Quantum algorithm for linear regression

NASA Astrophysics Data System (ADS)

Wang, Guoming

2017-07-01

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

The role of shoe design on the prediction of free torque at the shoe-surface interface using pressure insole technology.

PubMed

Weaver, Brian Thomas; Fitzsimons, Kathleen; Braman, Jerrod; Haut, Roger

2016-09-01

The goal of the current study was to expand on previous work to validate the use of pressure insole technology in conjunction with linear regression models to predict the free torque at the shoe-surface interface that is generated while wearing different athletic shoes. Three distinctly different shoe designs were utilised. The stiffness of each shoe was determined with a material's testing machine. Six participants wore each shoe that was fitted with an insole pressure measurement device and performed rotation trials on an embedded force plate. A pressure sensor mask was constructed from those sensors having a high linear correlation with free torque values. Linear regression models were developed to predict free torques from these pressure sensor data. The models were able to accurately predict their own free torque well (RMS error 3.72 ± 0.74 Nm), but not that of the other shoes (RMS error 10.43 ± 3.79 Nm). Models performing self-prediction were also able to measure differences in shoe stiffness. The results of the current study showed the need for participant-shoe specific linear regression models to insure high prediction accuracy of free torques from pressure sensor data during isolated internal and external rotations of the body with respect to a planted foot.

Comparing Linear Discriminant Function with Logistic Regression for the Two-Group Classification Problem.

ERIC Educational Resources Information Center

Fan, Xitao; Wang, Lin

The Monte Carlo study compared the performance of predictive discriminant analysis (PDA) and that of logistic regression (LR) for the two-group classification problem. Prior probabilities were used for classification, but the cost of misclassification was assumed to be equal. The study used a fully crossed three-factor experimental design (with…

Cactus: An Introduction to Regression

ERIC Educational Resources Information Center

Hyde, Hartley

2008-01-01

When the author first used "VisiCalc," the author thought it a very useful tool when he had the formulas. But how could he design a spreadsheet if there was no known formula for the quantities he was trying to predict? A few months later, the author relates he learned to use multiple linear regression software and suddenly it all clicked into…

Missing-value estimation using linear and non-linear regression with Bayesian gene selection.

PubMed

Zhou, Xiaobo; Wang, Xiaodong; Dougherty, Edward R

2003-11-22

Data from microarray experiments are usually in the form of large matrices of expression levels of genes under different experimental conditions. Owing to various reasons, there are frequently missing values. Estimating these missing values is important because they affect downstream analysis, such as clustering, classification and network design. Several methods of missing-value estimation are in use. The problem has two parts: (1) selection of genes for estimation and (2) design of an estimation rule. We propose Bayesian variable selection to obtain genes to be used for estimation, and employ both linear and nonlinear regression for the estimation rule itself. Fast implementation issues for these methods are discussed, including the use of QR decomposition for parameter estimation. The proposed methods are tested on data sets arising from hereditary breast cancer and small round blue-cell tumors. The results compare very favorably with currently used methods based on the normalized root-mean-square error. The appendix is available from http://gspsnap.tamu.edu/gspweb/zxb/missing_zxb/ (user: gspweb; passwd: gsplab).

Image interpolation via regularized local linear regression.

PubMed

Liu, Xianming; Zhao, Debin; Xiong, Ruiqin; Ma, Siwei; Gao, Wen; Sun, Huifang

2011-12-01

The linear regression model is a very attractive tool to design effective image interpolation schemes. Some regression-based image interpolation algorithms have been proposed in the literature, in which the objective functions are optimized by ordinary least squares (OLS). However, it is shown that interpolation with OLS may have some undesirable properties from a robustness point of view: even small amounts of outliers can dramatically affect the estimates. To address these issues, in this paper we propose a novel image interpolation algorithm based on regularized local linear regression (RLLR). Starting with the linear regression model where we replace the OLS error norm with the moving least squares (MLS) error norm leads to a robust estimator of local image structure. To keep the solution stable and avoid overfitting, we incorporate the l(2)-norm as the estimator complexity penalty. Moreover, motivated by recent progress on manifold-based semi-supervised learning, we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points. Specifically, our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state-of-the-art interpolation algorithms, especially in image edge structure preservation. © 2011 IEEE

Precision Interval Estimation of the Response Surface by Means of an Integrated Algorithm of Neural Network and Linear Regression

NASA Technical Reports Server (NTRS)

Lo, Ching F.

1999-01-01

The integration of Radial Basis Function Networks and Back Propagation Neural Networks with the Multiple Linear Regression has been accomplished to map nonlinear response surfaces over a wide range of independent variables in the process of the Modem Design of Experiments. The integrated method is capable to estimate the precision intervals including confidence and predicted intervals. The power of the innovative method has been demonstrated by applying to a set of wind tunnel test data in construction of response surface and estimation of precision interval.

42 CFR 433.68 - Permissible health care-related taxes.

Code of Federal Regulations, 2011 CFR

2011-10-01

...-related tax is imposed by a unit of local government, the tax must extend to all items or services or... least squares, the slope (designated as (B) (that is. the value of the x coefficient) of two linear... linear regression, as described in paragraph (e)(2)(i) of this section, for the State's tax program, if...

42 CFR 433.68 - Permissible health care-related taxes.

Code of Federal Regulations, 2013 CFR

2013-10-01

...-related tax is imposed by a unit of local government, the tax must extend to all items or services or... least squares, the slope (designated as (B) (that is. the value of the x coefficient) of two linear... linear regression, as described in paragraph (e)(2)(i) of this section, for the State's tax program, if...

Regression dilution bias: tools for correction methods and sample size calculation.

PubMed

Berglund, Lars

2012-08-01

Random errors in measurement of a risk factor will introduce downward bias of an estimated association to a disease or a disease marker. This phenomenon is called regression dilution bias. A bias correction may be made with data from a validity study or a reliability study. In this article we give a non-technical description of designs of reliability studies with emphasis on selection of individuals for a repeated measurement, assumptions of measurement error models, and correction methods for the slope in a simple linear regression model where the dependent variable is a continuous variable. Also, we describe situations where correction for regression dilution bias is not appropriate. The methods are illustrated with the association between insulin sensitivity measured with the euglycaemic insulin clamp technique and fasting insulin, where measurement of the latter variable carries noticeable random error. We provide software tools for estimation of a corrected slope in a simple linear regression model assuming data for a continuous dependent variable and a continuous risk factor from a main study and an additional measurement of the risk factor in a reliability study. Also, we supply programs for estimation of the number of individuals needed in the reliability study and for choice of its design. Our conclusion is that correction for regression dilution bias is seldom applied in epidemiological studies. This may cause important effects of risk factors with large measurement errors to be neglected.

Multiple regression for physiological data analysis: the problem of multicollinearity.

PubMed

Slinker, B K; Glantz, S A

1985-07-01

Multiple linear regression, in which several predictor variables are related to a response variable, is a powerful statistical tool for gaining quantitative insight into complex in vivo physiological systems. For these insights to be correct, all predictor variables must be uncorrelated. However, in many physiological experiments the predictor variables cannot be precisely controlled and thus change in parallel (i.e., they are highly correlated). There is a redundancy of information about the response, a situation called multicollinearity, that leads to numerical problems in estimating the parameters in regression equations; the parameters are often of incorrect magnitude or sign or have large standard errors. Although multicollinearity can be avoided with good experimental design, not all interesting physiological questions can be studied without encountering multicollinearity. In these cases various ad hoc procedures have been proposed to mitigate multicollinearity. Although many of these procedures are controversial, they can be helpful in applying multiple linear regression to some physiological problems.

Prediction of siRNA potency using sparse logistic regression.

PubMed

Hu, Wei; Hu, John

2014-06-01

RNA interference (RNAi) can modulate gene expression at post-transcriptional as well as transcriptional levels. Short interfering RNA (siRNA) serves as a trigger for the RNAi gene inhibition mechanism, and therefore is a crucial intermediate step in RNAi. There have been extensive studies to identify the sequence characteristics of potent siRNAs. One such study built a linear model using LASSO (Least Absolute Shrinkage and Selection Operator) to measure the contribution of each siRNA sequence feature. This model is simple and interpretable, but it requires a large number of nonzero weights. We have introduced a novel technique, sparse logistic regression, to build a linear model using single-position specific nucleotide compositions which has the same prediction accuracy of the linear model based on LASSO. The weights in our new model share the same general trend as those in the previous model, but have only 25 nonzero weights out of a total 84 weights, a 54% reduction compared to the previous model. Contrary to the linear model based on LASSO, our model suggests that only a few positions are influential on the efficacy of the siRNA, which are the 5' and 3' ends and the seed region of siRNA sequences. We also employed sparse logistic regression to build a linear model using dual-position specific nucleotide compositions, a task LASSO is not able to accomplish well due to its high dimensional nature. Our results demonstrate the superiority of sparse logistic regression as a technique for both feature selection and regression over LASSO in the context of siRNA design.

