, it is necessary to estimate the energy performance of a building using predictive models and different weather conditions. Physics-based whole building energy simulation modeling is the most common approach. However, these physics-based models include underlying assumptions and require significant amounts of information in order to specify the input parameter values. An alternative approach to test the performance of a building is to develop a statistically derived predictive regression model using post-occupancy data that can accurately predict energy consumption and production based on a few common weather-based factors, thus requiring less information than simulation models. A regression model based on measured data should be able to predict energy performance of a building for a given day as long as the weather conditions are similar to those during the data collection time frame. This article uses data from the National Institute of Standards and Technology (NIST) Net-Zero Energy Residential Test Facility (NZERTF) to develop and validate a regression model to predict the energy performance of the NZERTF using two weather variables aggregated to the daily level, applies the model to estimate the energy performance of hypothetical NZERTFs located in different cities in the Mixed-Humid climate zone, and compares these estimates to the results from already existing EnergyPlus whole building energy simulations. This regression model exhibits agreement with EnergyPlus predictive trends in energy production and net consumption, but differs greatly in energy consumption. The model can be used as a framework for alternative and more complex models based on the experimental data collected from the NZERTF.

Fast Identification of Biological Pathways Associated with a Quantitative Trait Using Group Lasso with Overlaps

PubMed Central

Silver, Matt; Montana, Giovanni

2012-01-01

Where causal SNPs (single nucleotide polymorphisms) tend to accumulate within biological pathways, the incorporation of prior pathways information into a statistical model is expected to increase the power to detect true associations in a genetic association study. Most existing pathways-based methods rely on marginal SNP statistics and do not fully exploit the dependence patterns among SNPs within pathways. We use a sparse regression model, with SNPs grouped into pathways, to identify causal pathways associated with a quantitative trait. Notable features of our “pathways group lasso with adaptive weights” (P-GLAW) algorithm include the incorporation of all pathways in a single regression model, an adaptive pathway weighting procedure that accounts for factors biasing pathway selection, and the use of a bootstrap sampling procedure for the ranking of important pathways. P-GLAW takes account of the presence of overlapping pathways and uses a novel combination of techniques to optimise model estimation, making it fast to run, even on whole genome datasets. In a comparison study with an alternative pathways method based on univariate SNP statistics, our method demonstrates high sensitivity and specificity for the detection of important pathways, showing the greatest relative gains in performance where marginal SNP effect sizes are small. PMID:22499682

Data mining of tree-based models to analyze freeway accident frequency.

PubMed

Chang, Li-Yen; Chen, Wen-Chieh

2005-01-01

Statistical models, such as Poisson or negative binomial regression models, have been employed to analyze vehicle accident frequency for many years. However, these models have their own model assumptions and pre-defined underlying relationship between dependent and independent variables. If these assumptions are violated, the model could lead to erroneous estimation of accident likelihood. Classification and Regression Tree (CART), one of the most widely applied data mining techniques, has been commonly employed in business administration, industry, and engineering. CART does not require any pre-defined underlying relationship between target (dependent) variable and predictors (independent variables) and has been shown to be a powerful tool, particularly for dealing with prediction and classification problems. This study collected the 2001-2002 accident data of National Freeway 1 in Taiwan. A CART model and a negative binomial regression model were developed to establish the empirical relationship between traffic accidents and highway geometric variables, traffic characteristics, and environmental factors. The CART findings indicated that the average daily traffic volume and precipitation variables were the key determinants for freeway accident frequencies. By comparing the prediction performance between the CART and the negative binomial regression models, this study demonstrates that CART is a good alternative method for analyzing freeway accident frequencies. By comparing the prediction performance between the CART and the negative binomial regression models, this study demonstrates that CART is a good alternative method for analyzing freeway accident frequencies.

Using decision trees to understand structure in missing data

PubMed Central

Tierney, Nicholas J; Harden, Fiona A; Harden, Maurice J; Mengersen, Kerrie L

2015-01-01

Objectives Demonstrate the application of decision trees—classification and regression trees (CARTs), and their cousins, boosted regression trees (BRTs)—to understand structure in missing data. Setting Data taken from employees at 3 different industrial sites in Australia. Participants 7915 observations were included. Materials and methods The approach was evaluated using an occupational health data set comprising results of questionnaires, medical tests and environmental monitoring. Statistical methods included standard statistical tests and the ‘rpart’ and ‘gbm’ packages for CART and BRT analyses, respectively, from the statistical software ‘R’. A simulation study was conducted to explore the capability of decision tree models in describing data with missingness artificially introduced. Results CART and BRT models were effective in highlighting a missingness structure in the data, related to the type of data (medical or environmental), the site in which it was collected, the number of visits, and the presence of extreme values. The simulation study revealed that CART models were able to identify variables and values responsible for inducing missingness. There was greater variation in variable importance for unstructured as compared to structured missingness. Discussion Both CART and BRT models were effective in describing structural missingness in data. CART models may be preferred over BRT models for exploratory analysis of missing data, and selecting variables important for predicting missingness. BRT models can show how values of other variables influence missingness, which may prove useful for researchers. Conclusions Researchers are encouraged to use CART and BRT models to explore and understand missing data. PMID:26124509

Validation of Statistical Predictive Models Meant to Select Melanoma Patients for Sentinel Lymph Node Biopsy

PubMed Central

Sabel, Michael S.; Rice, John D.; Griffith, Kent A.; Lowe, Lori; Wong, Sandra L.; Chang, Alfred E.; Johnson, Timothy M.; Taylor, Jeremy M.G.

2013-01-01

Introduction To identify melanoma patients at sufficiently low risk of nodal metastases who could avoid SLN biopsy (SLNB). Several statistical models have been proposed based upon patient/tumor characteristics, including logistic regression, classification trees, random forests and support vector machines. We sought to validate recently published models meant to predict sentinel node status. Methods We queried our comprehensive, prospectively-collected melanoma database for consecutive melanoma patients undergoing SLNB. Prediction values were estimated based upon 4 published models, calculating the same reported metrics: negative predictive value (NPV), rate of negative predictions (RNP), and false negative rate (FNR). Results Logistic regression performed comparably with our data when considering NPV (89.4% vs. 93.6%); however the model’s specificity was not high enough to significantly reduce the rate of biopsies (SLN reduction rate of 2.9%). When applied to our data, the classification tree produced NPV and reduction in biopsies rates that were lower 87.7% vs. 94.1% and 29.8% vs. 14.3%, respectively. Two published models could not be applied to our data due to model complexity and the use of proprietary software. Conclusions Published models meant to reduce the SLNB rate among patients with melanoma either underperformed when applied to our larger dataset, or could not be validated. Differences in selection criteria and histopathologic interpretation likely resulted in underperformance. Development of statistical predictive models must be created in a clinically applicable manner to allow for both validation and ultimately clinical utility. PMID:21822550

Drivers willingness to pay progressive rate for street parking.

DOT National Transportation Integrated Search

2015-01-01

This study finds willingness to pay and price elasticity for on-street parking demand using stated : preference data obtained from 238 respondents. Descriptive, statistical and economic analyses including : regression, generalized linear model, and f...

MANCOVA for one way classification with homogeneity of regression coefficient vectors

NASA Astrophysics Data System (ADS)

Mokesh Rayalu, G.; Ravisankar, J.; Mythili, G. Y.

2017-11-01

The MANOVA and MANCOVA are the extensions of the univariate ANOVA and ANCOVA techniques to multidimensional or vector valued observations. The assumption of a Gaussian distribution has been replaced with the Multivariate Gaussian distribution for the vectors data and residual term variables in the statistical models of these techniques. The objective of MANCOVA is to determine if there are statistically reliable mean differences that can be demonstrated between groups later modifying the newly created variable. When randomization assignment of samples or subjects to groups is not possible, multivariate analysis of covariance (MANCOVA) provides statistical matching of groups by adjusting dependent variables as if all subjects scored the same on the covariates. In this research article, an extension has been made to the MANCOVA technique with more number of covariates and homogeneity of regression coefficient vectors is also tested.

A Method of Relating General Circulation Model Simulated Climate to the Observed Local Climate. Part I: Seasonal Statistics.

NASA Astrophysics Data System (ADS)

Karl, Thomas R.; Wang, Wei-Chyung; Schlesinger, Michael E.; Knight, Richard W.; Portman, David

1990-10-01

Important surface observations such as the daily maximum and minimum temperature, daily precipitation, and cloud ceilings often have localized characteristics that are difficult to reproduce with the current resolution and the physical parameterizations in state-of-the-art General Circulation climate Models (GCMs). Many of the difficulties can be partially attributed to mismatches in scale, local topography. regional geography and boundary conditions between models and surface-based observations. Here, we present a method, called climatological projection by model statistics (CPMS), to relate GCM grid-point flee-atmosphere statistics, the predictors, to these important local surface observations. The method can be viewed as a generalization of the model output statistics (MOS) and perfect prog (PP) procedures used in numerical weather prediction (NWP) models. It consists of the application of three statistical methods: 1) principle component analysis (FICA), 2) canonical correlation, and 3) inflated regression analysis. The PCA reduces the redundancy of the predictors The canonical correlation is used to develop simultaneous relationships between linear combinations of the predictors, the canonical variables, and the surface-based observations. Finally, inflated regression is used to relate the important canonical variables to each of the surface-based observed variables.We demonstrate that even an early version of the Oregon State University two-level atmospheric GCM (with prescribed sea surface temperature) produces free-atmosphere statistics than can, when standardized using the model's internal means and variances (the MOS-like version of CPMS), closely approximate the observed local climate. When the model data are standardized by the observed free-atmosphere means and variances (the PP version of CPMS), however, the model does not reproduce the observed surface climate as well. Our results indicate that in the MOS-like version of CPMS the differences between the output of a ten-year GCM control run and the surface-based observations are often smaller than the differences between the observations of two ten-year periods. Such positive results suggest that GCMs may already contain important climatological information that can be used to infer the local climate.

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory.

PubMed

Lord, Dominique; Washington, Simon P; Ivan, John N

2005-01-01

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states-perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of "excess" zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to "excess" zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed-and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros.

Longitudinal analysis of the strengths and difficulties questionnaire scores of the Millennium Cohort Study children in England using M-quantile random-effects regression.

PubMed

Tzavidis, Nikos; Salvati, Nicola; Schmid, Timo; Flouri, Eirini; Midouhas, Emily

2016-02-01

Multilevel modelling is a popular approach for longitudinal data analysis. Statistical models conventionally target a parameter at the centre of a distribution. However, when the distribution of the data is asymmetric, modelling other location parameters, e.g. percentiles, may be more informative. We present a new approach, M -quantile random-effects regression, for modelling multilevel data. The proposed method is used for modelling location parameters of the distribution of the strengths and difficulties questionnaire scores of children in England who participate in the Millennium Cohort Study. Quantile mixed models are also considered. The analyses offer insights to child psychologists about the differential effects of risk factors on children's outcomes.

Efficient Regressions via Optimally Combining Quantile Information*

PubMed Central

Zhao, Zhibiao; Xiao, Zhijie

2014-01-01

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance between the efficiency of the proposed estimator and the Fisher information. As the number of quantiles increases, this upper bound decreases and the asymptotic variance of the proposed estimator approaches the Cramér-Rao lower bound under appropriate conditions. In the case of non-regular statistical estimation, the proposed estimator leads to super-efficient estimation. We illustrate the proposed method for several widely used regression models. Both asymptotic theory and Monte Carlo experiments show the superior performance over existing methods. PMID:25484481

Regression-assisted deconvolution.

PubMed

McIntyre, Julie; Stefanski, Leonard A

2011-06-30

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availability of a covariate vector statistically related to X by a mean-variance function regression model, where regression errors are normally distributed and independent of the measurement errors. Simulations suggest that the estimator achieves a much lower integrated squared error than the observed-data kernel density estimator when models are correctly specified and the assumption of normal regression errors is met. We illustrate the method using anthropometric measurements of newborns to estimate the density function of newborn length. Copyright © 2011 John Wiley & Sons, Ltd.

Predicting survival of Escherichia coli O157:H7 in dry fermented sausage using artificial neural networks.

PubMed

Palanichamy, A; Jayas, D S; Holley, R A

2008-01-01

The Canadian Food Inspection Agency required the meat industry to ensure Escherichia coli O157:H7 does not survive (experiences > or = 5 log CFU/g reduction) in dry fermented sausage (salami) during processing after a series of foodborne illness outbreaks resulting from this pathogenic bacterium occurred. The industry is in need of an effective technique like predictive modeling for estimating bacterial viability, because traditional microbiological enumeration is a time-consuming and laborious method. The accuracy and speed of artificial neural networks (ANNs) for this purpose is an attractive alternative (developed from predictive microbiology), especially for on-line processing in industry. Data from a study of interactive effects of different levels of pH, water activity, and the concentrations of allyl isothiocyanate at various times during sausage manufacture in reducing numbers of E. coli O157:H7 were collected. Data were used to develop predictive models using a general regression neural network (GRNN), a form of ANN, and a statistical linear polynomial regression technique. Both models were compared for their predictive error, using various statistical indices. GRNN predictions for training and test data sets had less serious errors when compared with the statistical model predictions. GRNN models were better and slightly better for training and test sets, respectively, than was the statistical model. Also, GRNN accurately predicted the level of allyl isothiocyanate required, ensuring a 5-log reduction, when an appropriate production set was created by interpolation. Because they are simple to generate, fast, and accurate, ANN models may be of value for industrial use in dry fermented sausage manufacture to reduce the hazard associated with E. coli O157:H7 in fresh beef and permit production of consistently safe products from this raw material.

A comparison of large-scale climate signals and the North American Multi-Model Ensemble (NMME) for drought prediction in China

NASA Astrophysics Data System (ADS)

Xu, Lei; Chen, Nengcheng; Zhang, Xiang

2018-02-01

Drought is an extreme natural disaster that can lead to huge socioeconomic losses. Drought prediction ahead of months is helpful for early drought warning and preparations. In this study, we developed a statistical model, two weighted dynamic models and a statistical-dynamic (hybrid) model for 1-6 month lead drought prediction in China. Specifically, statistical component refers to climate signals weighting by support vector regression (SVR), dynamic components consist of the ensemble mean (EM) and Bayesian model averaging (BMA) of the North American Multi-Model Ensemble (NMME) climatic models, and the hybrid part denotes a combination of statistical and dynamic components by assigning weights based on their historical performances. The results indicate that the statistical and hybrid models show better rainfall predictions than NMME-EM and NMME-BMA models, which have good predictability only in southern China. In the 2011 China winter-spring drought event, the statistical model well predicted the spatial extent and severity of drought nationwide, although the severity was underestimated in the mid-lower reaches of Yangtze River (MLRYR) region. The NMME-EM and NMME-BMA models largely overestimated rainfall in northern and western China in 2011 drought. In the 2013 China summer drought, the NMME-EM model forecasted the drought extent and severity in eastern China well, while the statistical and hybrid models falsely detected negative precipitation anomaly (NPA) in some areas. Model ensembles such as multiple statistical approaches, multiple dynamic models or multiple hybrid models for drought predictions were highlighted. These conclusions may be helpful for drought prediction and early drought warnings in China.

Optimizing methods for linking cinematic features to fMRI data.

PubMed

Kauttonen, Janne; Hlushchuk, Yevhen; Tikka, Pia

2015-04-15

One of the challenges of naturalistic neurosciences using movie-viewing experiments is how to interpret observed brain activations in relation to the multiplicity of time-locked stimulus features. As previous studies have shown less inter-subject synchronization across viewers of random video footage than story-driven films, new methods need to be developed for analysis of less story-driven contents. To optimize the linkage between our fMRI data collected during viewing of a deliberately non-narrative silent film 'At Land' by Maya Deren (1944) and its annotated content, we combined the method of elastic-net regularization with the model-driven linear regression and the well-established data-driven independent component analysis (ICA) and inter-subject correlation (ISC) methods. In the linear regression analysis, both IC and region-of-interest (ROI) time-series were fitted with time-series of a total of 36 binary-valued and one real-valued tactile annotation of film features. The elastic-net regularization and cross-validation were applied in the ordinary least-squares linear regression in order to avoid over-fitting due to the multicollinearity of regressors, the results were compared against both the partial least-squares (PLS) regression and the un-regularized full-model regression. Non-parametric permutation testing scheme was applied to evaluate the statistical significance of regression. We found statistically significant correlation between the annotation model and 9 ICs out of 40 ICs. Regression analysis was also repeated for a large set of cubic ROIs covering the grey matter. Both IC- and ROI-based regression analyses revealed activations in parietal and occipital regions, with additional smaller clusters in the frontal lobe. Furthermore, we found elastic-net based regression more sensitive than PLS and un-regularized regression since it detected a larger number of significant ICs and ROIs. Along with the ISC ranking methods, our regression analysis proved a feasible method for ordering the ICs based on their functional relevance to the annotated cinematic features. The novelty of our method is - in comparison to the hypothesis-driven manual pre-selection and observation of some individual regressors biased by choice - in applying data-driven approach to all content features simultaneously. We found especially the combination of regularized regression and ICA useful when analyzing fMRI data obtained using non-narrative movie stimulus with a large set of complex and correlated features. Copyright © 2015. Published by Elsevier Inc.

Effects of metal- and fiber-reinforced composite root canal posts on flexural properties.

PubMed

Kim, Su-Hyeon; Oh, Tack-Oon; Kim, Ju-Young; Park, Chun-Woong; Baek, Seung-Ho; Park, Eun-Seok

2016-01-01

The aim of this study was to observe the effects of different test conditions on the flexural properties of root canal post. Metal- and fiber-reinforced composite root canal posts of various diameters were measured to determine flexural properties using a threepoint bending test at different conditions. In this study, the span length/post diameter ratio of root canal posts varied from 3.0 to 10.0. Multiple regression models for maximum load as a dependent variable were statistically significant. The models for flexural properties as dependent variables were statistically significant, but linear regression models could not be fitted to data sets. At a low span length/post diameter ratio, the flexural properties were distorted by occurrence of shear stress in short samples. It was impossible to obtain high span length/post diameter ratio with root canal posts. The addition of parameters or coefficients is necessary to appropriately represent the flexural properties of root canal posts.

Methods for estimating drought streamflow probabilities for Virginia streams

USGS Publications Warehouse

Austin, Samuel H.

2014-01-01

Maximum likelihood logistic regression model equations used to estimate drought flow probabilities for Virginia streams are presented for 259 hydrologic basins in Virginia. Winter streamflows were used to estimate the likelihood of streamflows during the subsequent drought-prone summer months. The maximum likelihood logistic regression models identify probable streamflows from 5 to 8 months in advance. More than 5 million streamflow daily values collected over the period of record (January 1, 1900 through May 16, 2012) were compiled and analyzed over a minimum 10-year (maximum 112-year) period of record. The analysis yielded the 46,704 equations with statistically significant fit statistics and parameter ranges published in two tables in this report. These model equations produce summer month (July, August, and September) drought flow threshold probabilities as a function of streamflows during the previous winter months (November, December, January, and February). Example calculations are provided, demonstrating how to use the equations to estimate probable streamflows as much as 8 months in advance.

A climate-based multivariate extreme emulator of met-ocean-hydrological events for coastal flooding

NASA Astrophysics Data System (ADS)

Camus, Paula; Rueda, Ana; Mendez, Fernando J.; Tomas, Antonio; Del Jesus, Manuel; Losada, Iñigo J.

2015-04-01

Atmosphere-ocean general circulation models (AOGCMs) are useful to analyze large-scale climate variability (long-term historical periods, future climate projections). However, applications such as coastal flood modeling require climate information at finer scale. Besides, flooding events depend on multiple climate conditions: waves, surge levels from the open-ocean and river discharge caused by precipitation. Therefore, a multivariate statistical downscaling approach is adopted to reproduce relationships between variables and due to its low computational cost. The proposed method can be considered as a hybrid approach which combines a probabilistic weather type downscaling model with a stochastic weather generator component. Predictand distributions are reproduced modeling the relationship with AOGCM predictors based on a physical division in weather types (Camus et al., 2012). The multivariate dependence structure of the predictand (extreme events) is introduced linking the independent marginal distributions of the variables by a probabilistic copula regression (Ben Ayala et al., 2014). This hybrid approach is applied for the downscaling of AOGCM data to daily precipitation and maximum significant wave height and storm-surge in different locations along the Spanish coast. Reanalysis data is used to assess the proposed method. A commonly predictor for the three variables involved is classified using a regression-guided clustering algorithm. The most appropriate statistical model (general extreme value distribution, pareto distribution) for daily conditions is fitted. Stochastic simulation of the present climate is performed obtaining the set of hydraulic boundary conditions needed for high resolution coastal flood modeling. References: Camus, P., Menéndez, M., Méndez, F.J., Izaguirre, C., Espejo, A., Cánovas, V., Pérez, J., Rueda, A., Losada, I.J., Medina, R. (2014b). A weather-type statistical downscaling framework for ocean wave climate. Journal of Geophysical Research, doi: 10.1002/2014JC010141. Ben Ayala, M.A., Chebana, F., Ouarda, T.B.M.J. (2014). Probabilistic Gaussian Copula Regression Model for Multisite and Multivariable Downscaling, Journal of Climate, 27, 3331-3347.

Paleotemperature reconstruction from mammalian phosphate δ18O records - an alternative view on data processing

NASA Astrophysics Data System (ADS)

Skrzypek, Grzegorz; Sadler, Rohan; Wiśniewski, Andrzej

2017-04-01

The stable oxygen isotope composition of phosphates (δ18O) extracted from mammalian bone and teeth material is commonly used as a proxy for paleotemperature. Historically, several different analytical and statistical procedures for determining air paleotemperatures from the measured δ18O of phosphates have been applied. This inconsistency in both stable isotope data processing and the application of statistical procedures has led to large and unwanted differences between calculated results. This study presents the uncertainty associated with two of the most commonly used regression methods: least squares inverted fit and transposed fit. We assessed the performance of these methods by designing and applying calculation experiments to multiple real-life data sets, calculating in reverse temperatures, and comparing them with true recorded values. Our calculations clearly show that the mean absolute errors are always substantially higher for the inverted fit (a causal model), with the transposed fit (a predictive model) returning mean values closer to the measured values (Skrzypek et al. 2015). The predictive models always performed better than causal models, with 12-65% lower mean absolute errors. Moreover, the least-squares regression (LSM) model is more appropriate than Reduced Major Axis (RMA) regression for calculating the environmental water stable oxygen isotope composition from phosphate signatures, as well as for calculating air temperature from the δ18O value of environmental water. The transposed fit introduces a lower overall error than the inverted fit for both the δ18O of environmental water and Tair calculations; therefore, the predictive models are more statistically efficient than the causal models in this instance. The direct comparison of paleotemperature results from different laboratories and studies may only be achieved if a single method of calculation is applied. Reference Skrzypek G., Sadler R., Wiśniewski A., 2016. Reassessment of recommendations for processing mammal phosphate δ18O data for paleotemperature reconstruction. Palaeogeography, Palaeoclimatology, Palaeoecology 446, 162-167.

Statistical Approaches for Spatiotemporal Prediction of Low Flows

NASA Astrophysics Data System (ADS)

Fangmann, A.; Haberlandt, U.

2017-12-01

An adequate assessment of regional climate change impacts on streamflow requires the integration of various sources of information and modeling approaches. This study proposes simple statistical tools for inclusion into model ensembles, which are fast and straightforward in their application, yet able to yield accurate streamflow predictions in time and space. Target variables for all approaches are annual low flow indices derived from a data set of 51 records of average daily discharge for northwestern Germany. The models require input of climatic data in the form of meteorological drought indices, derived from observed daily climatic variables, averaged over the streamflow gauges' catchments areas. Four different modeling approaches are analyzed. Basis for all pose multiple linear regression models that estimate low flows as a function of a set of meteorological indices and/or physiographic and climatic catchment descriptors. For the first method, individual regression models are fitted at each station, predicting annual low flow values from a set of annual meteorological indices, which are subsequently regionalized using a set of catchment characteristics. The second method combines temporal and spatial prediction within a single panel data regression model, allowing estimation of annual low flow values from input of both annual meteorological indices and catchment descriptors. The third and fourth methods represent non-stationary low flow frequency analyses and require fitting of regional distribution functions. Method three is subject to a spatiotemporal prediction of an index value, method four to estimation of L-moments that adapt the regional frequency distribution to the at-site conditions. The results show that method two outperforms successive prediction in time and space. Method three also shows a high performance in the near future period, but since it relies on a stationary distribution, its application for prediction of far future changes may be problematic. Spatiotemporal prediction of L-moments appeared highly uncertain for higher-order moments resulting in unrealistic future low flow values. All in all, the results promote an inclusion of simple statistical methods in climate change impact assessment.

Design of experiments enhanced statistical process control for wind tunnel check standard testing

NASA Astrophysics Data System (ADS)

Phillips, Ben D.

The current wind tunnel check standard testing program at NASA Langley Research Center is focused on increasing data quality, uncertainty quantification and overall control and improvement of wind tunnel measurement processes. The statistical process control (SPC) methodology employed in the check standard testing program allows for the tracking of variations in measurements over time as well as an overall assessment of facility health. While the SPC approach can and does provide researchers with valuable information, it has certain limitations in the areas of process improvement and uncertainty quantification. It is thought by utilizing design of experiments methodology in conjunction with the current SPC practices that one can efficiently and more robustly characterize uncertainties and develop enhanced process improvement procedures. In this research, methodologies were developed to generate regression models for wind tunnel calibration coefficients, balance force coefficients and wind tunnel flow angularities. The coefficients of these regression models were then tracked in statistical process control charts, giving a higher level of understanding of the processes. The methodology outlined is sufficiently generic such that this research can be applicable to any wind tunnel check standard testing program.

Application of statistical shape analysis for the estimation of bone and forensic age using the shapes of the 2nd, 3rd, and 4th cervical vertebrae in a young Japanese population.

PubMed

Rhee, Chang-Hoon; Shin, Sang Min; Choi, Yong-Seok; Yamaguchi, Tetsutaro; Maki, Koutaro; Kim, Yong-Il; Kim, Seong-Sik; Park, Soo-Byung; Son, Woo-Sung

2015-12-01

From computed tomographic images, the dentocentral synchondrosis can be identified in the second cervical vertebra. This can demarcate the border between the odontoid process and the body of the 2nd cervical vertebra and serve as a good model for the prediction of bone and forensic age. Nevertheless, until now, there has been no application of the 2nd cervical vertebra based on the dentocentral synchondrosis. In this study, statistical shape analysis was used to build bone and forensic age estimation regression models. Following the principles of statistical shape analysis and principal components analysis, we used cone-beam computed tomography (CBCT) to evaluate a Japanese population (35 males and 45 females, from 5 to 19 years old). The narrowest prediction intervals among the multivariate regression models were 19.63 for bone age and 2.99 for forensic age. There was no significant difference between form space and shape space in the bone and forensic age estimation models. However, for gender comparison, the bone and forensic age estimation models for males had the higher explanatory power. This study derived an improved objective and quantitative method for bone and forensic age estimation based on only the 2nd, 3rd and 4th cervical vertebral shapes. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

A simple linear regression method for quantitative trait loci linkage analysis with censored observations.

PubMed

Anderson, Carl A; McRae, Allan F; Visscher, Peter M

2006-07-01

Standard quantitative trait loci (QTL) mapping techniques commonly assume that the trait is both fully observed and normally distributed. When considering survival or age-at-onset traits these assumptions are often incorrect. Methods have been developed to map QTL for survival traits; however, they are both computationally intensive and not available in standard genome analysis software packages. We propose a grouped linear regression method for the analysis of continuous survival data. Using simulation we compare this method to both the Cox and Weibull proportional hazards models and a standard linear regression method that ignores censoring. The grouped linear regression method is of equivalent power to both the Cox and Weibull proportional hazards methods and is significantly better than the standard linear regression method when censored observations are present. The method is also robust to the proportion of censored individuals and the underlying distribution of the trait. On the basis of linear regression methodology, the grouped linear regression model is computationally simple and fast and can be implemented readily in freely available statistical software.

A Selective Review of Group Selection in High-Dimensional Models

PubMed Central

Huang, Jian; Breheny, Patrick; Ma, Shuangge

2013-01-01

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group selection methods. In this article, we give a selective review of group selection concerning methodological developments, theoretical properties and computational algorithms. We pay particular attention to group selection methods involving concave penalties. We address both group selection and bi-level selection methods. We describe several applications of these methods in nonparametric additive models, semiparametric regression, seemingly unrelated regressions, genomic data analysis and genome wide association studies. We also highlight some issues that require further study. PMID:24174707

Regression modeling and prediction of road sweeping brush load characteristics from finite element analysis and experimental results.

PubMed

Wang, Chong; Sun, Qun; Wahab, Magd Abdel; Zhang, Xingyu; Xu, Limin

2015-09-01

Rotary cup brushes mounted on each side of a road sweeper undertake heavy debris removal tasks but the characteristics have not been well known until recently. A Finite Element (FE) model that can analyze brush deformation and predict brush characteristics have been developed to investigate the sweeping efficiency and to assist the controller design. However, the FE model requires large amount of CPU time to simulate each brush design and operating scenario, which may affect its applications in a real-time system. This study develops a mathematical regression model to summarize the FE modeled results. The complex brush load characteristic curves were statistically analyzed to quantify the effects of cross-section, length, mounting angle, displacement and rotational speed etc. The data were then fitted by a multiple variable regression model using the maximum likelihood method. The fitted results showed good agreement with the FE analysis results and experimental results, suggesting that the mathematical regression model may be directly used in a real-time system to predict characteristics of different brushes under varying operating conditions. The methodology may also be used in the design and optimization of rotary brush tools. Copyright © 2015 Elsevier Ltd. All rights reserved.

Applications of statistics to medical science, III. Correlation and regression.

PubMed

Watanabe, Hiroshi

2012-01-01

In this third part of a series surveying medical statistics, the concepts of correlation and regression are reviewed. In particular, methods of linear regression and logistic regression are discussed. Arguments related to survival analysis will be made in a subsequent paper.

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

Regression modeling of particle size distributions in urban storm water: advancements through improved sample collection methods

USGS Publications Warehouse

Fienen, Michael N.; Selbig, William R.

2012-01-01

A new sample collection system was developed to improve the representation of sediment entrained in urban storm water by integrating water quality samples from the entire water column. The depth-integrated sampler arm (DISA) was able to mitigate sediment stratification bias in storm water, thereby improving the characterization of suspended-sediment concentration and particle size distribution at three independent study locations. Use of the DISA decreased variability, which improved statistical regression to predict particle size distribution using surrogate environmental parameters, such as precipitation depth and intensity. The performance of this statistical modeling technique was compared to results using traditional fixed-point sampling methods and was found to perform better. When environmental parameters can be used to predict particle size distributions, environmental managers have more options when characterizing concentrations, loads, and particle size distributions in urban runoff.

Discovering human germ cell mutagens with whole genome sequencing: Insights from power calculations reveal the importance of controlling for between-family variability.

PubMed

Webster, R J; Williams, A; Marchetti, F; Yauk, C L

2018-07-01

Mutations in germ cells pose potential genetic risks to offspring. However, de novo mutations are rare events that are spread across the genome and are difficult to detect. Thus, studies in this area have generally been under-powered, and no human germ cell mutagen has been identified. Whole Genome Sequencing (WGS) of human pedigrees has been proposed as an approach to overcome these technical and statistical challenges. WGS enables analysis of a much wider breadth of the genome than traditional approaches. Here, we performed power analyses to determine the feasibility of using WGS in human families to identify germ cell mutagens. Different statistical models were compared in the power analyses (ANOVA and multiple regression for one-child families, and mixed effect model sampling between two to four siblings per family). Assumptions were made based on parameters from the existing literature, such as the mutation-by-paternal age effect. We explored two scenarios: a constant effect due to an exposure that occurred in the past, and an accumulating effect where the exposure is continuing. Our analysis revealed the importance of modeling inter-family variability of the mutation-by-paternal age effect. Statistical power was improved by models accounting for the family-to-family variability. Our power analyses suggest that sufficient statistical power can be attained with 4-28 four-sibling families per treatment group, when the increase in mutations ranges from 40 to 10% respectively. Modeling family variability using mixed effect models provided a reduction in sample size compared to a multiple regression approach. Much larger sample sizes were required to detect an interaction effect between environmental exposures and paternal age. These findings inform study design and statistical modeling approaches to improve power and reduce sequencing costs for future studies in this area. Crown Copyright © 2018. Published by Elsevier B.V. All rights reserved.

Statistical learning theory for high dimensional prediction: Application to criterion-keyed scale development.

PubMed

Chapman, Benjamin P; Weiss, Alexander; Duberstein, Paul R

2016-12-01

Statistical learning theory (SLT) is the statistical formulation of machine learning theory, a body of analytic methods common in "big data" problems. Regression-based SLT algorithms seek to maximize predictive accuracy for some outcome, given a large pool of potential predictors, without overfitting the sample. Research goals in psychology may sometimes call for high dimensional regression. One example is criterion-keyed scale construction, where a scale with maximal predictive validity must be built from a large item pool. Using this as a working example, we first introduce a core principle of SLT methods: minimization of expected prediction error (EPE). Minimizing EPE is fundamentally different than maximizing the within-sample likelihood, and hinges on building a predictive model of sufficient complexity to predict the outcome well, without undue complexity leading to overfitting. We describe how such models are built and refined via cross-validation. We then illustrate how 3 common SLT algorithms-supervised principal components, regularization, and boosting-can be used to construct a criterion-keyed scale predicting all-cause mortality, using a large personality item pool within a population cohort. Each algorithm illustrates a different approach to minimizing EPE. Finally, we consider broader applications of SLT predictive algorithms, both as supportive analytic tools for conventional methods, and as primary analytic tools in discovery phase research. We conclude that despite their differences from the classic null-hypothesis testing approach-or perhaps because of them-SLT methods may hold value as a statistically rigorous approach to exploratory regression. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Regional regression of flood characteristics employing historical information

USGS Publications Warehouse

Tasker, Gary D.; Stedinger, J.R.