A Study of the Effect of the Front-End Styling of Sport Utility Vehicles on Pedestrian Head Injuries

PubMed Central

Qin, Qin; Chen, Zheng; Bai, Zhonghao; Cao, Libo

2018-01-01

Background The number of sport utility vehicles (SUVs) on China market is continuously increasing. It is necessary to investigate the relationships between the front-end styling features of SUVs and head injuries at the styling design stage for improving the pedestrian protection performance and product development efficiency. Methods Styling feature parameters were extracted from the SUV side contour line. And simplified finite element models were established based on the 78 SUV side contour lines. Pedestrian headform impact simulations were performed and validated. The head injury criterion of 15 ms (HIC15) at four wrap-around distances was obtained. A multiple linear regression analysis method was employed to describe the relationships between the styling feature parameters and the HIC15 at each impact point. Results The relationship between the selected styling features and the HIC15 showed reasonable correlations, and the regression models and the selected independent variables showed statistical significance. Conclusions The regression equations obtained by multiple linear regression can be used to assess the performance of SUV styling in protecting pedestrians' heads and provide styling designers with technical guidance regarding their artistic creations.

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.

Equilibrium, kinetics and process design of acid yellow 132 adsorption onto red pine sawdust.

PubMed

Can, Mustafa

2015-01-01

Linear and non-linear regression procedures have been applied to the Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and Redlich-Peterson isotherms for adsorption of acid yellow 132 (AY132) dye onto red pine (Pinus resinosa) sawdust. The effects of parameters such as particle size, stirring rate, contact time, dye concentration, adsorption dose, pH, and temperature were investigated, and interaction was characterized by Fourier transform infrared spectroscopy and field emission scanning electron microscope. The non-linear method of the Langmuir isotherm equation was found to be the best fitting model to the equilibrium data. The maximum monolayer adsorption capacity was found as 79.5 mg/g. The calculated thermodynamic results suggested that AY132 adsorption onto red pine sawdust was an exothermic, physisorption, and spontaneous process. Kinetics was analyzed by four different kinetic equations using non-linear regression analysis. The pseudo-second-order equation provides the best fit with experimental data.

Partitioning sources of variation in vertebrate species richness

USGS Publications Warehouse

Boone, R.B.; Krohn, W.B.

2000-01-01

Aim: To explore biogeographic patterns of terrestrial vertebrates in Maine, USA using techniques that would describe local and spatial correlations with the environment. Location: Maine, USA. Methods: We delineated the ranges within Maine (86,156 km2) of 275 species using literature and expert review. Ranges were combined into species richness maps, and compared to geomorphology, climate, and woody plant distributions. Methods were adapted that compared richness of all vertebrate classes to each environmental correlate, rather than assessing a single explanatory theory. We partitioned variation in species richness into components using tree and multiple linear regression. Methods were used that allowed for useful comparisons between tree and linear regression results. For both methods we partitioned variation into broad-scale (spatially autocorrelated) and fine-scale (spatially uncorrelated) explained and unexplained components. By partitioning variance, and using both tree and linear regression in analyses, we explored the degree of variation in species richness for each vertebrate group that Could be explained by the relative contribution of each environmental variable. Results: In tree regression, climate variation explained richness better (92% of mean deviance explained for all species) than woody plant variation (87%) and geomorphology (86%). Reptiles were highly correlated with environmental variation (93%), followed by mammals, amphibians, and birds (each with 84-82% deviance explained). In multiple linear regression, climate was most closely associated with total vertebrate richness (78%), followed by woody plants (67%) and geomorphology (56%). Again, reptiles were closely correlated with the environment (95%), followed by mammals (73%), amphibians (63%) and birds (57%). Main conclusions: Comparing variation explained using tree and multiple linear regression quantified the importance of nonlinear relationships and local interactions between species richness and environmental variation, identifying the importance of linear relationships between reptiles and the environment, and nonlinear relationships between birds and woody plants, for example. Conservation planners should capture climatic variation in broad-scale designs; temperatures may shift during climate change, but the underlying correlations between the environment and species richness will presumably remain.

Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs. NBER Working Paper No. 20405

ERIC Educational Resources Information Center

Gelman, Andrew; Imbens, Guido

2014-01-01

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

Surgery for left ventricular aneurysm: early and late survival after simple linear repair and endoventricular patch plasty.

PubMed

Lundblad, Runar; Abdelnoor, Michel; Svennevig, Jan Ludvig

2004-09-01

Simple linear resection and endoventricular patch plasty are alternative techniques to repair postinfarction left ventricular aneurysm. The aim of the study was to compare these 2 methods with regard to early mortality and long-term survival. We retrospectively reviewed 159 patients undergoing operations between 1989 and 2003. The epidemiologic design was of an exposed (simple linear repair, n = 74) versus nonexposed (endoventricular patch plasty, n = 85) cohort with 2 endpoints: early mortality and long-term survival. The crude effect of aneurysm repair technique versus endpoint was estimated by odds ratio, rate ratio, or relative risk and their 95% confidence intervals. Stratification analysis by using the Mantel-Haenszel method was done to quantify confounders and pinpoint effect modifiers. Adjustment for multiconfounders was performed by using logistic regression and Cox regression analysis. Survival curves were analyzed with the Breslow test and the log-rank test. Early mortality was 8.2% for all patients, 13.5% after linear repair and 3.5% after endoventricular patch plasty. When adjusted for multiconfounders, the risk of early mortality was significantly higher after simple linear repair than after endoventricular patch plasty (odds ratio, 4.4; 95% confidence interval, 1.1-17.8). Mean follow-up was 5.8 +/- 3.8 years (range, 0-14.0 years). Overall 5-year cumulative survival was 78%, 70.1% after linear repair and 91.4% after endoventricular patch plasty. The risk of total mortality was significantly higher after linear repair than after endoventricular patch plasty when controlled for multiconfounders (relative risk, 4.5; 95% confidence interval, 2.0-9.7). Linear repair dominated early in the series and patch plasty dominated later, giving a possible learning-curve bias in favor of patch plasty that could not be adjusted for in the regression analysis. Postinfarction left ventricular aneurysm can be repaired with satisfactory early and late results. Surgical risk was lower and long-term survival was higher after endoventricular patch plasty than simple linear repair. Differences in outcome should be interpreted with care because of the retrospective study design and the chronology of the 2 repair methods.

Understanding Child Stunting in India: A Comprehensive Analysis of Socio-Economic, Nutritional and Environmental Determinants Using Additive Quantile Regression

PubMed Central

Fenske, Nora; Burns, Jacob; Hothorn, Torsten; Rehfuess, Eva A.

2013-01-01

Background Most attempts to address undernutrition, responsible for one third of global child deaths, have fallen behind expectations. This suggests that the assumptions underlying current modelling and intervention practices should be revisited. Objective We undertook a comprehensive analysis of the determinants of child stunting in India, and explored whether the established focus on linear effects of single risks is appropriate. Design Using cross-sectional data for children aged 0–24 months from the Indian National Family Health Survey for 2005/2006, we populated an evidence-based diagram of immediate, intermediate and underlying determinants of stunting. We modelled linear, non-linear, spatial and age-varying effects of these determinants using additive quantile regression for four quantiles of the Z-score of standardized height-for-age and logistic regression for stunting and severe stunting. Results At least one variable within each of eleven groups of determinants was significantly associated with height-for-age in the 35% Z-score quantile regression. The non-modifiable risk factors child age and sex, and the protective factors household wealth, maternal education and BMI showed the largest effects. Being a twin or multiple birth was associated with dramatically decreased height-for-age. Maternal age, maternal BMI, birth order and number of antenatal visits influenced child stunting in non-linear ways. Findings across the four quantile and two logistic regression models were largely comparable. Conclusions Our analysis confirms the multifactorial nature of child stunting. It emphasizes the need to pursue a systems-based approach and to consider non-linear effects, and suggests that differential effects across the height-for-age distribution do not play a major role. PMID:24223839

On the use and misuse of scalar scores of confounders in design and analysis of observational studies.