1987-01-01

Streamflow gauging networks provide hydrologic information for use in estimating the parameters of regional regression models. The regional regression models can be used to estimate flood statistics, such as the 100 yr peak, at ungauged sites as functions of drainage basin characteristics. A recent innovation in regional regression is the use of a generalized least squares (GLS) estimator that accounts for unequal station record lengths and sample cross correlation among the flows. However, this technique does not account for historical flood information. A method is proposed here to adjust this generalized least squares estimator to account for possible information about historical floods available at some stations in a region. The historical information is assumed to be in the form of observations of all peaks above a threshold during a long period outside the systematic record period. A Monte Carlo simulation experiment was performed to compare the GLS estimator adjusted for historical floods with the unadjusted GLS estimator and the ordinary least squares estimator. Results indicate that using the GLS estimator adjusted for historical information significantly improves the regression model. ?? 1987.

Modeling the milling tool wear by using an evolutionary SVM-based model from milling runs experimental data

NASA Astrophysics Data System (ADS)

Nieto, Paulino José García; García-Gonzalo, Esperanza; Vilán, José Antonio Vilán; Robleda, Abraham Segade

2015-12-01

The main aim of this research work is to build a new practical hybrid regression model to predict the milling tool wear in a regular cut as well as entry cut and exit cut of a milling tool. The model was based on Particle Swarm Optimization (PSO) in combination with support vector machines (SVMs). This optimization mechanism involved kernel parameter setting in the SVM training procedure, which significantly influences the regression accuracy. Bearing this in mind, a PSO-SVM-based model, which is based on the statistical learning theory, was successfully used here to predict the milling tool flank wear (output variable) as a function of the following input variables: the time duration of experiment, depth of cut, feed, type of material, etc. To accomplish the objective of this study, the experimental dataset represents experiments from runs on a milling machine under various operating conditions. In this way, data sampled by three different types of sensors (acoustic emission sensor, vibration sensor and current sensor) were acquired at several positions. A second aim is to determine the factors with the greatest bearing on the milling tool flank wear with a view to proposing milling machine's improvements. Firstly, this hybrid PSO-SVM-based regression model captures the main perception of statistical learning theory in order to obtain a good prediction of the dependence among the flank wear (output variable) and input variables (time, depth of cut, feed, etc.). Indeed, regression with optimal hyperparameters was performed and a determination coefficient of 0.95 was obtained. The agreement of this model with experimental data confirmed its good performance. Secondly, the main advantages of this PSO-SVM-based model are its capacity to produce a simple, easy-to-interpret model, its ability to estimate the contributions of the input variables, and its computational efficiency. Finally, the main conclusions of this study are exposed.

The Development of Statistical Models for Predicting Surgical Site Infections in Japan: Toward a Statistical Model-Based Standardized Infection Ratio.

PubMed

Fukuda, Haruhisa; Kuroki, Manabu

2016-03-01

To develop and internally validate a surgical site infection (SSI) prediction model for Japan. Retrospective observational cohort study. We analyzed surveillance data submitted to the Japan Nosocomial Infections Surveillance system for patients who had undergone target surgical procedures from January 1, 2010, through December 31, 2012. Logistic regression analyses were used to develop statistical models for predicting SSIs. An SSI prediction model was constructed for each of the procedure categories by statistically selecting the appropriate risk factors from among the collected surveillance data and determining their optimal categorization. Standard bootstrapping techniques were applied to assess potential overfitting. The C-index was used to compare the predictive performances of the new statistical models with those of models based on conventional risk index variables. The study sample comprised 349,987 cases from 428 participant hospitals throughout Japan, and the overall SSI incidence was 7.0%. The C-indices of the new statistical models were significantly higher than those of the conventional risk index models in 21 (67.7%) of the 31 procedure categories (P<.05). No significant overfitting was detected. Japan-specific SSI prediction models were shown to generally have higher accuracy than conventional risk index models. These new models may have applications in assessing hospital performance and identifying high-risk patients in specific procedure categories.

Comparison of two landslide susceptibility assessments in the Champagne-Ardenne region (France)

NASA Astrophysics Data System (ADS)

Den Eeckhaut, M. Van; Marre, A.; Poesen, J.

2010-02-01

The vineyards of the Montagne de Reims are mostly planted on steep south-oriented cuesta fronts receiving a maximum of sun radiation. Due to the location of the vineyards on steep hillslopes, the viticultural activity is threatened by slope failures. This study attempts to better understand the spatial patterns of landslide susceptibility in the Champagne-Ardenne region by comparing a heuristic (qualitative) and a statistical (quantitative) model in a 1120 km² study area. The heuristic landslide susceptibility model was adopted from the Bureau de Recherches Géologiques et Minières, the GEGEAA - Reims University and the Comité Interprofessionnel du Vin de Champagne. In this model, expert knowledge of the region was used to assign weights to all slope classes and lithologies present in the area, but the final susceptibility map was never evaluated with the location of mapped landslides. For the statistical landslide susceptibility assessment, logistic regression was applied to a dataset of 291 'old' (Holocene) landslides. The robustness of the logistic regression model was evaluated and ROC curves were used for model calibration and validation. With regard to the variables assumed to be important environmental factors controlling landslides, the two models are in agreement. They both indicate that present and future landslides are mainly controlled by slope gradient and lithology. However, the comparison of the two landslide susceptibility maps through (1) an evaluation with the location of mapped 'old' landslides and through (2) a temporal validation with spatial data of 'recent' (1960-1999; n = 48) and 'very recent' (2000-2008; n = 46) landslides showed a better prediction capacity for the statistical model produced in this study compared to the heuristic model. In total, the statistically-derived landslide susceptibility map succeeded in correctly classifying 81.0% of the 'old' and 91.6% of the 'recent' and 'very recent' landslides. On the susceptibility map derived from the heuristic model, on the other hand, only 54.6% of the 'old' and 64.0% of the 'recent' and 'very recent' landslides were correctly classified as unstable. Hence, the landslide susceptibility map obtained from logistic regression is a better tool for regional landslide susceptibility analysis in the study area of the Montagne de Reims. The accurate classification of zones with very high and high susceptibility allows delineating zones where viticulturists should be informed and where implementation of precaution measures is needed to secure slope stability.

Alternative Regression Equations for Estimation of Annual Peak-Streamflow Frequency for Undeveloped Watersheds in Texas using PRESS Minimization

USGS Publications Warehouse

Asquith, William H.; Thompson, David B.

2008-01-01

The U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, investigated a refinement of the regional regression method and developed alternative equations for estimation of peak-streamflow frequency for undeveloped watersheds in Texas. A common model for estimation of peak-streamflow frequency is based on the regional regression method. The current (2008) regional regression equations for 11 regions of Texas are based on log10 transformations of all regression variables (drainage area, main-channel slope, and watershed shape). Exclusive use of log10-transformation does not fully linearize the relations between the variables. As a result, some systematic bias remains in the current equations. The bias results in overestimation of peak streamflow for both the smallest and largest watersheds. The bias increases with increasing recurrence interval. The primary source of the bias is the discernible curvilinear relation in log10 space between peak streamflow and drainage area. Bias is demonstrated by selected residual plots with superimposed LOWESS trend lines. To address the bias, a statistical framework based on minimization of the PRESS statistic through power transformation of drainage area is described and implemented, and the resulting regression equations are reported. Compared to log10-exclusive equations, the equations derived from PRESS minimization have PRESS statistics and residual standard errors less than the log10 exclusive equations. Selected residual plots for the PRESS-minimized equations are presented to demonstrate that systematic bias in regional regression equations for peak-streamflow frequency estimation in Texas can be reduced. Because the overall error is similar to the error associated with previous equations and because the bias is reduced, the PRESS-minimized equations reported here provide alternative equations for peak-streamflow frequency estimation.

Models for predicting the mass of lime fruits by some engineering properties.

PubMed

Miraei Ashtiani, Seyed-Hassan; Baradaran Motie, Jalal; Emadi, Bagher; Aghkhani, Mohammad-Hosein

2014-11-01

Grading fruits based on mass is important in packaging and reduces the waste, also increases the marketing value of agricultural produce. The aim of this study was mass modeling of two major cultivars of Iranian limes based on engineering attributes. Models were classified into three: 1-Single and multiple variable regressions of lime mass and dimensional characteristics. 2-Single and multiple variable regressions of lime mass and projected areas. 3-Single regression of lime mass based on its actual volume and calculated volume assumed as ellipsoid and prolate spheroid shapes. All properties considered in the current study were found to be statistically significant (ρ < 0.01). The results indicated that mass modeling of lime based on minor diameter and first projected area are the most appropriate models in the first and the second classifications, respectively. In third classification, the best model was obtained on the basis of the prolate spheroid volume. It was finally concluded that the suitable grading system of lime mass is based on prolate spheroid volume.

Innovating patient care delivery: DSRIP's interrupted time series analysis paradigm.

PubMed

Shenoy, Amrita G; Begley, Charles E; Revere, Lee; Linder, Stephen H; Daiger, Stephen P

2017-12-08

Adoption of Medicaid Section 1115 waiver is one of the many ways of innovating healthcare delivery system. The Delivery System Reform Incentive Payment (DSRIP) pool, one of the two funding pools of the waiver has four categories viz. infrastructure development, program innovation and redesign, quality improvement reporting and lastly, bringing about population health improvement. A metric of the fourth category, preventable hospitalization (PH) rate was analyzed in the context of eight conditions for two time periods, pre-reporting years (2010-2012) and post-reporting years (2013-2015) for two hospital cohorts, DSRIP participating and non-participating hospitals. The study explains how DSRIP impacted Preventable Hospitalization (PH) rates of eight conditions for both hospital cohorts within two time periods. Eight PH rates were regressed as the dependent variable with time, intervention and post-DSRIP Intervention as independent variables. PH rates of eight conditions were then consolidated into one rate for regressing with the above independent variables to evaluate overall impact of DSRIP. An interrupted time series regression was performed after accounting for auto-correlation, stationarity and seasonality in the dataset. In the individual regression model, PH rates showed statistically significant coefficients for seven out of eight conditions in DSRIP participating hospitals. In the combined regression model, the coefficient of the PH rate showed a statistically significant decrease with negative p-values for regression coefficients in DSRIP participating hospitals compared to positive/increased p-values for regression coefficients in DSRIP non-participating hospitals. Several macro- and micro-level factors may have likely contributed DSRIP hospitals outperforming DSRIP non-participating hospitals. Healthcare organization/provider collaboration, support from healthcare professionals, DSRIP's design, state reimbursement and coordination in care delivery methods may have led to likely success of DSRIP. IV, a retrospective cohort study based on longitudinal data. Copyright © 2017 Elsevier Inc. All rights reserved.

A statistical learning framework for groundwater nitrate models of the Central Valley, California, USA

USGS Publications Warehouse

Nolan, Bernard T.; Fienen, Michael N.; Lorenz, David L.

2015-01-01

We used a statistical learning framework to evaluate the ability of three machine-learning methods to predict nitrate concentration in shallow groundwater of the Central Valley, California: boosted regression trees (BRT), artificial neural networks (ANN), and Bayesian networks (BN). Machine learning methods can learn complex patterns in the data but because of overfitting may not generalize well to new data. The statistical learning framework involves cross-validation (CV) training and testing data and a separate hold-out data set for model evaluation, with the goal of optimizing predictive performance by controlling for model overfit. The order of prediction performance according to both CV testing R2 and that for the hold-out data set was BRT > BN > ANN. For each method we identified two models based on CV testing results: that with maximum testing R2 and a version with R2 within one standard error of the maximum (the 1SE model). The former yielded CV training R2 values of 0.94–1.0. Cross-validation testing R2 values indicate predictive performance, and these were 0.22–0.39 for the maximum R2 models and 0.19–0.36 for the 1SE models. Evaluation with hold-out data suggested that the 1SE BRT and ANN models predicted better for an independent data set compared with the maximum R2 versions, which is relevant to extrapolation by mapping. Scatterplots of predicted vs. observed hold-out data obtained for final models helped identify prediction bias, which was fairly pronounced for ANN and BN. Lastly, the models were compared with multiple linear regression (MLR) and a previous random forest regression (RFR) model. Whereas BRT results were comparable to RFR, MLR had low hold-out R2 (0.07) and explained less than half the variation in the training data. Spatial patterns of predictions by the final, 1SE BRT model agreed reasonably well with previously observed patterns of nitrate occurrence in groundwater of the Central Valley.

Pattern Recognition Analysis of Age-Related Retinal Ganglion Cell Signatures in the Human Eye

PubMed Central

Yoshioka, Nayuta; Zangerl, Barbara; Nivison-Smith, Lisa; Khuu, Sieu K.; Jones, Bryan W.; Pfeiffer, Rebecca L.; Marc, Robert E.; Kalloniatis, Michael

2017-01-01

Purpose To characterize macular ganglion cell layer (GCL) changes with age and provide a framework to assess changes in ocular disease. This study used data clustering to analyze macular GCL patterns from optical coherence tomography (OCT) in a large cohort of subjects without ocular disease. Methods Single eyes of 201 patients evaluated at the Centre for Eye Health (Sydney, Australia) were retrospectively enrolled (age range, 20–85); 8 × 8 grid locations obtained from Spectralis OCT macular scans were analyzed with unsupervised classification into statistically separable classes sharing common GCL thickness and change with age. The resulting classes and gridwise data were fitted with linear and segmented linear regression curves. Additionally, normalized data were analyzed to determine regression as a percentage. Accuracy of each model was examined through comparison of predicted 50-year-old equivalent macular GCL thickness for the entire cohort to a true 50-year-old reference cohort. Results Pattern recognition clustered GCL thickness across the macula into five to eight spatially concentric classes. F-test demonstrated segmented linear regression to be the most appropriate model for macular GCL change. The pattern recognition–derived and normalized model revealed less difference between the predicted macular GCL thickness and the reference cohort (average ± SD 0.19 ± 0.92 and −0.30 ± 0.61 μm) than a gridwise model (average ± SD 0.62 ± 1.43 μm). Conclusions Pattern recognition successfully identified statistically separable macular areas that undergo a segmented linear reduction with age. This regression model better predicted macular GCL thickness. The various unique spatial patterns revealed by pattern recognition combined with core GCL thickness data provide a framework to analyze GCL loss in ocular disease. PMID:28632847

Analysis of Sting Balance Calibration Data Using Optimized Regression Models

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert; Bader, Jon B.

2009-01-01

Calibration data of a wind tunnel sting balance was processed using a search algorithm that identifies an optimized regression model for the data analysis. The selected sting balance had two moment gages that were mounted forward and aft of the balance moment center. The difference and the sum of the two gage outputs were fitted in the least squares sense using the normal force and the pitching moment at the balance moment center as independent variables. The regression model search algorithm predicted that the difference of the gage outputs should be modeled using the intercept and the normal force. The sum of the two gage outputs, on the other hand, should be modeled using the intercept, the pitching moment, and the square of the pitching moment. Equations of the deflection of a cantilever beam are used to show that the search algorithm s two recommended math models can also be obtained after performing a rigorous theoretical analysis of the deflection of the sting balance under load. The analysis of the sting balance calibration data set is a rare example of a situation when regression models of balance calibration data can directly be derived from first principles of physics and engineering. In addition, it is interesting to see that the search algorithm recommended the same regression models for the data analysis using only a set of statistical quality metrics.

Logistic regression analysis of conventional ultrasonography, strain elastosonography, and contrast-enhanced ultrasound characteristics for the differentiation of benign and malignant thyroid nodules

PubMed Central

Deng, Yingyuan; Wang, Tianfu; Chen, Siping; Liu, Weixiang

2017-01-01

The aim of the study is to screen the significant sonographic features by logistic regression analysis and fit a model to diagnose thyroid nodules. A total of 525 pathological thyroid nodules were retrospectively analyzed. All the nodules underwent conventional ultrasonography (US), strain elastosonography (SE), and contrast -enhanced ultrasound (CEUS). Those nodules’ 12 suspicious sonographic features were used to assess thyroid nodules. The significant features of diagnosing thyroid nodules were picked out by logistic regression analysis. All variables that were statistically related to diagnosis of thyroid nodules, at a level of p < 0.05 were embodied in a logistic regression analysis model. The significant features in the logistic regression model of diagnosing thyroid nodules were calcification, suspected cervical lymph node metastasis, hypoenhancement pattern, margin, shape, vascularity, posterior acoustic, echogenicity, and elastography score. According to the results of logistic regression analysis, the formula that could predict whether or not thyroid nodules are malignant was established. The area under the receiver operating curve (ROC) was 0.930 and the sensitivity, specificity, accuracy, positive predictive value, and negative predictive value were 83.77%, 89.56%, 87.05%, 86.04%, and 87.79% respectively. PMID:29228030

Logistic regression analysis of conventional ultrasonography, strain elastosonography, and contrast-enhanced ultrasound characteristics for the differentiation of benign and malignant thyroid nodules.

PubMed

Pang, Tiantian; Huang, Leidan; Deng, Yingyuan; Wang, Tianfu; Chen, Siping; Gong, Xuehao; Liu, Weixiang

2017-01-01

The aim of the study is to screen the significant sonographic features by logistic regression analysis and fit a model to diagnose thyroid nodules. A total of 525 pathological thyroid nodules were retrospectively analyzed. All the nodules underwent conventional ultrasonography (US), strain elastosonography (SE), and contrast -enhanced ultrasound (CEUS). Those nodules' 12 suspicious sonographic features were used to assess thyroid nodules. The significant features of diagnosing thyroid nodules were picked out by logistic regression analysis. All variables that were statistically related to diagnosis of thyroid nodules, at a level of p < 0.05 were embodied in a logistic regression analysis model. The significant features in the logistic regression model of diagnosing thyroid nodules were calcification, suspected cervical lymph node metastasis, hypoenhancement pattern, margin, shape, vascularity, posterior acoustic, echogenicity, and elastography score. According to the results of logistic regression analysis, the formula that could predict whether or not thyroid nodules are malignant was established. The area under the receiver operating curve (ROC) was 0.930 and the sensitivity, specificity, accuracy, positive predictive value, and negative predictive value were 83.77%, 89.56%, 87.05%, 86.04%, and 87.79% respectively.

Sentinel node status prediction by four statistical models: results from a large bi-institutional series (n = 1132).

PubMed

Mocellin, Simone; Thompson, John F; Pasquali, Sandro; Montesco, Maria C; Pilati, Pierluigi; Nitti, Donato; Saw, Robyn P; Scolyer, Richard A; Stretch, Jonathan R; Rossi, Carlo R

2009-12-01

To improve selection for sentinel node (SN) biopsy (SNB) in patients with cutaneous melanoma using statistical models predicting SN status. About 80% of patients currently undergoing SNB are node negative. In the absence of conclusive evidence of a SNBassociated survival benefit, these patients may be over-treated. Here, we tested the efficiency of 4 different models in predicting SN status. The clinicopathologic data (age, gender, tumor thickness, Clark level, regression, ulceration, histologic subtype, and mitotic index) of 1132 melanoma patients who had undergone SNB at institutions in Italy and Australia were analyzed. Logistic regression, classification tree, random forest, and support vector machine models were fitted to the data. The predictive models were built with the aim of maximizing the negative predictive value (NPV) and reducing the rate of SNB procedures though minimizing the error rate. After cross-validation logistic regression, classification tree, random forest, and support vector machine predictive models obtained clinically relevant NPV (93.6%, 94.0%, 97.1%, and 93.0%, respectively), SNB reduction (27.5%, 29.8%, 18.2%, and 30.1%, respectively), and error rates (1.8%, 1.8%, 0.5%, and 2.1%, respectively). Using commonly available clinicopathologic variables, predictive models can preoperatively identify a proportion of patients ( approximately 25%) who might be spared SNB, with an acceptable (1%-2%) error. If validated in large prospective series, these models might be implemented in the clinical setting for improved patient selection, which ultimately would lead to better quality of life for patients and optimization of resource allocation for the health care system.

A novel variational Bayes multiple locus Z-statistic for genome-wide association studies with Bayesian model averaging

PubMed Central

Logsdon, Benjamin A.; Carty, Cara L.; Reiner, Alexander P.; Dai, James Y.; Kooperberg, Charles

2012-01-01

Motivation: For many complex traits, including height, the majority of variants identified by genome-wide association studies (GWAS) have small effects, leaving a significant proportion of the heritable variation unexplained. Although many penalized multiple regression methodologies have been proposed to increase the power to detect associations for complex genetic architectures, they generally lack mechanisms for false-positive control and diagnostics for model over-fitting. Our methodology is the first penalized multiple regression approach that explicitly controls Type I error rates and provide model over-fitting diagnostics through a novel normally distributed statistic defined for every marker within the GWAS, based on results from a variational Bayes spike regression algorithm. Results: We compare the performance of our method to the lasso and single marker analysis on simulated data and demonstrate that our approach has superior performance in terms of power and Type I error control. In addition, using the Women's Health Initiative (WHI) SNP Health Association Resource (SHARe) GWAS of African-Americans, we show that our method has power to detect additional novel associations with body height. These findings replicate by reaching a stringent cutoff of marginal association in a larger cohort. Availability: An R-package, including an implementation of our variational Bayes spike regression (vBsr) algorithm, is available at http://kooperberg.fhcrc.org/soft.html. Contact: blogsdon@fhcrc.org Supplementary information: Supplementary data are available at Bioinformatics online. PMID:22563072

Statistical considerations in the development of injury risk functions.

PubMed

McMurry, Timothy L; Poplin, Gerald S

2015-01-01

We address 4 frequently misunderstood and important statistical ideas in the construction of injury risk functions. These include the similarities of survival analysis and logistic regression, the correct scale on which to construct pointwise confidence intervals for injury risk, the ability to discern which form of injury risk function is optimal, and the handling of repeated tests on the same subject. The statistical models are explored through simulation and examination of the underlying mathematics. We provide recommendations for the statistically valid construction and correct interpretation of single-predictor injury risk functions. This article aims to provide useful and understandable statistical guidance to improve the practice in constructing injury risk functions.

A comparison of time dependent Cox regression, pooled logistic regression and cross sectional pooling with simulations and an application to the Framingham Heart Study.

PubMed

Ngwa, Julius S; Cabral, Howard J; Cheng, Debbie M; Pencina, Michael J; Gagnon, David R; LaValley, Michael P; Cupples, L Adrienne

2016-11-03

Typical survival studies follow individuals to an event and measure explanatory variables for that event, sometimes repeatedly over the course of follow up. The Cox regression model has been used widely in the analyses of time to diagnosis or death from disease. The associations between the survival outcome and time dependent measures may be biased unless they are modeled appropriately. In this paper we explore the Time Dependent Cox Regression Model (TDCM), which quantifies the effect of repeated measures of covariates in the analysis of time to event data. This model is commonly used in biomedical research but sometimes does not explicitly adjust for the times at which time dependent explanatory variables are measured. This approach can yield different estimates of association compared to a model that adjusts for these times. In order to address the question of how different these estimates are from a statistical perspective, we compare the TDCM to Pooled Logistic Regression (PLR) and Cross Sectional Pooling (CSP), considering models that adjust and do not adjust for time in PLR and CSP. In a series of simulations we found that time adjusted CSP provided identical results to the TDCM while the PLR showed larger parameter estimates compared to the time adjusted CSP and the TDCM in scenarios with high event rates. We also observed upwardly biased estimates in the unadjusted CSP and unadjusted PLR methods. The time adjusted PLR had a positive bias in the time dependent Age effect with reduced bias when the event rate is low. The PLR methods showed a negative bias in the Sex effect, a subject level covariate, when compared to the other methods. The Cox models yielded reliable estimates for the Sex effect in all scenarios considered. We conclude that survival analyses that explicitly account in the statistical model for the times at which time dependent covariates are measured provide more reliable estimates compared to unadjusted analyses. We present results from the Framingham Heart Study in which lipid measurements and myocardial infarction data events were collected over a period of 26 years.

Prediction of rainfall anomalies during the dry to wet transition season over the Southern Amazonia using machine learning tools

NASA Astrophysics Data System (ADS)

Shan, X.; Zhang, K.; Zhuang, Y.; Fu, R.; Hong, Y.

2017-12-01

Seasonal prediction of rainfall during the dry-to-wet transition season in austral spring (September-November) over southern Amazonia is central for improving planting crops and fire mitigation in that region. Previous studies have identified the key large-scale atmospheric dynamic and thermodynamics pre-conditions during the dry season (June-August) that influence the rainfall anomalies during the dry to wet transition season over Southern Amazonia. Based on these key pre-conditions during dry season, we have evaluated several statistical models and developed a Neural Network based statistical prediction system to predict rainfall during the dry to wet transition for Southern Amazonia (5-15°S, 50-70°W). Multivariate Empirical Orthogonal Function (EOF) Analysis is applied to the following four fields during JJA from the ECMWF Reanalysis (ERA-Interim) spanning from year 1979 to 2015: geopotential height at 200 hPa, surface relative humidity, convective inhibition energy (CIN) index and convective available potential energy (CAPE), to filter out noise and highlight the most coherent spatial and temporal variations. The first 10 EOF modes are retained for inputs to the statistical models, accounting for at least 70% of the total variance in the predictor fields. We have tested several linear and non-linear statistical methods. While the regularized Ridge Regression and Lasso Regression can generally capture the spatial pattern and magnitude of rainfall anomalies, we found that that Neural Network performs best with an accuracy greater than 80%, as expected from the non-linear dependence of the rainfall on the large-scale atmospheric thermodynamic conditions and circulation. Further tests of various prediction skill metrics and hindcasts also suggest this Neural Network prediction approach can significantly improve seasonal prediction skill than the dynamic predictions and regression based statistical predictions. Thus, this statistical prediction system could have shown potential to improve real-time seasonal rainfall predictions in the future.

Endoscopic third ventriculostomy in the treatment of childhood hydrocephalus.

PubMed

Kulkarni, Abhaya V; Drake, James M; Mallucci, Conor L; Sgouros, Spyros; Roth, Jonathan; Constantini, Shlomi

2009-08-01

To develop a model to predict the probability of endoscopic third ventriculostomy (ETV) success in the treatment for hydrocephalus on the basis of a child's individual characteristics. We analyzed 618 ETVs performed consecutively on children at 12 international institutions to identify predictors of ETV success at 6 months. A multivariable logistic regression model was developed on 70% of the dataset (training set) and validated on 30% of the dataset (validation set). In the training set, 305/455 ETVs (67.0%) were successful. The regression model (containing patient age, cause of hydrocephalus, and previous cerebrospinal fluid shunt) demonstrated good fit (Hosmer-Lemeshow, P = .78) and discrimination (C statistic = 0.70). In the validation set, 105/163 ETVs (64.4%) were successful and the model maintained good fit (Hosmer-Lemeshow, P = .45), discrimination (C statistic = 0.68), and calibration (calibration slope = 0.88). A simplified ETV Success Score was devised that closely approximates the predicted probability of ETV success. Children most likely to succeed with ETV can now be accurately identified and spared the long-term complications of CSF shunting.

Does money matter in inflation forecasting?

NASA Astrophysics Data System (ADS)

Binner, J. M.; Tino, P.; Tepper, J.; Anderson, R.; Jones, B.; Kendall, G.

2010-11-01

This paper provides the most fully comprehensive evidence to date on whether or not monetary aggregates are valuable for forecasting US inflation in the early to mid 2000s. We explore a wide range of different definitions of money, including different methods of aggregation and different collections of included monetary assets. In our forecasting experiment we use two nonlinear techniques, namely, recurrent neural networks and kernel recursive least squares regression-techniques that are new to macroeconomics. Recurrent neural networks operate with potentially unbounded input memory, while the kernel regression technique is a finite memory predictor. The two methodologies compete to find the best fitting US inflation forecasting models and are then compared to forecasts from a naïve random walk model. The best models were nonlinear autoregressive models based on kernel methods. Our findings do not provide much support for the usefulness of monetary aggregates in forecasting inflation. Beyond its economic findings, our study is in the tradition of physicists’ long-standing interest in the interconnections among statistical mechanics, neural networks, and related nonparametric statistical methods, and suggests potential avenues of extension for such studies.

On statistical analysis of factors affecting anthocyanin extraction from Ixora siamensis

NASA Astrophysics Data System (ADS)

Mat Nor, N. A.; Arof, A. K.

2016-10-01

This study focused on designing an experimental model in order to evaluate the influence of operative extraction parameters employed for anthocyanin extraction from Ixora siamensis on CIE color measurements (a*, b* and color saturation). Extractions were conducted at temperatures of 30, 55 and 80°C, soaking time of 60, 120 and 180 min using acidified methanol solvent with different trifluoroacetic acid (TFA) contents of 0.5, 1.75 and 3% (v/v). The statistical evaluation was performed by running analysis of variance (ANOVA) and regression calculation to investigate the significance of the generated model. Results show that the generated regression models adequately explain the data variation and significantly represented the actual relationship between the independent variables and the responses. Analysis of variance (ANOVA) showed high coefficient determination values (R2) of 0.9687 for a*, 0.9621 for b* and 0.9758 for color saturation, thus ensuring a satisfactory fit of the developed models with the experimental data. Interaction between TFA content and extraction temperature exhibited to the highest significant influence on CIE color parameter.

Modeling Antimicrobial Activity of Clorox(R) Using an Agar-Diffusion Test: A New Twist On an Old Experiment.

ERIC Educational Resources Information Center

Mitchell, James K.; Carter, William E.

2000-01-01

Describes using a computer statistical software package called Minitab to model the sensitivity of several microbes to the disinfectant NaOCl (Clorox') using the Kirby-Bauer technique. Each group of students collects data from one microbe, conducts regression analyses, then chooses the best-fit model based on the highest r-values obtained.…

Model Selection and Psychological Theory: A Discussion of the Differences between the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)

ERIC Educational Resources Information Center

Vrieze, Scott I.

2012-01-01

This article reviews the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in model selection and the appraisal of psychological theory. The focus is on latent variable models, given their growing use in theory testing and construction. Theoretical statistical results in regression are discussed, and more important…

Application of Bayesian methods to habitat selection modeling of the northern spotted owl in California: new statistical methods for wildlife research

Treesearch

Howard B. Stauffer; Cynthia J. Zabel; Jeffrey R. Dunk

2005-01-01

We compared a set of competing logistic regression habitat selection models for Northern Spotted Owls (Strix occidentalis caurina) in California. The habitat selection models were estimated, compared, evaluated, and tested using multiple sample datasets collected on federal forestlands in northern California. We used Bayesian methods in interpreting...

Can air temperature be used to project influences of climate change on stream temperature?

Treesearch

Ivan Arismendi; Mohammad Safeeq; Jason B Dunham; Sherri L Johnson

2014-01-01

Worldwide, lack of data on stream temperature has motivated the use of regression-based statistical models to predict stream temperatures based on more widely available data on air temperatures. Such models have been widely applied to project responses of stream temperatures under climate change, but the performance of these models has not been fully evaluated. To...

[Regression on order statistics and its application in estimating nondetects for food exposure assessment].

PubMed

Yu, Xiaojin; Liu, Pei; Min, Jie; Chen, Qiguang

2009-01-01

To explore the application of regression on order statistics (ROS) in estimating nondetects for food exposure assessment. Regression on order statistics was adopted in analysis of cadmium residual data set from global food contaminant monitoring, the mean residual was estimated basing SAS programming and compared with the results from substitution methods. The results show that ROS method performs better obviously than substitution methods for being robust and convenient for posterior analysis. Regression on order statistics is worth to adopt,but more efforts should be make for details of application of this method.

Groundwater-level prediction using multiple linear regression and artificial neural network techniques: a comparative assessment

NASA Astrophysics Data System (ADS)

Sahoo, Sasmita; Jha, Madan K.

2013-12-01

The potential of multiple linear regression (MLR) and artificial neural network (ANN) techniques in predicting transient water levels over a groundwater basin were compared. MLR and ANN modeling was carried out at 17 sites in Japan, considering all significant inputs: rainfall, ambient temperature, river stage, 11 seasonal dummy variables, and influential lags of rainfall, ambient temperature, river stage and groundwater level. Seventeen site-specific ANN models were developed, using multi-layer feed-forward neural networks trained with Levenberg-Marquardt backpropagation algorithms. The performance of the models was evaluated using statistical and graphical indicators. Comparison of the goodness-of-fit statistics of the MLR models with those of the ANN models indicated that there is better agreement between the ANN-predicted groundwater levels and the observed groundwater levels at all the sites, compared to the MLR. This finding was supported by the graphical indicators and the residual analysis. Thus, it is concluded that the ANN technique is superior to the MLR technique in predicting spatio-temporal distribution of groundwater levels in a basin. However, considering the practical advantages of the MLR technique, it is recommended as an alternative and cost-effective groundwater modeling tool.

3D statistical shape models incorporating 3D random forest regression voting for robust CT liver segmentation

NASA Astrophysics Data System (ADS)

Norajitra, Tobias; Meinzer, Hans-Peter; Maier-Hein, Klaus H.

2015-03-01

During image segmentation, 3D Statistical Shape Models (SSM) usually conduct a limited search for target landmarks within one-dimensional search profiles perpendicular to the model surface. In addition, landmark appearance is modeled only locally based on linear profiles and weak learners, altogether leading to segmentation errors from landmark ambiguities and limited search coverage. We present a new method for 3D SSM segmentation based on 3D Random Forest Regression Voting. For each surface landmark, a Random Regression Forest is trained that learns a 3D spatial displacement function between the according reference landmark and a set of surrounding sample points, based on an infinite set of non-local randomized 3D Haar-like features. Landmark search is then conducted omni-directionally within 3D search spaces, where voxelwise forest predictions on landmark position contribute to a common voting map which reflects the overall position estimate. Segmentation experiments were conducted on a set of 45 CT volumes of the human liver, of which 40 images were randomly chosen for training and 5 for testing. Without parameter optimization, using a simple candidate selection and a single resolution approach, excellent results were achieved, while faster convergence and better concavity segmentation were observed, altogether underlining the potential of our approach in terms of increased robustness from distinct landmark detection and from better search coverage.

A land use regression model for ambient ultrafine particles in Montreal, Canada: A comparison of linear regression and a machine learning approach.