PubMed

Pfeiffer, R M; Riedl, R

2015-08-15

We assess the asymptotic bias of estimates of exposure effects conditional on covariates when summary scores of confounders, instead of the confounders themselves, are used to analyze observational data. First, we study regression models for cohort data that are adjusted for summary scores. Second, we derive the asymptotic bias for case-control studies when cases and controls are matched on a summary score, and then analyzed either using conditional logistic regression or by unconditional logistic regression adjusted for the summary score. Two scores, the propensity score (PS) and the disease risk score (DRS) are studied in detail. For cohort analysis, when regression models are adjusted for the PS, the estimated conditional treatment effect is unbiased only for linear models, or at the null for non-linear models. Adjustment of cohort data for DRS yields unbiased estimates only for linear regression; all other estimates of exposure effects are biased. Matching cases and controls on DRS and analyzing them using conditional logistic regression yields unbiased estimates of exposure effect, whereas adjusting for the DRS in unconditional logistic regression yields biased estimates, even under the null hypothesis of no association. Matching cases and controls on the PS yield unbiased estimates only under the null for both conditional and unconditional logistic regression, adjusted for the PS. We study the bias for various confounding scenarios and compare our asymptotic results with those from simulations with limited sample sizes. To create realistic correlations among multiple confounders, we also based simulations on a real dataset. Copyright © 2015 John Wiley & Sons, Ltd.

Effect Size Measure and Analysis of Single Subject Designs

ERIC Educational Resources Information Center

Society for Research on Educational Effectiveness, 2013

2013-01-01

One of the vexing problems in the analysis of SSD is in the assessment of the effect of intervention. Serial dependence notwithstanding, the linear model approach that has been advanced involves, in general, the fitting of regression lines (or curves) to the set of observations within each phase of the design and comparing the parameters of these…

Using Generalized Additive Models to Analyze Single-Case Designs

ERIC Educational Resources Information Center

Shadish, William; Sullivan, Kristynn

2013-01-01

Many analyses for single-case designs (SCDs)--including nearly all the effect size indicators-- currently assume no trend in the data. Regression and multilevel models allow for trend, but usually test only linear trend and have no principled way of knowing if higher order trends should be represented in the model. This paper shows how Generalized…

Stress Regression Analysis of Asphalt Concrete Deck Pavement Based on Orthogonal Experimental Design and Interlayer Contact

NASA Astrophysics Data System (ADS)

Wang, Xuntao; Feng, Jianhu; Wang, Hu; Hong, Shidi; Zheng, Supei

2018-03-01

A three-dimensional finite element box girder bridge and its asphalt concrete deck pavement were established by ANSYS software, and the interlayer bonding condition of asphalt concrete deck pavement was assumed to be contact bonding condition. Orthogonal experimental design is used to arrange the testing plans of material parameters, and an evaluation of the effect of different material parameters in the mechanical response of asphalt concrete surface layer was conducted by multiple linear regression model and using the results from the finite element analysis. Results indicated that stress regression equations can well predict the stress of the asphalt concrete surface layer, and elastic modulus of waterproof layer has a significant influence on stress values of asphalt concrete surface layer.

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.

Digital controllers for VTOL aircraft

NASA Technical Reports Server (NTRS)

Stengel, R. F.; Broussard, J. R.; Berry, P. W.

1976-01-01

Using linear-optimal estimation and control techniques, digital-adaptive control laws have been designed for a tandem-rotor helicopter which is equipped for fully automatic flight in terminal area operations. Two distinct discrete-time control laws are designed to interface with velocity-command and attitude-command guidance logic, and each incorporates proportional-integral compensation for non-zero-set-point regulation, as well as reduced-order Kalman filters for sensor blending and noise rejection. Adaptation to flight condition is achieved with a novel gain-scheduling method based on correlation and regression analysis. The linear-optimal design approach is found to be a valuable tool in the development of practical multivariable control laws for vehicles which evidence significant coupling and insufficient natural stability.

Users manual for flight control design programs

NASA Technical Reports Server (NTRS)

Nalbandian, J. Y.

1975-01-01

Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.

Predicting the dissolution kinetics of silicate glasses using machine learning

NASA Astrophysics Data System (ADS)

Anoop Krishnan, N. M.; Mangalathu, Sujith; Smedskjaer, Morten M.; Tandia, Adama; Burton, Henry; Bauchy, Mathieu

2018-05-01

Predicting the dissolution rates of silicate glasses in aqueous conditions is a complex task as the underlying mechanism(s) remain poorly understood and the dissolution kinetics can depend on a large number of intrinsic and extrinsic factors. Here, we assess the potential of data-driven models based on machine learning to predict the dissolution rates of various aluminosilicate glasses exposed to a wide range of solution pH values, from acidic to caustic conditions. Four classes of machine learning methods are investigated, namely, linear regression, support vector machine regression, random forest, and artificial neural network. We observe that, although linear methods all fail to describe the dissolution kinetics, the artificial neural network approach offers excellent predictions, thanks to its inherent ability to handle non-linear data. Overall, we suggest that a more extensive use of machine learning approaches could significantly accelerate the design of novel glasses with tailored properties.

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.

Conditional Monte Carlo randomization tests for regression models.

PubMed

Parhat, Parwen; Rosenberger, William F; Diao, Guoqing

2014-08-15

We discuss the computation of randomization tests for clinical trials of two treatments when the primary outcome is based on a regression model. We begin by revisiting the seminal paper of Gail, Tan, and Piantadosi (1988), and then describe a method based on Monte Carlo generation of randomization sequences. The tests based on this Monte Carlo procedure are design based, in that they incorporate the particular randomization procedure used. We discuss permuted block designs, complete randomization, and biased coin designs. We also use a new technique by Plamadeala and Rosenberger (2012) for simple computation of conditional randomization tests. Like Gail, Tan, and Piantadosi, we focus on residuals from generalized linear models and martingale residuals from survival models. Such techniques do not apply to longitudinal data analysis, and we introduce a method for computation of randomization tests based on the predicted rate of change from a generalized linear mixed model when outcomes are longitudinal. We show, by simulation, that these randomization tests preserve the size and power well under model misspecification. Copyright © 2014 John Wiley & Sons, Ltd.

The Use of Linear Instrumental Variables Methods in Health Services Research and Health Economics: A Cautionary Note

PubMed Central

Terza, Joseph V; Bradford, W David; Dismuke, Clara E

2008-01-01

Objective To investigate potential bias in the use of the conventional linear instrumental variables (IV) method for the estimation of causal effects in inherently nonlinear regression settings. Data Sources Smoking Supplement to the 1979 National Health Interview Survey, National Longitudinal Alcohol Epidemiologic Survey, and simulated data. Study Design Potential bias from the use of the linear IV method in nonlinear models is assessed via simulation studies and real world data analyses in two commonly encountered regression setting: (1) models with a nonnegative outcome (e.g., a count) and a continuous endogenous regressor; and (2) models with a binary outcome and a binary endogenous regressor. Principle Findings The simulation analyses show that substantial bias in the estimation of causal effects can result from applying the conventional IV method in inherently nonlinear regression settings. Moreover, the bias is not attenuated as the sample size increases. This point is further illustrated in the survey data analyses in which IV-based estimates of the relevant causal effects diverge substantially from those obtained with appropriate nonlinear estimation methods. Conclusions We offer this research as a cautionary note to those who would opt for the use of linear specifications in inherently nonlinear settings involving endogeneity. PMID:18546544

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

The use of experimental design in the development of an HPLC-ECD method for the analysis of captopril.

PubMed

Khamanga, Sandile M; Walker, Roderick B

2011-01-15

An accurate, sensitive and specific high performance liquid chromatography-electrochemical detection (HPLC-ECD) method that was developed and validated for captopril (CPT) is presented. Separation was achieved using a Phenomenex(®) Luna 5 μm (C(18)) column and a mobile phase comprised of phosphate buffer (adjusted to pH 3.0): acetonitrile in a ratio of 70:30 (v/v). Detection was accomplished using a full scan multi channel ESA Coulometric detector in the "oxidative-screen" mode with the upstream electrode (E(1)) set at +600 mV and the downstream (analytical) electrode (E(2)) set at +950 mV, while the potential of the guard cell was maintained at +1050 mV. The detector gain was set at 300. Experimental design using central composite design (CCD) was used to facilitate method development. Mobile phase pH, molarity and concentration of acetonitrile (ACN) were considered the critical factors to be studied to establish the retention time of CPT and cyclizine (CYC) that was used as the internal standard. Twenty experiments including centre points were undertaken and a quadratic model was derived for the retention time for CPT using the experimental data. The method was validated for linearity, accuracy, precision, limits of quantitation and detection, as per the ICH guidelines. The system was found to produce sharp and well-resolved peaks for CPT and CYC with retention times of 3.08 and 7.56 min, respectively. Linear regression analysis for the calibration curve showed a good linear relationship with a regression coefficient of 0.978 in the concentration range of 2-70 μg/mL. The linear regression equation was y=0.0131x+0.0275. The limits of detection (LOQ) and quantitation (LOD) were found to be 2.27 and 0.6 μg/mL, respectively. The method was used to analyze CPT in tablets. The wide range for linearity, accuracy, sensitivity, short retention time and composition of the mobile phase indicated that this method is better for the quantification of CPT than the pharmacopoeial methods. Copyright © 2010 Elsevier B.V. All rights reserved.

Virtual Beach v2.2 User Guide

EPA Science Inventory

Virtual Beach version 2.2 (VB 2.2) is a decision support tool. It is designed to construct site-specific Multi-Linear Regression (MLR) models to predict pathogen indicator levels (or fecal indicator bacteria, FIB) at recreational beaches. MLR analysis has outperformed persisten...

A Technique of Fuzzy C-Mean in Multiple Linear Regression Model toward Paddy Yield

NASA Astrophysics Data System (ADS)

Syazwan Wahab, Nur; Saifullah Rusiman, Mohd; Mohamad, Mahathir; Amira Azmi, Nur; Che Him, Norziha; Ghazali Kamardan, M.; Ali, Maselan

2018-04-01

In this paper, we propose a hybrid model which is a combination of multiple linear regression model and fuzzy c-means method. This research involved a relationship between 20 variates of the top soil that are analyzed prior to planting of paddy yields at standard fertilizer rates. Data used were from the multi-location trials for rice carried out by MARDI at major paddy granary in Peninsular Malaysia during the period from 2009 to 2012. Missing observations were estimated using mean estimation techniques. The data were analyzed using multiple linear regression model and a combination of multiple linear regression model and fuzzy c-means method. Analysis of normality and multicollinearity indicate that the data is normally scattered without multicollinearity among independent variables. Analysis of fuzzy c-means cluster the yield of paddy into two clusters before the multiple linear regression model can be used. The comparison between two method indicate that the hybrid of multiple linear regression model and fuzzy c-means method outperform the multiple linear regression model with lower value of mean square error.

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.

Linear regression crash prediction models : issues and proposed solutions.

DOT National Transportation Integrated Search

2010-05-01

The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...

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…

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.

Predictors of postoperative outcomes of cubital tunnel syndrome treatments using multiple logistic regression analysis.

PubMed

Suzuki, Taku; Iwamoto, Takuji; Shizu, Kanae; Suzuki, Katsuji; Yamada, Harumoto; Sato, Kazuki

2017-05-01

This retrospective study was designed to investigate prognostic factors for postoperative outcomes for cubital tunnel syndrome (CubTS) using multiple logistic regression analysis with a large number of patients. Eighty-three patients with CubTS who underwent surgeries were enrolled. The following potential prognostic factors for disease severity were selected according to previous reports: sex, age, type of surgery, disease duration, body mass index, cervical lesion, presence of diabetes mellitus, Workers' Compensation status, preoperative severity, and preoperative electrodiagnostic testing. Postoperative severity of disease was assessed 2 years after surgery by Messina's criteria which is an outcome measure specifically for CubTS. Bivariate analysis was performed to select candidate prognostic factors for multiple linear regression analyses. Multiple logistic regression analysis was conducted to identify the association between postoperative severity and selected prognostic factors. Both bivariate and multiple linear regression analysis revealed only preoperative severity as an independent risk factor for poor prognosis, while other factors did not show any significant association. Although conflicting results exist regarding prognosis of CubTS, this study supports evidence from previous studies and concludes early surgical intervention portends the most favorable prognosis. Copyright © 2017 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved.

Engine With Regression and Neural Network Approximators Designed

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.

2001-01-01

At the NASA Glenn Research Center, the NASA engine performance program (NEPP, ref. 1) and the design optimization testbed COMETBOARDS (ref. 2) with regression and neural network analysis-approximators have been coupled to obtain a preliminary engine design methodology. The solution to a high-bypass-ratio subsonic waverotor-topped turbofan engine, which is shown in the preceding figure, was obtained by the simulation depicted in the following figure. This engine is made of 16 components mounted on two shafts with 21 flow stations. The engine is designed for a flight envelope with 47 operating points. The design optimization utilized both neural network and regression approximations, along with the cascade strategy (ref. 3). The cascade used three algorithms in sequence: the method of feasible directions, the sequence of unconstrained minimizations technique, and sequential quadratic programming. The normalized optimum thrusts obtained by the three methods are shown in the following figure: the cascade algorithm with regression approximation is represented by a triangle, a circle is shown for the neural network solution, and a solid line indicates original NEPP results. The solutions obtained from both approximate methods lie within one standard deviation of the benchmark solution for each operating point. The simulation improved the maximum thrust by 5 percent. The performance of the linear regression and neural network methods as alternate engine analyzers was found to be satisfactory for the analysis and operation optimization of air-breathing propulsion engines (ref. 4).

Linear regression models for solvent accessibility prediction in proteins.

PubMed

Wagner, Michael; Adamczak, Rafał; Porollo, Aleksey; Meller, Jarosław

2005-04-01

The relative solvent accessibility (RSA) of an amino acid residue in a protein structure is a real number that represents the solvent exposed surface area of this residue in relative terms. The problem of predicting the RSA from the primary amino acid sequence can therefore be cast as a regression problem. Nevertheless, RSA prediction has so far typically been cast as a classification problem. Consequently, various machine learning techniques have been used within the classification framework to predict whether a given amino acid exceeds some (arbitrary) RSA threshold and would thus be predicted to be "exposed," as opposed to "buried." We have recently developed novel methods for RSA prediction using nonlinear regression techniques which provide accurate estimates of the real-valued RSA and outperform classification-based approaches with respect to commonly used two-class projections. However, while their performance seems to provide a significant improvement over previously published approaches, these Neural Network (NN) based methods are computationally expensive to train and involve several thousand parameters. In this work, we develop alternative regression models for RSA prediction which are computationally much less expensive, involve orders-of-magnitude fewer parameters, and are still competitive in terms of prediction quality. In particular, we investigate several regression models for RSA prediction using linear L1-support vector regression (SVR) approaches as well as standard linear least squares (LS) regression. Using rigorously derived validation sets of protein structures and extensive cross-validation analysis, we compare the performance of the SVR with that of LS regression and NN-based methods. In particular, we show that the flexibility of the SVR (as encoded by metaparameters such as the error insensitivity and the error penalization terms) can be very beneficial to optimize the prediction accuracy for buried residues. We conclude that the simple and computationally much more efficient linear SVR performs comparably to nonlinear models and thus can be used in order to facilitate further attempts to design more accurate RSA prediction methods, with applications to fold recognition and de novo protein structure prediction methods.

The Application of the Cumulative Logistic Regression Model to Automated Essay Scoring

ERIC Educational Resources Information Center

Haberman, Shelby J.; Sinharay, Sandip

2010-01-01

Most automated essay scoring programs use a linear regression model to predict an essay score from several essay features. This article applied a cumulative logit model instead of the linear regression model to automated essay scoring. Comparison of the performances of the linear regression model and the cumulative logit model was performed on a…

Transmission of linear regression patterns between time series: From relationship in time series to complex networks

NASA Astrophysics Data System (ADS)

Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui

2014-07-01

The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.

Transmission of linear regression patterns between time series: from relationship in time series to complex networks.

PubMed

Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui

2014-07-01

The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.

Do clinical and translational science graduate students understand linear regression? Development and early validation of the REGRESS quiz.