PubMed

Weichenthal, Scott; Ryswyk, Keith Van; Goldstein, Alon; Bagg, Scott; Shekkarizfard, Maryam; Hatzopoulou, Marianne

2016-04-01

Existing evidence suggests that ambient ultrafine particles (UFPs) (<0.1µm) may contribute to acute cardiorespiratory morbidity. However, few studies have examined the long-term health effects of these pollutants owing in part to a need for exposure surfaces that can be applied in large population-based studies. To address this need, we developed a land use regression model for UFPs in Montreal, Canada using mobile monitoring data collected from 414 road segments during the summer and winter months between 2011 and 2012. Two different approaches were examined for model development including standard multivariable linear regression and a machine learning approach (kernel-based regularized least squares (KRLS)) that learns the functional form of covariate impacts on ambient UFP concentrations from the data. The final models included parameters for population density, ambient temperature and wind speed, land use parameters (park space and open space), length of local roads and rail, and estimated annual average NOx emissions from traffic. The final multivariable linear regression model explained 62% of the spatial variation in ambient UFP concentrations whereas the KRLS model explained 79% of the variance. The KRLS model performed slightly better than the linear regression model when evaluated using an external dataset (R(2)=0.58 vs. 0.55) or a cross-validation procedure (R(2)=0.67 vs. 0.60). In general, our findings suggest that the KRLS approach may offer modest improvements in predictive performance compared to standard multivariable linear regression models used to estimate spatial variations in ambient UFPs. However, differences in predictive performance were not statistically significant when evaluated using the cross-validation procedure. Crown Copyright © 2015. Published by Elsevier Inc. All rights reserved.

Development of hybrid genetic-algorithm-based neural networks using regression trees for modeling air quality inside a public transportation bus.

PubMed

Kadiyala, Akhil; Kaur, Devinder; Kumar, Ashok

2013-02-01

The present study developed a novel approach to modeling indoor air quality (IAQ) of a public transportation bus by the development of hybrid genetic-algorithm-based neural networks (also known as evolutionary neural networks) with input variables optimized from using the regression trees, referred as the GART approach. This study validated the applicability of the GART modeling approach in solving complex nonlinear systems by accurately predicting the monitored contaminants of carbon dioxide (CO2), carbon monoxide (CO), nitric oxide (NO), sulfur dioxide (SO2), 0.3-0.4 microm sized particle numbers, 0.4-0.5 microm sized particle numbers, particulate matter (PM) concentrations less than 1.0 microm (PM10), and PM concentrations less than 2.5 microm (PM2.5) inside a public transportation bus operating on 20% grade biodiesel in Toledo, OH. First, the important variables affecting each monitored in-bus contaminant were determined using regression trees. Second, the analysis of variance was used as a complimentary sensitivity analysis to the regression tree results to determine a subset of statistically significant variables affecting each monitored in-bus contaminant. Finally, the identified subsets of statistically significant variables were used as inputs to develop three artificial neural network (ANN) models. The models developed were regression tree-based back-propagation network (BPN-RT), regression tree-based radial basis function network (RBFN-RT), and GART models. Performance measures were used to validate the predictive capacity of the developed IAQ models. The results from this approach were compared with the results obtained from using a theoretical approach and a generalized practicable approach to modeling IAQ that included the consideration of additional independent variables when developing the aforementioned ANN models. The hybrid GART models were able to capture majority of the variance in the monitored in-bus contaminants. The genetic-algorithm-based neural network IAQ models outperformed the traditional ANN methods of the back-propagation and the radial basis function networks. The novelty of this research is the development of a novel approach to modeling vehicular indoor air quality by integration of the advanced methods of genetic algorithms, regression trees, and the analysis of variance for the monitored in-vehicle gaseous and particulate matter contaminants, and comparing the results obtained from using the developed approach with conventional artificial intelligence techniques of back propagation networks and radial basis function networks. This study validated the newly developed approach using holdout and threefold cross-validation methods. These results are of great interest to scientists, researchers, and the public in understanding the various aspects of modeling an indoor microenvironment. This methodology can easily be extended to other fields of study also.

Statistically Modeling I-V Characteristics of CNT-FET with LASSO

NASA Astrophysics Data System (ADS)

Ma, Dongsheng; Ye, Zuochang; Wang, Yan

2017-08-01

With the advent of internet of things (IOT), the need for studying new material and devices for various applications is increasing. Traditionally we build compact models for transistors on the basis of physics. But physical models are expensive and need a very long time to adjust for non-ideal effects. As the vision for the application of many novel devices is not certain or the manufacture process is not mature, deriving generalized accurate physical models for such devices is very strenuous, whereas statistical modeling is becoming a potential method because of its data oriented property and fast implementation. In this paper, one classical statistical regression method, LASSO, is used to model the I-V characteristics of CNT-FET and a pseudo-PMOS inverter simulation based on the trained model is implemented in Cadence. The normalized relative mean square prediction error of the trained model versus experiment sample data and the simulation results show that the model is acceptable for digital circuit static simulation. And such modeling methodology can extend to general devices.

Fluctuations in air pollution give risk warning signals of asthma hospitalization

NASA Astrophysics Data System (ADS)

Hsieh, Nan-Hung; Liao, Chung-Min

2013-08-01

Recent studies have implicated that air pollution has been associated with asthma exacerbations. However, the key link between specific air pollutant and the consequent impact on asthma has not been shown. The purpose of this study was to quantify the fluctuations in air pollution time-series dynamics to correlate the relationships between statistical indicators and age-specific asthma hospital admissions. An indicators-based regression model was developed to predict the time-trend of asthma hospital admissions in Taiwan in the period 1998-2010. Five major pollutants such as particulate matters with aerodynamic diameter less than 10 μm (PM10), ozone (O3), nitrogen dioxide (NO2), sulfur dioxide (SO2), and carbon monoxide (CO) were included. We used Spearman's rank correlation to detect the relationships between time-series based statistical indicators of standard deviation, coefficient of variation, skewness, and kurtosis and monthly asthma hospitalization. We further used the indicators-guided Poisson regression model to test and predict the impact of target air pollutants on asthma incidence. Here we showed that standard deviation of PM10 data was the most correlated indicators for asthma hospitalization for all age groups, particularly for elderly. The skewness of O3 data gives the highest correlation to adult asthmatics. The proposed regression model shows a better predictability in annual asthma hospitalization trends for pediatrics. Our results suggest that a set of statistical indicators inferred from time-series information of major air pollutants can provide advance risk warning signals in complex air pollution-asthma systems and aid in asthma management that depends heavily on monitoring the dynamics of asthma incidence and environmental stimuli.

Can air temperature be used to project influences of climate change on stream temperature?

USGS Publications Warehouse

Arismendi, Ivan; Safeeq, Mohammad; Dunham, Jason B.; Johnson, Sherri L.

2014-01-01

Worldwide, lack of data on stream temperature has motivated the use of regression-based statistical models to predict stream temperatures based on more widely available data on air temperatures. Such models have been widely applied to project responses of stream temperatures under climate change, but the performance of these models has not been fully evaluated. To address this knowledge gap, we examined the performance of two widely used linear and nonlinear regression models that predict stream temperatures based on air temperatures. We evaluated model performance and temporal stability of model parameters in a suite of regulated and unregulated streams with 11–44 years of stream temperature data. Although such models may have validity when predicting stream temperatures within the span of time that corresponds to the data used to develop them, model predictions did not transfer well to other time periods. Validation of model predictions of most recent stream temperatures, based on air temperature–stream temperature relationships from previous time periods often showed poor performance when compared with observed stream temperatures. Overall, model predictions were less robust in regulated streams and they frequently failed in detecting the coldest and warmest temperatures within all sites. In many cases, the magnitude of errors in these predictions falls within a range that equals or exceeds the magnitude of future projections of climate-related changes in stream temperatures reported for the region we studied (between 0.5 and 3.0 °C by 2080). The limited ability of regression-based statistical models to accurately project stream temperatures over time likely stems from the fact that underlying processes at play, namely the heat budgets of air and water, are distinctive in each medium and vary among localities and through time.

Reflexion on linear regression trip production modelling method for ensuring good model quality

NASA Astrophysics Data System (ADS)

Suprayitno, Hitapriya; Ratnasari, Vita

2017-11-01

Transport Modelling is important. For certain cases, the conventional model still has to be used, in which having a good trip production model is capital. A good model can only be obtained from a good sample. Two of the basic principles of a good sampling is having a sample capable to represent the population characteristics and capable to produce an acceptable error at a certain confidence level. It seems that this principle is not yet quite understood and used in trip production modeling. Therefore, investigating the Trip Production Modelling practice in Indonesia and try to formulate a better modeling method for ensuring the Model Quality is necessary. This research result is presented as follows. Statistics knows a method to calculate span of prediction value at a certain confidence level for linear regression, which is called Confidence Interval of Predicted Value. The common modeling practice uses R2 as the principal quality measure, the sampling practice varies and not always conform to the sampling principles. An experiment indicates that small sample is already capable to give excellent R2 value and sample composition can significantly change the model. Hence, good R2 value, in fact, does not always mean good model quality. These lead to three basic ideas for ensuring good model quality, i.e. reformulating quality measure, calculation procedure, and sampling method. A quality measure is defined as having a good R2 value and a good Confidence Interval of Predicted Value. Calculation procedure must incorporate statistical calculation method and appropriate statistical tests needed. A good sampling method must incorporate random well distributed stratified sampling with a certain minimum number of samples. These three ideas need to be more developed and tested.

Identifying Autocorrelation Generated by Various Error Processes in Interrupted Time-Series Regression Designs: A Comparison of AR1 and Portmanteau Tests

ERIC Educational Resources Information Center

Huitema, Bradley E.; McKean, Joseph W.

2007-01-01

Regression models used in the analysis of interrupted time-series designs assume statistically independent errors. Four methods of evaluating this assumption are the Durbin-Watson (D-W), Huitema-McKean (H-M), Box-Pierce (B-P), and Ljung-Box (L-B) tests. These tests were compared with respect to Type I error and power under a wide variety of error…

Comparison of methods for the analysis of relatively simple mediation models.

PubMed

Rijnhart, Judith J M; Twisk, Jos W R; Chinapaw, Mai J M; de Boer, Michiel R; Heymans, Martijn W

2017-09-01

Statistical mediation analysis is an often used method in trials, to unravel the pathways underlying the effect of an intervention on a particular outcome variable. Throughout the years, several methods have been proposed, such as ordinary least square (OLS) regression, structural equation modeling (SEM), and the potential outcomes framework. Most applied researchers do not know that these methods are mathematically equivalent when applied to mediation models with a continuous mediator and outcome variable. Therefore, the aim of this paper was to demonstrate the similarities between OLS regression, SEM, and the potential outcomes framework in three mediation models: 1) a crude model, 2) a confounder-adjusted model, and 3) a model with an interaction term for exposure-mediator interaction. Secondary data analysis of a randomized controlled trial that included 546 schoolchildren. In our data example, the mediator and outcome variable were both continuous. We compared the estimates of the total, direct and indirect effects, proportion mediated, and 95% confidence intervals (CIs) for the indirect effect across OLS regression, SEM, and the potential outcomes framework. OLS regression, SEM, and the potential outcomes framework yielded the same effect estimates in the crude mediation model, the confounder-adjusted mediation model, and the mediation model with an interaction term for exposure-mediator interaction. Since OLS regression, SEM, and the potential outcomes framework yield the same results in three mediation models with a continuous mediator and outcome variable, researchers can continue using the method that is most convenient to them.

A Method for Calculating the Probability of Successfully Completing a Rocket Propulsion Ground Test

NASA Technical Reports Server (NTRS)

Messer, Bradley

2007-01-01

Propulsion ground test facilities face the daily challenge of scheduling multiple customers into limited facility space and successfully completing their propulsion test projects. Over the last decade NASA s propulsion test facilities have performed hundreds of tests, collected thousands of seconds of test data, and exceeded the capabilities of numerous test facility and test article components. A logistic regression mathematical modeling technique has been developed to predict the probability of successfully completing a rocket propulsion test. A logistic regression model is a mathematical modeling approach that can be used to describe the relationship of several independent predictor variables X(sub 1), X(sub 2),.., X(sub k) to a binary or dichotomous dependent variable Y, where Y can only be one of two possible outcomes, in this case Success or Failure of accomplishing a full duration test. The use of logistic regression modeling is not new; however, modeling propulsion ground test facilities using logistic regression is both a new and unique application of the statistical technique. Results from this type of model provide project managers with insight and confidence into the effectiveness of rocket propulsion ground testing.

Computing mammographic density from a multiple regression model constructed with image-acquisition parameters from a full-field digital mammographic unit

PubMed Central

Lu, Lee-Jane W.; Nishino, Thomas K.; Khamapirad, Tuenchit; Grady, James J; Leonard, Morton H.; Brunder, Donald G.

2009-01-01

Breast density (the percentage of fibroglandular tissue in the breast) has been suggested to be a useful surrogate marker for breast cancer risk. It is conventionally measured using screen-film mammographic images by a labor intensive histogram segmentation method (HSM). We have adapted and modified the HSM for measuring breast density from raw digital mammograms acquired by full-field digital mammography. Multiple regression model analyses showed that many of the instrument parameters for acquiring the screening mammograms (e.g. breast compression thickness, radiological thickness, radiation dose, compression force, etc) and image pixel intensity statistics of the imaged breasts were strong predictors of the observed threshold values (model R2=0.93) and %density (R2=0.84). The intra-class correlation coefficient of the %-density for duplicate images was estimated to be 0.80, using the regression model-derived threshold values, and 0.94 if estimated directly from the parameter estimates of the %-density prediction regression model. Therefore, with additional research, these mathematical models could be used to compute breast density objectively, automatically bypassing the HSM step, and could greatly facilitate breast cancer research studies. PMID:17671343

A controlled experiment in ground water flow model calibration

USGS Publications Warehouse

Hill, M.C.; Cooley, R.L.; Pollock, D.W.

1998-01-01

Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.

Review and statistical analysis of the use of ultrasonic velocity for estimating the porosity fraction in polycrystalline materials

NASA Technical Reports Server (NTRS)

Roth, D. J.; Swickard, S. M.; Stang, D. B.; Deguire, M. R.

1991-01-01

A review and statistical analysis of the ultrasonic velocity method for estimating the porosity fraction in polycrystalline materials is presented. Initially, a semiempirical model is developed showing the origin of the linear relationship between ultrasonic velocity and porosity fraction. Then, from a compilation of data produced by many researchers, scatter plots of velocity versus percent porosity data are shown for Al2O3, MgO, porcelain-based ceramics, PZT, SiC, Si3N4, steel, tungsten, UO2,(U0.30Pu0.70)C, and YBa2Cu3O(7-x). Linear regression analysis produces predicted slope, intercept, correlation coefficient, level of significance, and confidence interval statistics for the data. Velocity values predicted from regression analysis of fully-dense materials are in good agreement with those calculated from elastic properties.

Review and statistical analysis of the ultrasonic velocity method for estimating the porosity fraction in polycrystalline materials

NASA Technical Reports Server (NTRS)

Roth, D. J.; Swickard, S. M.; Stang, D. B.; Deguire, M. R.

1990-01-01

A review and statistical analysis of the ultrasonic velocity method for estimating the porosity fraction in polycrystalline materials is presented. Initially, a semi-empirical model is developed showing the origin of the linear relationship between ultrasonic velocity and porosity fraction. Then, from a compilation of data produced by many researchers, scatter plots of velocity versus percent porosity data are shown for Al2O3, MgO, porcelain-based ceramics, PZT, SiC, Si3N4, steel, tungsten, UO2,(U0.30Pu0.70)C, and YBa2Cu3O(7-x). Linear regression analysis produced predicted slope, intercept, correlation coefficient, level of significance, and confidence interval statistics for the data. Velocity values predicted from regression analysis for fully-dense materials are in good agreement with those calculated from elastic properties.

Statistical Evaluation of Time Series Analysis Techniques

NASA Technical Reports Server (NTRS)

Benignus, V. A.

1973-01-01

The performance of a modified version of NASA's multivariate spectrum analysis program is discussed. A multiple regression model was used to make the revisions. Performance improvements were documented and compared to the standard fast Fourier transform by Monte Carlo techniques.

Predicting exposure-response associations of ambient particulate matter with mortality in 73 Chinese cities.

PubMed

Madaniyazi, Lina; Guo, Yuming; Chen, Renjie; Kan, Haidong; Tong, Shilu

2016-01-01

Estimating the burden of mortality associated with particulates requires knowledge of exposure-response associations. However, the evidence on exposure-response associations is limited in many cities, especially in developing countries. In this study, we predicted associations of particulates smaller than 10 μm in aerodynamic diameter (PM10) with mortality in 73 Chinese cities. The meta-regression model was used to test and quantify which city-specific characteristics contributed significantly to the heterogeneity of PM10-mortality associations for 16 Chinese cities. Then, those city-specific characteristics with statistically significant regression coefficients were treated as independent variables to build multivariate meta-regression models. The model with the best fitness was used to predict PM10-mortality associations in 73 Chinese cities in 2010. Mean temperature, PM10 concentration and green space per capita could best explain the heterogeneity in PM10-mortality associations. Based on city-specific characteristics, we were able to develop multivariate meta-regression models to predict associations between air pollutants and health outcomes reasonably well. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analyzing hospitalization data: potential limitations of Poisson regression.