PubMed

Enders, Felicity

2013-12-01

Although regression is widely used for reading and publishing in the medical literature, no instruments were previously available to assess students' understanding. The goal of this study was to design and assess such an instrument for graduate students in Clinical and Translational Science and Public Health. A 27-item REsearch on Global Regression Expectations in StatisticS (REGRESS) quiz was developed through an iterative process. Consenting students taking a course on linear regression in a Clinical and Translational Science program completed the quiz pre- and postcourse. Student results were compared to practicing statisticians with a master's or doctoral degree in statistics or a closely related field. Fifty-two students responded precourse, 59 postcourse , and 22 practicing statisticians completed the quiz. The mean (SD) score was 9.3 (4.3) for students precourse and 19.0 (3.5) postcourse (P < 0.001). Postcourse students had similar results to practicing statisticians (mean (SD) of 20.1(3.5); P = 0.21). Students also showed significant improvement pre/postcourse in each of six domain areas (P < 0.001). The REGRESS quiz was internally reliable (Cronbach's alpha 0.89). The initial validation is quite promising with statistically significant and meaningful differences across time and study populations. Further work is needed to validate the quiz across multiple institutions. © 2013 Wiley Periodicals, Inc.

Product unit neural network models for predicting the growth limits of Listeria monocytogenes.

PubMed

Valero, A; Hervás, C; García-Gimeno, R M; Zurera, G

2007-08-01

A new approach to predict the growth/no growth interface of Listeria monocytogenes as a function of storage temperature, pH, citric acid (CA) and ascorbic acid (AA) is presented. A linear logistic regression procedure was performed and a non-linear model was obtained by adding new variables by means of a Neural Network model based on Product Units (PUNN). The classification efficiency of the training data set and the generalization data of the new Logistic Regression PUNN model (LRPU) were compared with Linear Logistic Regression (LLR) and Polynomial Logistic Regression (PLR) models. 92% of the total cases from the LRPU model were correctly classified, an improvement on the percentage obtained using the PLR model (90%) and significantly higher than the results obtained with the LLR model, 80%. On the other hand predictions of LRPU were closer to data observed which permits to design proper formulations in minimally processed foods. This novel methodology can be applied to predictive microbiology for describing growth/no growth interface of food-borne microorganisms such as L. monocytogenes. The optimal balance is trying to find models with an acceptable interpretation capacity and with good ability to fit the data on the boundaries of variable range. The results obtained conclude that these kinds of models might well be very a valuable tool for mathematical modeling.

Least median of squares and iteratively re-weighted least squares as robust linear regression methods for fluorimetric determination of α-lipoic acid in capsules in ideal and non-ideal cases of linearity.

PubMed

Korany, Mohamed A; Gazy, Azza A; Khamis, Essam F; Ragab, Marwa A A; Kamal, Miranda F

2018-06-01

This study outlines two robust regression approaches, namely least median of squares (LMS) and iteratively re-weighted least squares (IRLS) to investigate their application in instrument analysis of nutraceuticals (that is, fluorescence quenching of merbromin reagent upon lipoic acid addition). These robust regression methods were used to calculate calibration data from the fluorescence quenching reaction (∆F and F-ratio) under ideal or non-ideal linearity conditions. For each condition, data were treated using three regression fittings: Ordinary Least Squares (OLS), LMS and IRLS. Assessment of linearity, limits of detection (LOD) and quantitation (LOQ), accuracy and precision were carefully studied for each condition. LMS and IRLS regression line fittings showed significant improvement in correlation coefficients and all regression parameters for both methods and both conditions. In the ideal linearity condition, the intercept and slope changed insignificantly, but a dramatic change was observed for the non-ideal condition and linearity intercept. Under both linearity conditions, LOD and LOQ values after the robust regression line fitting of data were lower than those obtained before data treatment. The results obtained after statistical treatment indicated that the linearity ranges for drug determination could be expanded to lower limits of quantitation by enhancing the regression equation parameters after data treatment. Analysis results for lipoic acid in capsules, using both fluorimetric methods, treated by parametric OLS and after treatment by robust LMS and IRLS were compared for both linearity conditions. Copyright © 2018 John Wiley & Sons, Ltd.

Spatial structure, sampling design and scale in remotely-sensed imagery of a California savanna woodland

NASA Technical Reports Server (NTRS)

Mcgwire, K.; Friedl, M.; Estes, J. E.

1993-01-01

This article describes research related to sampling techniques for establishing linear relations between land surface parameters and remotely-sensed data. Predictive relations are estimated between percentage tree cover in a savanna environment and a normalized difference vegetation index (NDVI) derived from the Thematic Mapper sensor. Spatial autocorrelation in original measurements and regression residuals is examined using semi-variogram analysis at several spatial resolutions. Sampling schemes are then tested to examine the effects of autocorrelation on predictive linear models in cases of small sample sizes. Regression models between image and ground data are affected by the spatial resolution of analysis. Reducing the influence of spatial autocorrelation by enforcing minimum distances between samples may also improve empirical models which relate ground parameters to satellite data.

The Effects of Academic Optimism on Elementary Reading Achievement

ERIC Educational Resources Information Center

Bevel, Raymona K.; Mitchell, Roxanne M.

2012-01-01

Purpose: The purpose of this paper is to explore the relationship between academic optimism (AO) and elementary reading achievement (RA). Design/methodology/approach: Using correlation and hierarchical linear regression, the authors examined school-level effects of AO on fifth grade reading achievement in 29 elementary schools in Alabama.…

Authentic Practices as Contexts for Learning to Draw Inferences beyond Correlated Data

ERIC Educational Resources Information Center

Dierdorp, Adri; Bakker, Arthur; Eijkelhof, Harrie; van Maanen, Jan

2011-01-01

To support 11th-grade students' informal inferential reasoning, a teaching and learning strategy was designed based on authentic practices in which professionals use correlation or linear regression. These practices included identifying suitable physical training programmes, dyke monitoring, and the calibration of measurement instruments. The…

Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches

DTIC Science & Technology

1974-01-01

REGRESSION MODEL - THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January 1974 Nelson Delfino d’Avila Mascarenha;? Image...Report 520 DIGITAL IMAGE RESTORATION UNDER A REGRESSION MODEL THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January...a two- dimensional form adequately describes the linear model . A dis- cretization is performed by using quadrature methods. By trans

Missing heritability in the tails of quantitative traits? A simulation study on the impact of slightly altered true genetic models.

PubMed

Pütter, Carolin; Pechlivanis, Sonali; Nöthen, Markus M; Jöckel, Karl-Heinz; Wichmann, Heinz-Erich; Scherag, André

2011-01-01

Genome-wide association studies have identified robust associations between single nucleotide polymorphisms and complex traits. As the proportion of phenotypic variance explained is still limited for most of the traits, larger and larger meta-analyses are being conducted to detect additional associations. Here we investigate the impact of the study design and the underlying assumption about the true genetic effect in a bimodal mixture situation on the power to detect associations. We performed simulations of quantitative phenotypes analysed by standard linear regression and dichotomized case-control data sets from the extremes of the quantitative trait analysed by standard logistic regression. Using linear regression, markers with an effect in the extremes of the traits were almost undetectable, whereas analysing extremes by case-control design had superior power even for much smaller sample sizes. Two real data examples are provided to support our theoretical findings and to explore our mixture and parameter assumption. Our findings support the idea to re-analyse the available meta-analysis data sets to detect new loci in the extremes. Moreover, our investigation offers an explanation for discrepant findings when analysing quantitative traits in the general population and in the extremes. Copyright © 2011 S. Karger AG, Basel.

Element enrichment factor calculation using grain-size distribution and functional data regression.

PubMed

Sierra, C; Ordóñez, C; Saavedra, A; Gallego, J R

2015-01-01

In environmental geochemistry studies it is common practice to normalize element concentrations in order to remove the effect of grain size. Linear regression with respect to a particular grain size or conservative element is a widely used method of normalization. In this paper, the utility of functional linear regression, in which the grain-size curve is the independent variable and the concentration of pollutant the dependent variable, is analyzed and applied to detrital sediment. After implementing functional linear regression and classical linear regression models to normalize and calculate enrichment factors, we concluded that the former regression technique has some advantages over the latter. First, functional linear regression directly considers the grain-size distribution of the samples as the explanatory variable. Second, as the regression coefficients are not constant values but functions depending on the grain size, it is easier to comprehend the relationship between grain size and pollutant concentration. Third, regularization can be introduced into the model in order to establish equilibrium between reliability of the data and smoothness of the solutions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Who Will Win?: Predicting the Presidential Election Using Linear Regression

ERIC Educational Resources Information Center

Lamb, John H.

2007-01-01

This article outlines a linear regression activity that engages learners, uses technology, and fosters cooperation. Students generated least-squares linear regression equations using TI-83 Plus[TM] graphing calculators, Microsoft[C] Excel, and paper-and-pencil calculations using derived normal equations to predict the 2004 presidential election.…

The microcomputer scientific software series 2: general linear model--regression.

Treesearch

Harold M. Rauscher

1983-01-01

The general linear model regression (GLMR) program provides the microcomputer user with a sophisticated regression analysis capability. The output provides a regression ANOVA table, estimators of the regression model coefficients, their confidence intervals, confidence intervals around the predicted Y-values, residuals for plotting, a check for multicollinearity, a...

The regression discontinuity design showed to be a valid alternative to a randomized controlled trial for estimating treatment effects.

PubMed

Maas, Iris L; Nolte, Sandra; Walter, Otto B; Berger, Thomas; Hautzinger, Martin; Hohagen, Fritz; Lutz, Wolfgang; Meyer, Björn; Schröder, Johanna; Späth, Christina; Klein, Jan Philipp; Moritz, Steffen; Rose, Matthias

2017-02-01

To compare treatment effect estimates obtained from a regression discontinuity (RD) design with results from an actual randomized controlled trial (RCT). Data from an RCT (EVIDENT), which studied the effect of an Internet intervention on depressive symptoms measured with the Patient Health Questionnaire (PHQ-9), were used to perform an RD analysis, in which treatment allocation was determined by a cutoff value at baseline (PHQ-9 = 10). A linear regression model was fitted to the data, selecting participants above the cutoff who had received the intervention (n = 317) and control participants below the cutoff (n = 187). Outcome was PHQ-9 sum score 12 weeks after baseline. Robustness of the effect estimate was studied; the estimate was compared with the RCT treatment effect. The final regression model showed a regression coefficient of -2.29 [95% confidence interval (CI): -3.72 to -.85] compared with a treatment effect found in the RCT of -1.57 (95% CI: -2.07 to -1.07). Although the estimates obtained from two designs are not equal, their confidence intervals overlap, suggesting that an RD design can be a valid alternative for RCTs. This finding is particularly important for situations where an RCT may not be feasible or ethical as is often the case in clinical research settings. Copyright © 2016 Elsevier Inc. All rights reserved.

Healthcare Expenditures Associated with Depression Among Individuals with Osteoarthritis: Post-Regression Linear Decomposition Approach.

PubMed

Agarwal, Parul; Sambamoorthi, Usha

2015-12-01

Depression is common among individuals with osteoarthritis and leads to increased healthcare burden. The objective of this study was to examine excess total healthcare expenditures associated with depression among individuals with osteoarthritis in the US. Adults with self-reported osteoarthritis (n = 1881) were identified using data from the 2010 Medical Expenditure Panel Survey (MEPS). Among those with osteoarthritis, chi-square tests and ordinary least square regressions (OLS) were used to examine differences in healthcare expenditures between those with and without depression. Post-regression linear decomposition technique was used to estimate the relative contribution of different constructs of the Anderson's behavioral model, i.e., predisposing, enabling, need, personal healthcare practices, and external environment factors, to the excess expenditures associated with depression among individuals with osteoarthritis. All analysis accounted for the complex survey design of MEPS. Depression coexisted among 20.6 % of adults with osteoarthritis. The average total healthcare expenditures were $13,684 among adults with depression compared to $9284 among those without depression. Multivariable OLS regression revealed that adults with depression had 38.8 % higher healthcare expenditures (p < 0.001) compared to those without depression. Post-regression linear decomposition analysis indicated that 50 % of differences in expenditures among adults with and without depression can be explained by differences in need factors. Among individuals with coexisting osteoarthritis and depression, excess healthcare expenditures associated with depression were mainly due to comorbid anxiety, chronic conditions and poor health status. These expenditures may potentially be reduced by providing timely intervention for need factors or by providing care under a collaborative care model.

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee

2015-08-01

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

PubMed Central

Duarte, Belmiro P. M.; Wong, Weng Kee

2014-01-01

Summary This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted. PMID:26512159

The discovery of indicator variables for QSAR using inductive logic programming

NASA Astrophysics Data System (ADS)

King, Ross D.; Srinivasan, Ashwin

1997-11-01

A central problem in forming accurate regression equations in QSAR studies isthe selection of appropriate descriptors for the compounds under study. Wedescribe a novel procedure for using inductive logic programming (ILP) todiscover new indicator variables (attributes) for QSAR problems, and show thatthese improve the accuracy of the derived regression equations. ILP techniqueshave previously been shown to work well on drug design problems where thereis a large structural component or where clear comprehensible rules arerequired. However, ILP techniques have had the disadvantage of only being ableto make qualitative predictions (e.g. active, inactive) and not to predictreal numbers (regression). We unify ILP and linear regression techniques togive a QSAR method that has the strength of ILP at describing stericstructure, with the familiarity and power of linear regression. We evaluatedthe utility of this new QSAR technique by examining the prediction ofbiological activity with and without the addition of new structural indicatorvariables formed by ILP. In three out of five datasets examined the additionof ILP variables produced statistically better results (P < 0.01) over theoriginal description. The new ILP variables did not increase the overallcomplexity of the derived QSAR equations and added insight into possiblemechanisms of action. We conclude that ILP can aid in the process of drugdesign.

[Comparison of application of Cochran-Armitage trend test and linear regression analysis for rate trend analysis in epidemiology study].

PubMed

Wang, D Z; Wang, C; Shen, C F; Zhang, Y; Zhang, H; Song, G D; Xue, X D; Xu, Z L; Zhang, S; Jiang, G H

2017-05-10

We described the time trend of acute myocardial infarction (AMI) from 1999 to 2013 in Tianjin incidence rate with Cochran-Armitage trend (CAT) test and linear regression analysis, and the results were compared. Based on actual population, CAT test had much stronger statistical power than linear regression analysis for both overall incidence trend and age specific incidence trend (Cochran-Armitage trend P value

Design of an optimum computer vision-based automatic abalone (Haliotis discus hannai) grading algorithm.

PubMed

Lee, Donggil; Lee, Kyounghoon; Kim, Seonghun; Yang, Yongsu

2015-04-01

An automatic abalone grading algorithm that estimates abalone weights on the basis of computer vision using 2D images is developed and tested. The algorithm overcomes the problems experienced by conventional abalone grading methods that utilize manual sorting and mechanical automatic grading. To design an optimal algorithm, a regression formula and R(2) value were investigated by performing a regression analysis for each of total length, body width, thickness, view area, and actual volume against abalone weights. The R(2) value between the actual volume and abalone weight was 0.999, showing a relatively high correlation. As a result, to easily estimate the actual volumes of abalones based on computer vision, the volumes were calculated under the assumption that abalone shapes are half-oblate ellipsoids, and a regression formula was derived to estimate the volumes of abalones through linear regression analysis between the calculated and actual volumes. The final automatic abalone grading algorithm is designed using the abalone volume estimation regression formula derived from test results, and the actual volumes and abalone weights regression formula. In the range of abalones weighting from 16.51 to 128.01 g, the results of evaluation of the performance of algorithm via cross-validation indicate root mean square and worst-case prediction errors of are 2.8 and ±8 g, respectively. © 2015 Institute of Food Technologists®

[Ultrasonic measurements of fetal thalamus, caudate nucleus and lenticular nucleus in prenatal diagnosis].

PubMed

Yang, Ruiqi; Wang, Fei; Zhang, Jialing; Zhu, Chonglei; Fan, Limei

2015-05-19

To establish the reference values of thalamus, caudate nucleus and lenticular nucleus diameters through fetal thalamic transverse section. A total of 265 fetuses at our hospital were randomly selected from November 2012 to August 2014. And the transverse and length diameters of thalamus, caudate nucleus and lenticular nucleus were measured. SPSS 19.0 statistical software was used to calculate the regression curve of fetal diameter changes and gestational weeks of pregnancy. P < 0.05 was considered as having statistical significance. The linear regression equation of fetal thalamic length diameter and gestational week was: Y = 0.051X+0.201, R = 0.876, linear regression equation of thalamic transverse diameter and fetal gestational week was: Y = 0.031X+0.229, R = 0.817, linear regression equation of fetal head of caudate nucleus length diameter and gestational age was: Y = 0.033X+0.101, R = 0.722, linear regression equation of fetal head of caudate nucleus transverse diameter and gestational week was: R = 0.025 - 0.046, R = 0.711, linear regression equation of fetal lentiform nucleus length diameter and gestational week was: Y = 0.046+0.229, R = 0.765, linear regression equation of fetal lentiform nucleus diameter and gestational week was: Y = 0.025 - 0.05, R = 0.772. Ultrasonic measurement of diameter of fetal thalamus caudate nucleus, and lenticular nucleus through thalamic transverse section is simple and convenient. And measurements increase with fetal gestational weeks and there is linear regression relationship between them.