PubMed

Weaver, Colin G; Ravani, Pietro; Oliver, Matthew J; Austin, Peter C; Quinn, Robert R

2015-08-01

Poisson regression is commonly used to analyze hospitalization data when outcomes are expressed as counts (e.g. number of days in hospital). However, data often violate the assumptions on which Poisson regression is based. More appropriate extensions of this model, while available, are rarely used. We compared hospitalization data between 206 patients treated with hemodialysis (HD) and 107 treated with peritoneal dialysis (PD) using Poisson regression and compared results from standard Poisson regression with those obtained using three other approaches for modeling count data: negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression. We examined the appropriateness of each model and compared the results obtained with each approach. During a mean 1.9 years of follow-up, 183 of 313 patients (58%) were never hospitalized (indicating an excess of 'zeros'). The data also displayed overdispersion (variance greater than mean), violating another assumption of the Poisson model. Using four criteria, we determined that the NB and ZINB models performed best. According to these two models, patients treated with HD experienced similar hospitalization rates as those receiving PD {NB rate ratio (RR): 1.04 [bootstrapped 95% confidence interval (CI): 0.49-2.20]; ZINB summary RR: 1.21 (bootstrapped 95% CI 0.60-2.46)}. Poisson and ZIP models fit the data poorly and had much larger point estimates than the NB and ZINB models [Poisson RR: 1.93 (bootstrapped 95% CI 0.88-4.23); ZIP summary RR: 1.84 (bootstrapped 95% CI 0.88-3.84)]. We found substantially different results when modeling hospitalization data, depending on the approach used. Our results argue strongly for a sound model selection process and improved reporting around statistical methods used for modeling count data. © The Author 2015. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Selected Streamflow Statistics and Regression Equations for Predicting Statistics at Stream Locations in Monroe County, Pennsylvania

USGS Publications Warehouse

Thompson, Ronald E.; Hoffman, Scott A.

2006-01-01

A suite of 28 streamflow statistics, ranging from extreme low to high flows, was computed for 17 continuous-record streamflow-gaging stations and predicted for 20 partial-record stations in Monroe County and contiguous counties in north-eastern Pennsylvania. The predicted statistics for the partial-record stations were based on regression analyses relating inter-mittent flow measurements made at the partial-record stations indexed to concurrent daily mean flows at continuous-record stations during base-flow conditions. The same statistics also were predicted for 134 ungaged stream locations in Monroe County on the basis of regression analyses relating the statistics to GIS-determined basin characteristics for the continuous-record station drainage areas. The prediction methodology for developing the regression equations used to estimate statistics was developed for estimating low-flow frequencies. This study and a companion study found that the methodology also has application potential for predicting intermediate- and high-flow statistics. The statistics included mean monthly flows, mean annual flow, 7-day low flows for three recurrence intervals, nine flow durations, mean annual base flow, and annual mean base flows for two recurrence intervals. Low standard errors of prediction and high coefficients of determination (R2) indicated good results in using the regression equations to predict the statistics. Regression equations for the larger flow statistics tended to have lower standard errors of prediction and higher coefficients of determination (R2) than equations for the smaller flow statistics. The report discusses the methodologies used in determining the statistics and the limitations of the statistics and the equations used to predict the statistics. Caution is indicated in using the predicted statistics for small drainage area situations. Study results constitute input needed by water-resource managers in Monroe County for planning purposes and evaluation of water-resources availability.

Semiparametric time varying coefficient model for matched case-crossover studies.

PubMed

Ortega-Villa, Ana Maria; Kim, Inyoung; Kim, H

2017-03-15

In matched case-crossover studies, it is generally accepted that the covariates on which a case and associated controls are matched cannot exert a confounding effect on independent predictors included in the conditional logistic regression model. This is because any stratum effect is removed by the conditioning on the fixed number of sets of the case and controls in the stratum. Hence, the conditional logistic regression model is not able to detect any effects associated with the matching covariates by stratum. However, some matching covariates such as time often play an important role as an effect modification leading to incorrect statistical estimation and prediction. Therefore, we propose three approaches to evaluate effect modification by time. The first is a parametric approach, the second is a semiparametric penalized approach, and the third is a semiparametric Bayesian approach. Our parametric approach is a two-stage method, which uses conditional logistic regression in the first stage and then estimates polynomial regression in the second stage. Our semiparametric penalized and Bayesian approaches are one-stage approaches developed by using regression splines. Our semiparametric one stage approach allows us to not only detect the parametric relationship between the predictor and binary outcomes, but also evaluate nonparametric relationships between the predictor and time. We demonstrate the advantage of our semiparametric one-stage approaches using both a simulation study and an epidemiological example of a 1-4 bi-directional case-crossover study of childhood aseptic meningitis with drinking water turbidity. We also provide statistical inference for the semiparametric Bayesian approach using Bayes Factors. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Use of generalized ordered logistic regression for the analysis of multidrug resistance data.

PubMed

Agga, Getahun E; Scott, H Morgan

2015-10-01

Statistical analysis of antimicrobial resistance data largely focuses on individual antimicrobial's binary outcome (susceptible or resistant). However, bacteria are becoming increasingly multidrug resistant (MDR). Statistical analysis of MDR data is mostly descriptive often with tabular or graphical presentations. Here we report the applicability of generalized ordinal logistic regression model for the analysis of MDR data. A total of 1,152 Escherichia coli, isolated from the feces of weaned pigs experimentally supplemented with chlortetracycline (CTC) and copper, were tested for susceptibilities against 15 antimicrobials and were binary classified into resistant or susceptible. The 15 antimicrobial agents tested were grouped into eight different antimicrobial classes. We defined MDR as the number of antimicrobial classes to which E. coli isolates were resistant ranging from 0 to 8. Proportionality of the odds assumption of the ordinal logistic regression model was violated only for the effect of treatment period (pre-treatment, during-treatment and post-treatment); but not for the effect of CTC or copper supplementation. Subsequently, a partially constrained generalized ordinal logistic model was built that allows for the effect of treatment period to vary while constraining the effects of treatment (CTC and copper supplementation) to be constant across the levels of MDR classes. Copper (Proportional Odds Ratio [Prop OR]=1.03; 95% CI=0.73-1.47) and CTC (Prop OR=1.1; 95% CI=0.78-1.56) supplementation were not significantly associated with the level of MDR adjusted for the effect of treatment period. MDR generally declined over the trial period. In conclusion, generalized ordered logistic regression can be used for the analysis of ordinal data such as MDR data when the proportionality assumptions for ordered logistic regression are violated. Published by Elsevier B.V.

The prediction of intelligence in preschool children using alternative models to regression.

PubMed

Finch, W Holmes; Chang, Mei; Davis, Andrew S; Holden, Jocelyn E; Rothlisberg, Barbara A; McIntosh, David E

2011-12-01

Statistical prediction of an outcome variable using multiple independent variables is a common practice in the social and behavioral sciences. For example, neuropsychologists are sometimes called upon to provide predictions of preinjury cognitive functioning for individuals who have suffered a traumatic brain injury. Typically, these predictions are made using standard multiple linear regression models with several demographic variables (e.g., gender, ethnicity, education level) as predictors. Prior research has shown conflicting evidence regarding the ability of such models to provide accurate predictions of outcome variables such as full-scale intelligence (FSIQ) test scores. The present study had two goals: (1) to demonstrate the utility of a set of alternative prediction methods that have been applied extensively in the natural sciences and business but have not been frequently explored in the social sciences and (2) to develop models that can be used to predict premorbid cognitive functioning in preschool children. Predictions of Stanford-Binet 5 FSIQ scores for preschool-aged children is used to compare the performance of a multiple regression model with several of these alternative methods. Results demonstrate that classification and regression trees provided more accurate predictions of FSIQ scores than does the more traditional regression approach. Implications of these results are discussed.

Consequences of kriging and land use regression for PM2.5 predictions in epidemiologic analyses: Insights into spatial variability using high-resolution satellite data

PubMed Central

Alexeeff, Stacey E.; Schwartz, Joel; Kloog, Itai; Chudnovsky, Alexandra; Koutrakis, Petros; Coull, Brent A.

2016-01-01

Many epidemiological studies use predicted air pollution exposures as surrogates for true air pollution levels. These predicted exposures contain exposure measurement error, yet simulation studies have typically found negligible bias in resulting health effect estimates. However, previous studies typically assumed a statistical spatial model for air pollution exposure, which may be oversimplified. We address this shortcoming by assuming a realistic, complex exposure surface derived from fine-scale (1km x 1km) remote-sensing satellite data. Using simulation, we evaluate the accuracy of epidemiological health effect estimates in linear and logistic regression when using spatial air pollution predictions from kriging and land use regression models. We examined chronic (long-term) and acute (short-term) exposure to air pollution. Results varied substantially across different scenarios. Exposure models with low out-of-sample R2 yielded severe biases in the health effect estimates of some models, ranging from 60% upward bias to 70% downward bias. One land use regression exposure model with greater than 0.9 out-of-sample R2 yielded upward biases up to 13% for acute health effect estimates. Almost all models drastically underestimated the standard errors. Land use regression models performed better in chronic effects simulations. These results can help researchers when interpreting health effect estimates in these types of studies. PMID:24896768

Comparison of hypertabastic survival model with other unimodal hazard rate functions using a goodness-of-fit test.

PubMed

Tahir, M Ramzan; Tran, Quang X; Nikulin, Mikhail S

2017-05-30

We studied the problem of testing a hypothesized distribution in survival regression models when the data is right censored and survival times are influenced by covariates. A modified chi-squared type test, known as Nikulin-Rao-Robson statistic, is applied for the comparison of accelerated failure time models. This statistic is used to test the goodness-of-fit for hypertabastic survival model and four other unimodal hazard rate functions. The results of simulation study showed that the hypertabastic distribution can be used as an alternative to log-logistic and log-normal distribution. In statistical modeling, because of its flexible shape of hazard functions, this distribution can also be used as a competitor of Birnbaum-Saunders and inverse Gaussian distributions. The results for the real data application are shown. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Quantitative investigation of inappropriate regression model construction and the importance of medical statistics experts in observational medical research: a cross-sectional study.

PubMed

Nojima, Masanori; Tokunaga, Mutsumi; Nagamura, Fumitaka

2018-05-05

To investigate under what circumstances inappropriate use of 'multivariate analysis' is likely to occur and to identify the population that needs more support with medical statistics. The frequency of inappropriate regression model construction in multivariate analysis and related factors were investigated in observational medical research publications. The inappropriate algorithm of using only variables that were significant in univariate analysis was estimated to occur at 6.4% (95% CI 4.8% to 8.5%). This was observed in 1.1% of the publications with a medical statistics expert (hereinafter 'expert') as the first author, 3.5% if an expert was included as coauthor and in 12.2% if experts were not involved. In the publications where the number of cases was 50 or less and the study did not include experts, inappropriate algorithm usage was observed with a high proportion of 20.2%. The OR of the involvement of experts for this outcome was 0.28 (95% CI 0.15 to 0.53). A further, nation-level, analysis showed that the involvement of experts and the implementation of unfavourable multivariate analysis are associated at the nation-level analysis (R=-0.652). Based on the results of this study, the benefit of participation of medical statistics experts is obvious. Experts should be involved for proper confounding adjustment and interpretation of statistical models. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Quasi-Likelihood Techniques in a Logistic Regression Equation for Identifying Simulium damnosum s.l. Larval Habitats Intra-cluster Covariates in Togo.

PubMed

Jacob, Benjamin G; Novak, Robert J; Toe, Laurent; Sanfo, Moussa S; Afriyie, Abena N; Ibrahim, Mohammed A; Griffith, Daniel A; Unnasch, Thomas R

2012-01-01

The standard methods for regression analyses of clustered riverine larval habitat data of Simulium damnosum s.l. a major black-fly vector of Onchoceriasis, postulate models relating observational ecological-sampled parameter estimators to prolific habitats without accounting for residual intra-cluster error correlation effects. Generally, this correlation comes from two sources: (1) the design of the random effects and their assumed covariance from the multiple levels within the regression model; and, (2) the correlation structure of the residuals. Unfortunately, inconspicuous errors in residual intra-cluster correlation estimates can overstate precision in forecasted S.damnosum s.l. riverine larval habitat explanatory attributes regardless how they are treated (e.g., independent, autoregressive, Toeplitz, etc). In this research, the geographical locations for multiple riverine-based S. damnosum s.l. larval ecosystem habitats sampled from 2 pre-established epidemiological sites in Togo were identified and recorded from July 2009 to June 2010. Initially the data was aggregated into proc genmod. An agglomerative hierarchical residual cluster-based analysis was then performed. The sampled clustered study site data was then analyzed for statistical correlations using Monthly Biting Rates (MBR). Euclidean distance measurements and terrain-related geomorphological statistics were then generated in ArcGIS. A digital overlay was then performed also in ArcGIS using the georeferenced ground coordinates of high and low density clusters stratified by Annual Biting Rates (ABR). This data was overlain onto multitemporal sub-meter pixel resolution satellite data (i.e., QuickBird 0.61m wavbands ). Orthogonal spatial filter eigenvectors were then generated in SAS/GIS. Univariate and non-linear regression-based models (i.e., Logistic, Poisson and Negative Binomial) were also employed to determine probability distributions and to identify statistically significant parameter estimators from the sampled data. Thereafter, Durbin-Watson test statistics were used to test the null hypothesis that the regression residuals were not autocorrelated against the alternative that the residuals followed an autoregressive process in AUTOREG. Bayesian uncertainty matrices were also constructed employing normal priors for each of the sampled estimators in PROC MCMC. The residuals revealed both spatially structured and unstructured error effects in the high and low ABR-stratified clusters. The analyses also revealed that the estimators, levels of turbidity and presence of rocks were statistically significant for the high-ABR-stratified clusters, while the estimators distance between habitats and floating vegetation were important for the low-ABR-stratified cluster. Varying and constant coefficient regression models, ABR- stratified GIS-generated clusters, sub-meter resolution satellite imagery, a robust residual intra-cluster diagnostic test, MBR-based histograms, eigendecomposition spatial filter algorithms and Bayesian matrices can enable accurate autoregressive estimation of latent uncertainity affects and other residual error probabilities (i.e., heteroskedasticity) for testing correlations between georeferenced S. damnosum s.l. riverine larval habitat estimators. The asymptotic distribution of the resulting residual adjusted intra-cluster predictor error autocovariate coefficients can thereafter be established while estimates of the asymptotic variance can lead to the construction of approximate confidence intervals for accurately targeting productive S. damnosum s.l habitats based on spatiotemporal field-sampled count data.

Factor analysis and multiple regression between topography and precipitation on Jeju Island, Korea

NASA Astrophysics Data System (ADS)

Um, Myoung-Jin; Yun, Hyeseon; Jeong, Chang-Sam; Heo, Jun-Haeng

2011-11-01

SummaryIn this study, new factors that influence precipitation were extracted from geographic variables using factor analysis, which allow for an accurate estimation of orographic precipitation. Correlation analysis was also used to examine the relationship between nine topographic variables from digital elevation models (DEMs) and the precipitation in Jeju Island. In addition, a spatial analysis was performed in order to verify the validity of the regression model. From the results of the correlation analysis, it was found that all of the topographic variables had a positive correlation with the precipitation. The relations between the variables also changed in accordance with a change in the precipitation duration. However, upon examining the correlation matrix, no significant relationship between the latitude and the aspect was found. According to the factor analysis, eight topographic variables (latitude being the exception) were found to have a direct influence on the precipitation. Three factors were then extracted from the eight topographic variables. By directly comparing the multiple regression model with the factors (model 1) to the multiple regression model with the topographic variables (model 3), it was found that model 1 did not violate the limits of statistical significance and multicollinearity. As such, model 1 was considered to be appropriate for estimating the precipitation when taking into account the topography. In the study of model 1, the multiple regression model using factor analysis was found to be the best method for estimating the orographic precipitation on Jeju Island.

Multivariate random-parameters zero-inflated negative binomial regression model: an application to estimate crash frequencies at intersections.

PubMed

Dong, Chunjiao; Clarke, David B; Yan, Xuedong; Khattak, Asad; Huang, Baoshan

2014-09-01

Crash data are collected through police reports and integrated with road inventory data for further analysis. Integrated police reports and inventory data yield correlated multivariate data for roadway entities (e.g., segments or intersections). Analysis of such data reveals important relationships that can help focus on high-risk situations and coming up with safety countermeasures. To understand relationships between crash frequencies and associated variables, while taking full advantage of the available data, multivariate random-parameters models are appropriate since they can simultaneously consider the correlation among the specific crash types and account for unobserved heterogeneity. However, a key issue that arises with correlated multivariate data is the number of crash-free samples increases, as crash counts have many categories. In this paper, we describe a multivariate random-parameters zero-inflated negative binomial (MRZINB) regression model for jointly modeling crash counts. The full Bayesian method is employed to estimate the model parameters. Crash frequencies at urban signalized intersections in Tennessee are analyzed. The paper investigates the performance of MZINB and MRZINB regression models in establishing the relationship between crash frequencies, pavement conditions, traffic factors, and geometric design features of roadway intersections. Compared to the MZINB model, the MRZINB model identifies additional statistically significant factors and provides better goodness of fit in developing the relationships. The empirical results show that MRZINB model possesses most of the desirable statistical properties in terms of its ability to accommodate unobserved heterogeneity and excess zero counts in correlated data. Notably, in the random-parameters MZINB model, the estimated parameters vary significantly across intersections for different crash types. Copyright © 2014 Elsevier Ltd. All rights reserved.

Modern modeling techniques had limited external validity in predicting mortality from traumatic brain injury.