Local Linear Regression for Data with AR Errors.

PubMed

Li, Runze; Li, Yan

2009-07-01

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

Orthogonal Regression: A Teaching Perspective

ERIC Educational Resources Information Center

Carr, James R.

2012-01-01

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is…

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Practical Session: Simple Linear Regression

NASA Astrophysics Data System (ADS)

Clausel, M.; Grégoire, G.

2014-12-01

Two exercises are proposed to illustrate the simple linear regression. The first one is based on the famous Galton's data set on heredity. We use the lm R command and get coefficients estimates, standard error of the error, R2, residuals …In the second example, devoted to data related to the vapor tension of mercury, we fit a simple linear regression, predict values, and anticipate on multiple linear regression. This pratical session is an excerpt from practical exercises proposed by A. Dalalyan at EPNC (see Exercises 1 and 2 of http://certis.enpc.fr/~dalalyan/Download/TP_ENPC_4.pdf).

celerite: Scalable 1D Gaussian Processes in C++, Python, and Julia

NASA Astrophysics Data System (ADS)

Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth

2017-09-01

celerite provides fast and scalable Gaussian Process (GP) Regression in one dimension and is implemented in C++, Python, and Julia. The celerite API is designed to be familiar to users of george and, like george, celerite is designed to efficiently evaluate the marginalized likelihood of a dataset under a GP model. This is then be used alongside a non-linear optimization or posterior inference library for the best results.

Morse Code, Scrabble, and the Alphabet

ERIC Educational Resources Information Center

Richardson, Mary; Gabrosek, John; Reischman, Diann; Curtiss, Phyliss

2004-01-01

In this paper we describe an interactive activity that illustrates simple linear regression. Students collect data and analyze it using simple linear regression techniques taught in an introductory applied statistics course. The activity is extended to illustrate checks for regression assumptions and regression diagnostics taught in an…

Motivations and Benefits for Attaining HR Certifications

ERIC Educational Resources Information Center

Lester, Scott W.; Dwyer, Dale J.

2012-01-01

Purpose: The aim of this paper is to examine the motivations and benefits for pursuing or not pursuing the PHR and SPHR. Design/methodology/approach: Using a sample of 1,862 participants, the study used multinomial logistic and hierarchical linear regression to test six hypotheses. Findings: Participants pursuing SPHR were more likely to report…

Identifying Predictors of Physics Item Difficulty: A Linear Regression Approach

ERIC Educational Resources Information Center

Mesic, Vanes; Muratovic, Hasnija

2011-01-01

Large-scale assessments of student achievement in physics are often approached with an intention to discriminate students based on the attained level of their physics competencies. Therefore, for purposes of test design, it is important that items display an acceptable discriminatory behavior. To that end, it is recommended to avoid extraordinary…

The Role of Schools, Families, and Psychological Variables on Math Achievement of Black High School Students

ERIC Educational Resources Information Center

Strayhorn, Terrell L.

2010-01-01

Using data from the National Education Longitudinal Study (NELS;1988/2000), the author conducted hierarchical linear regression analyses, with a nested design, to estimate the influence of affective variables--parent involvement, teacher perceptions, and school environments--on Black students' math achievement in grade 10. Drawing on…

On the equivalence of case-crossover and time series methods in environmental epidemiology.

PubMed

Lu, Yun; Zeger, Scott L

2007-04-01

The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.

Performance of an Axisymmetric Rocket Based Combined Cycle Engine During Rocket Only Operation Using Linear Regression Analysis

NASA Technical Reports Server (NTRS)

Smith, Timothy D.; Steffen, Christopher J., Jr.; Yungster, Shaye; Keller, Dennis J.

1998-01-01

The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to 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 multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.

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.

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.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

PubMed

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

A comparison of methods for the analysis of binomial clustered outcomes in behavioral research.

PubMed

Ferrari, Alberto; Comelli, Mario

2016-12-01

In behavioral research, data consisting of a per-subject proportion of "successes" and "failures" over a finite number of trials often arise. This clustered binary data are usually non-normally distributed, which can distort inference if the usual general linear model is applied and sample size is small. A number of more advanced methods is available, but they are often technically challenging and a comparative assessment of their performances in behavioral setups has not been performed. We studied the performances of some methods applicable to the analysis of proportions; namely linear regression, Poisson regression, beta-binomial regression and Generalized Linear Mixed Models (GLMMs). We report on a simulation study evaluating power and Type I error rate of these models in hypothetical scenarios met by behavioral researchers; plus, we describe results from the application of these methods on data from real experiments. Our results show that, while GLMMs are powerful instruments for the analysis of clustered binary outcomes, beta-binomial regression can outperform them in a range of scenarios. Linear regression gave results consistent with the nominal level of significance, but was overall less powerful. Poisson regression, instead, mostly led to anticonservative inference. GLMMs and beta-binomial regression are generally more powerful than linear regression; yet linear regression is robust to model misspecification in some conditions, whereas Poisson regression suffers heavily from violations of the assumptions when used to model proportion data. We conclude providing directions to behavioral scientists dealing with clustered binary data and small sample sizes. Copyright © 2016 Elsevier B.V. All rights reserved.

OPLS statistical model versus linear regression to assess sonographic predictors of stroke prognosis.

PubMed

Vajargah, Kianoush Fathi; Sadeghi-Bazargani, Homayoun; Mehdizadeh-Esfanjani, Robab; Savadi-Oskouei, Daryoush; Farhoudi, Mehdi

2012-01-01

The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.

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.

Interpretation of commonly used statistical regression models.

PubMed

Kasza, Jessica; Wolfe, Rory

2014-01-01

A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.

Linear regression analysis for comparing two measurers or methods of measurement: but which regression?

PubMed

Ludbrook, John

2010-07-01

1. There are two reasons for wanting to compare measurers or methods of measurement. One is to calibrate one method or measurer against another; the other is to detect bias. Fixed bias is present when one method gives higher (or lower) values across the whole range of measurement. Proportional bias is present when one method gives values that diverge progressively from those of the other. 2. Linear regression analysis is a popular method for comparing methods of measurement, but the familiar ordinary least squares (OLS) method is rarely acceptable. The OLS method requires that the x values are fixed by the design of the study, whereas it is usual that both y and x values are free to vary and are subject to error. In this case, special regression techniques must be used. 3. Clinical chemists favour techniques such as major axis regression ('Deming's method'), the Passing-Bablok method or the bivariate least median squares method. Other disciplines, such as allometry, astronomy, biology, econometrics, fisheries research, genetics, geology, physics and sports science, have their own preferences. 4. Many Monte Carlo simulations have been performed to try to decide which technique is best, but the results are almost uninterpretable. 5. I suggest that pharmacologists and physiologists should use ordinary least products regression analysis (geometric mean regression, reduced major axis regression): it is versatile, can be used for calibration or to detect bias and can be executed by hand-held calculator or by using the loss function in popular, general-purpose, statistical software.

Use of probabilistic weights to enhance linear regression myoelectric control

NASA Astrophysics Data System (ADS)

Smith, Lauren H.; Kuiken, Todd A.; Hargrove, Levi J.

2015-12-01

Objective. Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Approach. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts’ law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Main results. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p < 0.05) by preventing extraneous movement at additional DOFs. Similar results were seen in experiments with two transradial amputees. Though goodness-of-fit evaluations suggested that the EMG feature distributions showed some deviations from the Gaussian, equal-covariance assumptions used in this experiment, the assumptions were sufficiently met to provide improved performance compared to linear regression control. Significance. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.

Estimating linear effects in ANOVA designs: the easy way.

PubMed

Pinhas, Michal; Tzelgov, Joseph; Ganor-Stern, Dana

2012-09-01

Research in cognitive science has documented numerous phenomena that are approximated by linear relationships. In the domain of numerical cognition, the use of linear regression for estimating linear effects (e.g., distance and SNARC effects) became common following Fias, Brysbaert, Geypens, and d'Ydewalle's (1996) study on the SNARC effect. While their work has become the model for analyzing linear effects in the field, it requires statistical analysis of individual participants and does not provide measures of the proportions of variability accounted for (cf. Lorch & Myers, 1990). In the present methodological note, using both the distance and SNARC effects as examples, we demonstrate how linear effects can be estimated in a simple way within the framework of repeated measures analysis of variance. This method allows for estimating effect sizes in terms of both slope and proportions of variability accounted for. Finally, we show that our method can easily be extended to estimate linear interaction effects, not just linear effects calculated as main effects.