PubMed

van der Ploeg, Tjeerd; Nieboer, Daan; Steyerberg, Ewout W

2016-10-01

Prediction of medical outcomes may potentially benefit from using modern statistical modeling techniques. We aimed to externally validate modeling strategies for prediction of 6-month mortality of patients suffering from traumatic brain injury (TBI) with predictor sets of increasing complexity. We analyzed individual patient data from 15 different studies including 11,026 TBI patients. We consecutively considered a core set of predictors (age, motor score, and pupillary reactivity), an extended set with computed tomography scan characteristics, and a further extension with two laboratory measurements (glucose and hemoglobin). With each of these sets, we predicted 6-month mortality using default settings with five statistical modeling techniques: logistic regression (LR), classification and regression trees, random forests (RFs), support vector machines (SVM) and neural nets. For external validation, a model developed on one of the 15 data sets was applied to each of the 14 remaining sets. This process was repeated 15 times for a total of 630 validations. The area under the receiver operating characteristic curve (AUC) was used to assess the discriminative ability of the models. For the most complex predictor set, the LR models performed best (median validated AUC value, 0.757), followed by RF and support vector machine models (median validated AUC value, 0.735 and 0.732, respectively). With each predictor set, the classification and regression trees models showed poor performance (median validated AUC value, <0.7). The variability in performance across the studies was smallest for the RF- and LR-based models (inter quartile range for validated AUC values from 0.07 to 0.10). In the area of predicting mortality from TBI, nonlinear and nonadditive effects are not pronounced enough to make modern prediction methods beneficial. Copyright © 2016 Elsevier Inc. All rights reserved.

Assessing Discriminative Performance at External Validation of Clinical Prediction Models

PubMed Central

Nieboer, Daan; van der Ploeg, Tjeerd; Steyerberg, Ewout W.

2016-01-01

Introduction External validation studies are essential to study the generalizability of prediction models. Recently a permutation test, focusing on discrimination as quantified by the c-statistic, was proposed to judge whether a prediction model is transportable to a new setting. We aimed to evaluate this test and compare it to previously proposed procedures to judge any changes in c-statistic from development to external validation setting. Methods We compared the use of the permutation test to the use of benchmark values of the c-statistic following from a previously proposed framework to judge transportability of a prediction model. In a simulation study we developed a prediction model with logistic regression on a development set and validated them in the validation set. We concentrated on two scenarios: 1) the case-mix was more heterogeneous and predictor effects were weaker in the validation set compared to the development set, and 2) the case-mix was less heterogeneous in the validation set and predictor effects were identical in the validation and development set. Furthermore we illustrated the methods in a case study using 15 datasets of patients suffering from traumatic brain injury. Results The permutation test indicated that the validation and development set were homogenous in scenario 1 (in almost all simulated samples) and heterogeneous in scenario 2 (in 17%-39% of simulated samples). Previously proposed benchmark values of the c-statistic and the standard deviation of the linear predictors correctly pointed at the more heterogeneous case-mix in scenario 1 and the less heterogeneous case-mix in scenario 2. Conclusion The recently proposed permutation test may provide misleading results when externally validating prediction models in the presence of case-mix differences between the development and validation population. To correctly interpret the c-statistic found at external validation it is crucial to disentangle case-mix differences from incorrect regression coefficients. PMID:26881753

Assessing Discriminative Performance at External Validation of Clinical Prediction Models.

PubMed

Nieboer, Daan; van der Ploeg, Tjeerd; Steyerberg, Ewout W

2016-01-01

External validation studies are essential to study the generalizability of prediction models. Recently a permutation test, focusing on discrimination as quantified by the c-statistic, was proposed to judge whether a prediction model is transportable to a new setting. We aimed to evaluate this test and compare it to previously proposed procedures to judge any changes in c-statistic from development to external validation setting. We compared the use of the permutation test to the use of benchmark values of the c-statistic following from a previously proposed framework to judge transportability of a prediction model. In a simulation study we developed a prediction model with logistic regression on a development set and validated them in the validation set. We concentrated on two scenarios: 1) the case-mix was more heterogeneous and predictor effects were weaker in the validation set compared to the development set, and 2) the case-mix was less heterogeneous in the validation set and predictor effects were identical in the validation and development set. Furthermore we illustrated the methods in a case study using 15 datasets of patients suffering from traumatic brain injury. The permutation test indicated that the validation and development set were homogenous in scenario 1 (in almost all simulated samples) and heterogeneous in scenario 2 (in 17%-39% of simulated samples). Previously proposed benchmark values of the c-statistic and the standard deviation of the linear predictors correctly pointed at the more heterogeneous case-mix in scenario 1 and the less heterogeneous case-mix in scenario 2. The recently proposed permutation test may provide misleading results when externally validating prediction models in the presence of case-mix differences between the development and validation population. To correctly interpret the c-statistic found at external validation it is crucial to disentangle case-mix differences from incorrect regression coefficients.

Application of Multiregressive Linear Models, Dynamic Kriging Models and Neural Network Models to Predictive Maintenance of Hydroelectric Power Systems

NASA Astrophysics Data System (ADS)

Lucifredi, A.; Mazzieri, C.; Rossi, M.

2000-05-01

Since the operational conditions of a hydroelectric unit can vary within a wide range, the monitoring system must be able to distinguish between the variations of the monitored variable caused by variations of the operation conditions and those due to arising and progressing of failures and misoperations. The paper aims to identify the best technique to be adopted for the monitoring system. Three different methods have been implemented and compared. Two of them use statistical techniques: the first, the linear multiple regression, expresses the monitored variable as a linear function of the process parameters (independent variables), while the second, the dynamic kriging technique, is a modified technique of multiple linear regression representing the monitored variable as a linear combination of the process variables in such a way as to minimize the variance of the estimate error. The third is based on neural networks. Tests have shown that the monitoring system based on the kriging technique is not affected by some problems common to the other two models e.g. the requirement of a large amount of data for their tuning, both for training the neural network and defining the optimum plane for the multiple regression, not only in the system starting phase but also after a trivial operation of maintenance involving the substitution of machinery components having a direct impact on the observed variable. Or, in addition, the necessity of different models to describe in a satisfactory way the different ranges of operation of the plant. The monitoring system based on the kriging statistical technique overrides the previous difficulties: it does not require a large amount of data to be tuned and is immediately operational: given two points, the third can be immediately estimated; in addition the model follows the system without adapting itself to it. The results of the experimentation performed seem to indicate that a model based on a neural network or on a linear multiple regression is not optimal, and that a different approach is necessary to reduce the amount of work during the learning phase using, when available, all the information stored during the initial phase of the plant to build the reference baseline, elaborating, if it is the case, the raw information available. A mixed approach using the kriging statistical technique and neural network techniques could optimise the result.

A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution

NASA Astrophysics Data System (ADS)

Dalkilic, Turkan Erbay; Apaydin, Aysen

2009-11-01

In a regression analysis, it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model; Y=f(X)+[epsilon]. However; a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters. When faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions, this regression model has been termed the [`]switching regression model' and it is expressed with . Here li indicates the class number of each independent variable and p is indicative of the number of independent variables [J.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transaction on Systems, Man and Cybernetics 23 (3) (1993) 665-685; M. Michel, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (2001) 363-399; E.Q. Richard, A new approach to estimating switching regressions, Journal of the American Statistical Association 67 (338) (1972) 306-310]. In this study, adaptive networks have been used to construct a model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, in defining the optimal class number of independent variables, the use of suggested validity criterion for fuzzy clustering has been aimed. In the case that independent variables have an exponential distribution, an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function, which is suitable for exponential distribution.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

Procedures for adjusting regional regression models of urban-runoff quality using local data

USGS Publications Warehouse

Hoos, A.B.; Sisolak, J.K.

1993-01-01

Statistical operations termed model-adjustment procedures (MAP?s) can be used to incorporate local data into existing regression models to improve the prediction of urban-runoff quality. Each MAP is a form of regression analysis in which the local data base is used as a calibration data set. Regression coefficients are determined from the local data base, and the resulting `adjusted? regression models can then be used to predict storm-runoff quality at unmonitored sites. The response variable in the regression analyses is the observed load or mean concentration of a constituent in storm runoff for a single storm. The set of explanatory variables used in the regression analyses is different for each MAP, but always includes the predicted value of load or mean concentration from a regional regression model. The four MAP?s examined in this study were: single-factor regression against the regional model prediction, P, (termed MAP-lF-P), regression against P,, (termed MAP-R-P), regression against P, and additional local variables (termed MAP-R-P+nV), and a weighted combination of P, and a local-regression prediction (termed MAP-W). The procedures were tested by means of split-sample analysis, using data from three cities included in the Nationwide Urban Runoff Program: Denver, Colorado; Bellevue, Washington; and Knoxville, Tennessee. The MAP that provided the greatest predictive accuracy for the verification data set differed among the three test data bases and among model types (MAP-W for Denver and Knoxville, MAP-lF-P and MAP-R-P for Bellevue load models, and MAP-R-P+nV for Bellevue concentration models) and, in many cases, was not clearly indicated by the values of standard error of estimate for the calibration data set. A scheme to guide MAP selection, based on exploratory data analysis of the calibration data set, is presented and tested. The MAP?s were tested for sensitivity to the size of a calibration data set. As expected, predictive accuracy of all MAP?s for the verification data set decreased as the calibration data-set size decreased, but predictive accuracy was not as sensitive for the MAP?s as it was for the local regression models.

Indiana chronic disease management program risk stratification analysis.

PubMed

Li, Jingjin; Holmes, Ann M; Rosenman, Marc B; Katz, Barry P; Downs, Stephen M; Murray, Michael D; Ackermann, Ronald T; Inui, Thomas S

2005-10-01

The objective of this study was to compare the ability of risk stratification models derived from administrative data to classify groups of patients for enrollment in a tailored chronic disease management program. This study included 19,548 Medicaid patients with chronic heart failure or diabetes in the Indiana Medicaid data warehouse during 2001 and 2002. To predict costs (total claims paid) in FY 2002, we considered candidate predictor variables available in FY 2001, including patient characteristics, the number and type of prescription medications, laboratory tests, pharmacy charges, and utilization of primary, specialty, inpatient, emergency department, nursing home, and home health care. We built prospective models to identify patients with different levels of expenditure. Model fit was assessed using R statistics, whereas discrimination was assessed using the weighted kappa statistic, predictive ratios, and the area under the receiver operating characteristic curve. We found a simple least-squares regression model in which logged total charges in FY 2002 were regressed on the log of total charges in FY 2001, the number of prescriptions filled in FY 2001, and the FY 2001 eligibility category, performed as well as more complex models. This simple 3-parameter model had an R of 0.30 and, in terms in classification efficiency, had a sensitivity of 0.57, a specificity of 0.90, an area under the receiver operator curve of 0.80, and a weighted kappa statistic of 0.51. This simple model based on readily available administrative data stratified Medicaid members according to predicted future utilization as well as more complicated models.

Monthly monsoon rainfall forecasting using artificial neural networks

NASA Astrophysics Data System (ADS)

Ganti, Ravikumar

2014-10-01

Indian agriculture sector heavily depends on monsoon rainfall for successful harvesting. In the past, prediction of rainfall was mainly performed using regression models, which provide reasonable accuracy in the modelling and forecasting of complex physical systems. Recently, Artificial Neural Networks (ANNs) have been proposed as efficient tools for modelling and forecasting. A feed-forward multi-layer perceptron type of ANN architecture trained using the popular back-propagation algorithm was employed in this study. Other techniques investigated for modeling monthly monsoon rainfall include linear and non-linear regression models for comparison purposes. The data employed in this study include monthly rainfall and monthly average of the daily maximum temperature in the North Central region in India. Specifically, four regression models and two ANN model's were developed. The performance of various models was evaluated using a wide variety of standard statistical parameters and scatter plots. The results obtained in this study for forecasting monsoon rainfalls using ANNs have been encouraging. India's economy and agricultural activities can be effectively managed with the help of the availability of the accurate monsoon rainfall forecasts.

Modeling landslide susceptibility in data-scarce environments using optimized data mining and statistical methods

NASA Astrophysics Data System (ADS)

Lee, Jung-Hyun; Sameen, Maher Ibrahim; Pradhan, Biswajeet; Park, Hyuck-Jin

2018-02-01

This study evaluated the generalizability of five models to select a suitable approach for landslide susceptibility modeling in data-scarce environments. In total, 418 landslide inventories and 18 landslide conditioning factors were analyzed. Multicollinearity and factor optimization were investigated before data modeling, and two experiments were then conducted. In each experiment, five susceptibility maps were produced based on support vector machine (SVM), random forest (RF), weight-of-evidence (WoE), ridge regression (Rid_R), and robust regression (RR) models. The highest accuracy (AUC = 0.85) was achieved with the SVM model when either the full or limited landslide inventories were used. Furthermore, the RF and WoE models were severely affected when less landslide samples were used for training. The other models were affected slightly when the training samples were limited.

The median hazard ratio: a useful measure of variance and general contextual effects in multilevel survival analysis.

PubMed

Austin, Peter C; Wagner, Philippe; Merlo, Juan

2017-03-15

Multilevel data occurs frequently in many research areas like health services research and epidemiology. A suitable way to analyze such data is through the use of multilevel regression models (MLRM). MLRM incorporate cluster-specific random effects which allow one to partition the total individual variance into between-cluster variation and between-individual variation. Statistically, MLRM account for the dependency of the data within clusters and provide correct estimates of uncertainty around regression coefficients. Substantively, the magnitude of the effect of clustering provides a measure of the General Contextual Effect (GCE). When outcomes are binary, the GCE can also be quantified by measures of heterogeneity like the Median Odds Ratio (MOR) calculated from a multilevel logistic regression model. Time-to-event outcomes within a multilevel structure occur commonly in epidemiological and medical research. However, the Median Hazard Ratio (MHR) that corresponds to the MOR in multilevel (i.e., 'frailty') Cox proportional hazards regression is rarely used. Analogously to the MOR, the MHR is the median relative change in the hazard of the occurrence of the outcome when comparing identical subjects from two randomly selected different clusters that are ordered by risk. We illustrate the application and interpretation of the MHR in a case study analyzing the hazard of mortality in patients hospitalized for acute myocardial infarction at hospitals in Ontario, Canada. We provide R code for computing the MHR. The MHR is a useful and intuitive measure for expressing cluster heterogeneity in the outcome and, thereby, estimating general contextual effects in multilevel survival analysis. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Bayesian inference for the spatio-temporal invasion of alien species.

PubMed

Cook, Alex; Marion, Glenn; Butler, Adam; Gibson, Gavin

2007-08-01

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.

Measuring the statistical validity of summary meta-analysis and meta-regression results for use in clinical practice.

PubMed

Willis, Brian H; Riley, Richard D

2017-09-20

An important question for clinicians appraising a meta-analysis is: are the findings likely to be valid in their own practice-does the reported effect accurately represent the effect that would occur in their own clinical population? To this end we advance the concept of statistical validity-where the parameter being estimated equals the corresponding parameter for a new independent study. Using a simple ('leave-one-out') cross-validation technique, we demonstrate how we may test meta-analysis estimates for statistical validity using a new validation statistic, Vn, and derive its distribution. We compare this with the usual approach of investigating heterogeneity in meta-analyses and demonstrate the link between statistical validity and homogeneity. Using a simulation study, the properties of Vn and the Q statistic are compared for univariate random effects meta-analysis and a tailored meta-regression model, where information from the setting (included as model covariates) is used to calibrate the summary estimate to the setting of application. Their properties are found to be similar when there are 50 studies or more, but for fewer studies Vn has greater power but a higher type 1 error rate than Q. The power and type 1 error rate of Vn are also shown to depend on the within-study variance, between-study variance, study sample size, and the number of studies in the meta-analysis. Finally, we apply Vn to two published meta-analyses and conclude that it usefully augments standard methods when deciding upon the likely validity of summary meta-analysis estimates in clinical practice. © 2017 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. © 2017 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

A study of machine learning regression methods for major elemental analysis of rocks using laser-induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Boucher, Thomas F.; Ozanne, Marie V.; Carmosino, Marco L.; Dyar, M. Darby; Mahadevan, Sridhar; Breves, Elly A.; Lepore, Kate H.; Clegg, Samuel M.

2015-05-01

The ChemCam instrument on the Mars Curiosity rover is generating thousands of LIBS spectra and bringing interest in this technique to public attention. The key to interpreting Mars or any other types of LIBS data are calibrations that relate laboratory standards to unknowns examined in other settings and enable predictions of chemical composition. Here, LIBS spectral data are analyzed using linear regression methods including partial least squares (PLS-1 and PLS-2), principal component regression (PCR), least absolute shrinkage and selection operator (lasso), elastic net, and linear support vector regression (SVR-Lin). These were compared against results from nonlinear regression methods including kernel principal component regression (K-PCR), polynomial kernel support vector regression (SVR-Py) and k-nearest neighbor (kNN) regression to discern the most effective models for interpreting chemical abundances from LIBS spectra of geological samples. The results were evaluated for 100 samples analyzed with 50 laser pulses at each of five locations averaged together. Wilcoxon signed-rank tests were employed to evaluate the statistical significance of differences among the nine models using their predicted residual sum of squares (PRESS) to make comparisons. For MgO, SiO2, Fe2O3, CaO, and MnO, the sparse models outperform all the others except for linear SVR, while for Na2O, K2O, TiO2, and P2O5, the sparse methods produce inferior results, likely because their emission lines in this energy range have lower transition probabilities. The strong performance of the sparse methods in this study suggests that use of dimensionality-reduction techniques as a preprocessing step may improve the performance of the linear models. Nonlinear methods tend to overfit the data and predict less accurately, while the linear methods proved to be more generalizable with better predictive performance. These results are attributed to the high dimensionality of the data (6144 channels) relative to the small number of samples studied. The best-performing models were SVR-Lin for SiO2, MgO, Fe2O3, and Na2O, lasso for Al2O3, elastic net for MnO, and PLS-1 for CaO, TiO2, and K2O. Although these differences in model performance between methods were identified, most of the models produce comparable results when p ≤ 0.05 and all techniques except kNN produced statistically-indistinguishable results. It is likely that a combination of models could be used together to yield a lower total error of prediction, depending on the requirements of the user.

Statistical methods for efficient design of community surveys of response to noise: Random coefficients regression models

NASA Technical Reports Server (NTRS)

Tomberlin, T. J.

1985-01-01

Research studies of residents' responses to noise consist of interviews with samples of individuals who are drawn from a number of different compact study areas. The statistical techniques developed provide a basis for those sample design decisions. These techniques are suitable for a wide range of sample survey applications. A sample may consist of a random sample of residents selected from a sample of compact study areas, or in a more complex design, of a sample of residents selected from a sample of larger areas (e.g., cities). The techniques may be applied to estimates of the effects on annoyance of noise level, numbers of noise events, the time-of-day of the events, ambient noise levels, or other factors. Methods are provided for determining, in advance, how accurately these effects can be estimated for different sample sizes and study designs. Using a simple cost function, they also provide for optimum allocation of the sample across the stages of the design for estimating these effects. These techniques are developed via a regression model in which the regression coefficients are assumed to be random, with components of variance associated with the various stages of a multi-stage sample design.

Supporting Regularized Logistic Regression Privately and Efficiently.

PubMed

Li, Wenfa; Liu, Hongzhe; Yang, Peng; Xie, Wei

2016-01-01

As one of the most popular statistical and machine learning models, logistic regression with regularization has found wide adoption in biomedicine, social sciences, information technology, and so on. These domains often involve data of human subjects that are contingent upon strict privacy regulations. Concerns over data privacy make it increasingly difficult to coordinate and conduct large-scale collaborative studies, which typically rely on cross-institution data sharing and joint analysis. Our work here focuses on safeguarding regularized logistic regression, a widely-used statistical model while at the same time has not been investigated from a data security and privacy perspective. We consider a common use scenario of multi-institution collaborative studies, such as in the form of research consortia or networks as widely seen in genetics, epidemiology, social sciences, etc. To make our privacy-enhancing solution practical, we demonstrate a non-conventional and computationally efficient method leveraging distributing computing and strong cryptography to provide comprehensive protection over individual-level and summary data. Extensive empirical evaluations on several studies validate the privacy guarantee, efficiency and scalability of our proposal. We also discuss the practical implications of our solution for large-scale studies and applications from various disciplines, including genetic and biomedical studies, smart grid, network analysis, etc.

Beyond Reading Alone: The Relationship Between Aural Literacy And Asthma Management

PubMed Central

Rosenfeld, Lindsay; Rudd, Rima; Emmons, Karen M.; Acevedo-García, Dolores; Martin, Laurie; Buka, Stephen

2010-01-01

Objectives To examine the relationship between literacy and asthma management with a focus on the oral exchange. Methods Study participants, all of whom reported asthma, were drawn from the New England Family Study (NEFS), an examination of links between education and health. NEFS data included reading, oral (speaking), and aural (listening) literacy measures. An additional survey was conducted with this group of study participants related to asthma issues, particularly asthma management. Data analysis focused on bivariate and multivariable logistic regression. Results In bivariate logistic regression models exploring aural literacy, there was a statistically significant association between those participants with lower aural literacy skills and less successful asthma management (OR:4.37, 95%CI:1.11, 17.32). In multivariable logistic regression analyses, controlling for gender, income, and race in separate models (one-at-a-time), there remained a statistically significant association between those participants with lower aural literacy skills and less successful asthma management. Conclusion Lower aural literacy skills seem to complicate asthma management capabilities. Practice Implications Greater attention to the oral exchange, in particular the listening skills highlighted by aural literacy, as well as other related literacy skills may help us develop strategies for clear communication related to asthma management. PMID:20399060

Supporting Regularized Logistic Regression Privately and Efficiently

PubMed Central

Li, Wenfa; Liu, Hongzhe; Yang, Peng; Xie, Wei

2016-01-01

As one of the most popular statistical and machine learning models, logistic regression with regularization has found wide adoption in biomedicine, social sciences, information technology, and so on. These domains often involve data of human subjects that are contingent upon strict privacy regulations. Concerns over data privacy make it increasingly difficult to coordinate and conduct large-scale collaborative studies, which typically rely on cross-institution data sharing and joint analysis. Our work here focuses on safeguarding regularized logistic regression, a widely-used statistical model while at the same time has not been investigated from a data security and privacy perspective. We consider a common use scenario of multi-institution collaborative studies, such as in the form of research consortia or networks as widely seen in genetics, epidemiology, social sciences, etc. To make our privacy-enhancing solution practical, we demonstrate a non-conventional and computationally efficient method leveraging distributing computing and strong cryptography to provide comprehensive protection over individual-level and summary data. Extensive empirical evaluations on several studies validate the privacy guarantee, efficiency and scalability of our proposal. We also discuss the practical implications of our solution for large-scale studies and applications from various disciplines, including genetic and biomedical studies, smart grid, network analysis, etc. PMID:27271738

Aqua/Aura Updated Inclination Adjust Maneuver Performance Prediction Model

NASA Technical Reports Server (NTRS)

Boone, Spencer

2017-01-01

This presentation will discuss the updated Inclination Adjust Maneuver (IAM) performance prediction model that was developed for Aqua and Aura following the 2017 IAM series. This updated model uses statistical regression methods to identify potential long-term trends in maneuver parameters, yielding improved predictions when re-planning past maneuvers. The presentation has been reviewed and approved by Eric Moyer, ESMO Deputy Project Manager.

New insights into faster computation of uncertainties

NASA Astrophysics Data System (ADS)

Bhattacharya, Atreyee

2012-11-01

Heavy computation power, lengthy simulations, and an exhaustive number of model runs—often these seem like the only statistical tools that scientists have at their disposal when computing uncertainties associated with predictions, particularly in cases of environmental processes such as groundwater movement. However, calculation of uncertainties need not be as lengthy, a new study shows. Comparing two approaches—the classical Bayesian “credible interval” and a less commonly used regression-based “confidence interval” method—Lu et al. show that for many practical purposes both methods provide similar estimates of uncertainties. The advantage of the regression method is that it demands 10-1000 model runs, whereas the classical Bayesian approach requires 10,000 to millions of model runs.

Using the Graded Response Model to Control Spurious Interactions in Moderated Multiple Regression

ERIC Educational Resources Information Center

Morse, Brendan J.; Johanson, George A.; Griffeth, Rodger W.

2012-01-01

Recent simulation research has demonstrated that using simple raw score to operationalize a latent construct can result in inflated Type I error rates for the interaction term of a moderated statistical model when the interaction (or lack thereof) is proposed at the latent variable level. Rescaling the scores using an appropriate item response…

The Effect of Attending Tutoring on Course Grades in Calculus I

ERIC Educational Resources Information Center

Rickard, Brian; Mills, Melissa

2018-01-01

Tutoring centres are common in universities in the United States, but there are few published studies that statistically examine the effects of tutoring on student success. This study utilizes multiple regression analysis to model the effect of tutoring attendance on final course grades in Calculus I. Our model predicted that every three visits to…

Modeling Outcomes with Floor or Ceiling Effects: An Introduction to the Tobit Model

ERIC Educational Resources Information Center

McBee, Matthew

2010-01-01

In gifted education research, it is common for outcome variables to exhibit strong floor or ceiling effects due to insufficient range of measurement of many instruments when used with gifted populations. Common statistical methods (e.g., analysis of variance, linear regression) produce biased estimates when such effects are present. In practice,…

Faculty Salary Equity: Issues in Regression Model Selection. AIR 1992 Annual Forum Paper.

ERIC Educational Resources Information Center

Moore, Nelle

This paper discusses the determination of college faculty salary inequity and identifies the areas in which human judgment must be used in order to conduct a statistical analysis of salary equity. In addition, it provides some informed guidelines for making those judgments. The paper provides a framework for selecting salary equity models, based…

Helping Students Assess the Relative Importance of Different Intermolecular Interactions

ERIC Educational Resources Information Center

Jasien, Paul G.

2008-01-01

A semi-quantitative model has been developed to estimate the relative effects of dispersion, dipole-dipole interactions, and H-bonding on the normal boiling points ("T[subscript b]") for a subset of simple organic systems. The model is based upon a statistical analysis using multiple linear regression on a series of straight-chain organic…

Modeling vertebrate diversity in Oregon using satellite imagery

NASA Astrophysics Data System (ADS)

Cablk, Mary Elizabeth

Vertebrate diversity was modeled for the state of Oregon using a parametric approach to regression tree analysis. This exploratory data analysis effectively modeled the non-linear relationships between vertebrate richness and phenology, terrain, and climate. Phenology was derived from time-series NOAA-AVHRR satellite imagery for the year 1992 using two methods: principal component analysis and derivation of EROS data center greenness metrics. These two measures of spatial and temporal vegetation condition incorporated the critical temporal element in this analysis. The first three principal components were shown to contain spatial and temporal information about the landscape and discriminated phenologically distinct regions in Oregon. Principal components 2 and 3, 6 greenness metrics, elevation, slope, aspect, annual precipitation, and annual seasonal temperature difference were investigated as correlates to amphibians, birds, all vertebrates, reptiles, and mammals. Variation explained for each regression tree by taxa were: amphibians (91%), birds (67%), all vertebrates (66%), reptiles (57%), and mammals (55%). Spatial statistics were used to quantify the pattern of each taxa and assess validity of resulting predictions from regression tree models. Regression tree analysis was relatively robust against spatial autocorrelation in the response data and graphical results indicated models were well fit to the data.

Regression model development and computational procedures to support estimation of real-time concentrations and loads of selected constituents in two tributaries to Lake Houston near Houston, Texas, 2005-9

USGS Publications Warehouse

Lee, Michael T.; Asquith, William H.; Oden, Timothy D.

2012-01-01

In December 2005, the U.S. Geological Survey (USGS), in cooperation with the City of Houston, Texas, began collecting discrete water-quality samples for nutrients, total organic carbon, bacteria (Escherichia coli and total coliform), atrazine, and suspended sediment at two USGS streamflow-gaging stations that represent watersheds contributing to Lake Houston (08068500 Spring Creek near Spring, Tex., and 08070200 East Fork San Jacinto River near New Caney, Tex.). Data from the discrete water-quality samples collected during 2005–9, in conjunction with continuously monitored real-time data that included streamflow and other physical water-quality properties (specific conductance, pH, water temperature, turbidity, and dissolved oxygen), were used to develop regression models for the estimation of concentrations of water-quality constituents of substantial source watersheds to Lake Houston. The potential explanatory variables included discharge (streamflow), specific conductance, pH, water temperature, turbidity, dissolved oxygen, and time (to account for seasonal variations inherent in some water-quality data). The response variables (the selected constituents) at each site were nitrite plus nitrate nitrogen, total phosphorus, total organic carbon, E. coli, atrazine, and suspended sediment. The explanatory variables provide easily measured quantities to serve as potential surrogate variables to estimate concentrations of the selected constituents through statistical regression. Statistical regression also facilitates accompanying estimates of uncertainty in the form of prediction intervals. Each regression model potentially can be used to estimate concentrations of a given constituent in real time. Among other regression diagnostics, the diagnostics used as indicators of general model reliability and reported herein include the adjusted R-squared, the residual standard error, residual plots, and p-values. Adjusted R-squared values for the Spring Creek models ranged from .582–.922 (dimensionless). The residual standard errors ranged from .073–.447 (base-10 logarithm). Adjusted R-squared values for the East Fork San Jacinto River models ranged from .253–.853 (dimensionless). The residual standard errors ranged from .076–.388 (base-10 logarithm). In conjunction with estimated concentrations, constituent loads can be estimated by multiplying the estimated concentration by the corresponding streamflow and by applying the appropriate conversion factor. The regression models presented in this report are site specific, that is, they are specific to the Spring Creek and East Fork San Jacinto River streamflow-gaging stations; however, the general methods that were developed and documented could be applied to most perennial streams for the purpose of estimating real-time water quality data.

Explaining nitrate pollution pressure on the groundwater resource in Kinshasa using a multivariate statistical modelling approach

NASA Astrophysics Data System (ADS)

Mfumu Kihumba, Antoine; Vanclooster, Marnik

2013-04-01

Drinking water in Kinshasa, the capital of the Democratic Republic of Congo, is provided by extracting groundwater from the local aquifer, particularly in peripheral areas. The exploited groundwater body is mainly unconfined and located within a continuous detrital aquifer, primarily composed of sedimentary formations. However, the aquifer is subjected to an increasing threat of anthropogenic pollution pressure. Understanding the detailed origin of this pollution pressure is important for sustainable drinking water management in Kinshasa. The present study aims to explain the observed nitrate pollution problem, nitrate being considered as a good tracer for other pollution threats. The analysis is made in terms of physical attributes that are readily available using a statistical modelling approach. For the nitrate data, use was made of a historical groundwater quality assessment study, for which the data were re-analysed. The physical attributes are related to the topography, land use, geology and hydrogeology of the region. Prior to the statistical modelling, intrinsic and specific vulnerability for nitrate pollution was assessed. This vulnerability assessment showed that the alluvium area in the northern part of the region is the most vulnerable area. This area consists of urban land use with poor sanitation. Re-analysis of the nitrate pollution data demonstrated that the spatial variability of nitrate concentrations in the groundwater body is high, and coherent with the fragmented land use of the region and the intrinsic and specific vulnerability maps. For the statistical modeling use was made of multiple regression and regression tree analysis. The results demonstrated the significant impact of land use variables on the Kinshasa groundwater nitrate pollution and the need for a detailed delineation of groundwater capture zones around the monitoring stations. Key words: Groundwater , Isotopic, Kinshasa, Modelling, Pollution, Physico-chemical.

Quantifying the impact of between-study heterogeneity in multivariate meta-analyses

PubMed Central

Jackson, Dan; White, Ian R; Riley, Richard D

2012-01-01

Measures that quantify the impact of heterogeneity in univariate meta-analysis, including the very popular I2 statistic, are now well established. Multivariate meta-analysis, where studies provide multiple outcomes that are pooled in a single analysis, is also becoming more commonly used. The question of how to quantify heterogeneity in the multivariate setting is therefore raised. It is the univariate R2 statistic, the ratio of the variance of the estimated treatment effect under the random and fixed effects models, that generalises most naturally, so this statistic provides our basis. This statistic is then used to derive a multivariate analogue of I2, which we call . We also provide a multivariate H2 statistic, the ratio of a generalisation of Cochran's heterogeneity statistic and its associated degrees of freedom, with an accompanying generalisation of the usual I2 statistic, . Our proposed heterogeneity statistics can be used alongside all the usual estimates and inferential procedures used in multivariate meta-analysis. We apply our methods to some real datasets and show how our statistics are equally appropriate in the context of multivariate meta-regression, where study level covariate effects are included in the model. Our heterogeneity statistics may be used when applying any procedure for fitting the multivariate random effects model. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22763950

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

PubMed

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Tools to Support Interpreting Multiple Regression in the Face of Multicollinearity

PubMed Central

Kraha, Amanda; Turner, Heather; Nimon, Kim; Zientek, Linda Reichwein; Henson, Robin K.

2012-01-01

While multicollinearity may increase the difficulty of interpreting multiple regression (MR) results, it should not cause undue problems for the knowledgeable researcher. In the current paper, we argue that rather than using one technique to investigate regression results, researchers should consider multiple indices to understand the contributions that predictors make not only to a regression model, but to each other as well. Some of the techniques to interpret MR effects include, but are not limited to, correlation coefficients, beta weights, structure coefficients, all possible subsets regression, commonality coefficients, dominance weights, and relative importance weights. This article will review a set of techniques to interpret MR effects, identify the elements of the data on which the methods focus, and identify statistical software to support such analyses. PMID:22457655

Tools to support interpreting multiple regression in the face of multicollinearity.

PubMed

Kraha, Amanda; Turner, Heather; Nimon, Kim; Zientek, Linda Reichwein; Henson, Robin K

2012-01-01

While multicollinearity may increase the difficulty of interpreting multiple regression (MR) results, it should not cause undue problems for the knowledgeable researcher. In the current paper, we argue that rather than using one technique to investigate regression results, researchers should consider multiple indices to understand the contributions that predictors make not only to a regression model, but to each other as well. Some of the techniques to interpret MR effects include, but are not limited to, correlation coefficients, beta weights, structure coefficients, all possible subsets regression, commonality coefficients, dominance weights, and relative importance weights. This article will review a set of techniques to interpret MR effects, identify the elements of the data on which the methods focus, and identify statistical software to support such analyses.