Simplified large African carnivore density estimators from track indices.

PubMed

Winterbach, Christiaan W; Ferreira, Sam M; Funston, Paul J; Somers, Michael J

2016-01-01

The range, population size and trend of large carnivores are important parameters to assess their status globally and to plan conservation strategies. One can use linear models to assess population size and trends of large carnivores from track-based surveys on suitable substrates. The conventional approach of a linear model with intercept may not intercept at zero, but may fit the data better than linear model through the origin. We assess whether a linear regression through the origin is more appropriate than a linear regression with intercept to model large African carnivore densities and track indices. We did simple linear regression with intercept analysis and simple linear regression through the origin and used the confidence interval for ß in the linear model y  =  αx  + ß, Standard Error of Estimate, Mean Squares Residual and Akaike Information Criteria to evaluate the models. The Lion on Clay and Low Density on Sand models with intercept were not significant ( P  > 0.05). The other four models with intercept and the six models thorough origin were all significant ( P  < 0.05). The models using linear regression with intercept all included zero in the confidence interval for ß and the null hypothesis that ß = 0 could not be rejected. All models showed that the linear model through the origin provided a better fit than the linear model with intercept, as indicated by the Standard Error of Estimate and Mean Square Residuals. Akaike Information Criteria showed that linear models through the origin were better and that none of the linear models with intercept had substantial support. Our results showed that linear regression through the origin is justified over the more typical linear regression with intercept for all models we tested. A general model can be used to estimate large carnivore densities from track densities across species and study areas. The formula observed track density = 3.26 × carnivore density can be used to estimate densities of large African carnivores using track counts on sandy substrates in areas where carnivore densities are 0.27 carnivores/100 km 2 or higher. To improve the current models, we need independent data to validate the models and data to test for non-linear relationship between track indices and true density at low densities.

[From clinical judgment to linear regression model.

PubMed

Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O

2013-01-01

When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.

Comparison of Multiple Linear Regressions and Neural Networks based QSAR models for the design of new antitubercular compounds.

PubMed

Ventura, Cristina; Latino, Diogo A R S; Martins, Filomena

2013-01-01

The performance of two QSAR methodologies, namely Multiple Linear Regressions (MLR) and Neural Networks (NN), towards the modeling and prediction of antitubercular activity was evaluated and compared. A data set of 173 potentially active compounds belonging to the hydrazide family and represented by 96 descriptors was analyzed. Models were built with Multiple Linear Regressions (MLR), single Feed-Forward Neural Networks (FFNNs), ensembles of FFNNs and Associative Neural Networks (AsNNs) using four different data sets and different types of descriptors. The predictive ability of the different techniques used were assessed and discussed on the basis of different validation criteria and results show in general a better performance of AsNNs in terms of learning ability and prediction of antitubercular behaviors when compared with all other methods. MLR have, however, the advantage of pinpointing the most relevant molecular characteristics responsible for the behavior of these compounds against Mycobacterium tuberculosis. The best results for the larger data set (94 compounds in training set and 18 in test set) were obtained with AsNNs using seven descriptors (R(2) of 0.874 and RMSE of 0.437 against R(2) of 0.845 and RMSE of 0.472 in MLRs, for test set). Counter-Propagation Neural Networks (CPNNs) were trained with the same data sets and descriptors. From the scrutiny of the weight levels in each CPNN and the information retrieved from MLRs, a rational design of potentially active compounds was attempted. Two new compounds were synthesized and tested against M. tuberculosis showing an activity close to that predicted by the majority of the models. Copyright © 2013 Elsevier Masson SAS. All rights reserved.

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.

Linearity versus Nonlinearity of Offspring-Parent Regression: An Experimental Study of Drosophila Melanogaster

PubMed Central

Gimelfarb, A.; Willis, J. H.

1994-01-01

An experiment was conducted to investigate the offspring-parent regression for three quantitative traits (weight, abdominal bristles and wing length) in Drosophila melanogaster. Linear and polynomial models were fitted for the regressions of a character in offspring on both parents. It is demonstrated that responses by the characters to selection predicted by the nonlinear regressions may differ substantially from those predicted by the linear regressions. This is true even, and especially, if selection is weak. The realized heritability for a character under selection is shown to be determined not only by the offspring-parent regression but also by the distribution of the character and by the form and strength of selection. PMID:7828818

A practical approach for linearity assessment of calibration curves under the International Union of Pure and Applied Chemistry (IUPAC) guidelines for an in-house validation of method of analysis.

PubMed

Sanagi, M Marsin; Nasir, Zalilah; Ling, Susie Lu; Hermawan, Dadan; Ibrahim, Wan Aini Wan; Naim, Ahmedy Abu

2010-01-01

Linearity assessment as required in method validation has always been subject to different interpretations and definitions by various guidelines and protocols. However, there are very limited applicable implementation procedures that can be followed by a laboratory chemist in assessing linearity. Thus, this work proposes a simple method for linearity assessment in method validation by a regression analysis that covers experimental design, estimation of the parameters, outlier treatment, and evaluation of the assumptions according to the International Union of Pure and Applied Chemistry guidelines. The suitability of this procedure was demonstrated by its application to an in-house validation for the determination of plasticizers in plastic food packaging by GC.

Linear and nonlinear regression techniques for simultaneous and proportional myoelectric control.

PubMed

Hahne, J M; Biessmann, F; Jiang, N; Rehbaum, H; Farina, D; Meinecke, F C; Muller, K-R; Parra, L C

2014-03-01

In recent years the number of active controllable joints in electrically powered hand-prostheses has increased significantly. However, the control strategies for these devices in current clinical use are inadequate as they require separate and sequential control of each degree-of-freedom (DoF). In this study we systematically compare linear and nonlinear regression techniques for an independent, simultaneous and proportional myoelectric control of wrist movements with two DoF. These techniques include linear regression, mixture of linear experts (ME), multilayer-perceptron, and kernel ridge regression (KRR). They are investigated offline with electro-myographic signals acquired from ten able-bodied subjects and one person with congenital upper limb deficiency. The control accuracy is reported as a function of the number of electrodes and the amount and diversity of training data providing guidance for the requirements in clinical practice. The results showed that KRR, a nonparametric statistical learning method, outperformed the other methods. However, simple transformations in the feature space could linearize the problem, so that linear models could achieve similar performance as KRR at much lower computational costs. Especially ME, a physiologically inspired extension of linear regression represents a promising candidate for the next generation of prosthetic devices.

Unitary Response Regression Models

ERIC Educational Resources Information Center

Lipovetsky, S.

2007-01-01

The dependent variable in a regular linear regression is a numerical variable, and in a logistic regression it is a binary or categorical variable. In these models the dependent variable has varying values. However, there are problems yielding an identity output of a constant value which can also be modelled in a linear or logistic regression with…

An Expert System for the Evaluation of Cost Models

DTIC Science & Technology

1990-09-01

contrast to the condition of equal error variance, called homoscedasticity. (Reference: Applied Linear Regression Models by John Neter - page 423...normal. (Reference: Applied Linear Regression Models by John Neter - page 125) Click Here to continue -> Autocorrelation Click Here for the index - Index...over time. Error terms correlated over time are said to be autocorrelated or serially correlated. (REFERENCE: Applied Linear Regression Models by John

Maximum likelihood estimation of correction for dilution bias in simple linear regression using replicates from subjects with extreme first measurements.

PubMed

Berglund, Lars; Garmo, Hans; Lindbäck, Johan; Svärdsudd, Kurt; Zethelius, Björn

2008-09-30

The least-squares estimator of the slope in a simple linear regression model is biased towards zero when the predictor is measured with random error. A corrected slope may be estimated by adding data from a reliability study, which comprises a subset of subjects from the main study. The precision of this corrected slope depends on the design of the reliability study and estimator choice. Previous work has assumed that the reliability study constitutes a random sample from the main study. A more efficient design is to use subjects with extreme values on their first measurement. Previously, we published a variance formula for the corrected slope, when the correction factor is the slope in the regression of the second measurement on the first. In this paper we show that both designs improve by maximum likelihood estimation (MLE). The precision gain is explained by the inclusion of data from all subjects for estimation of the predictor's variance and by the use of the second measurement for estimation of the covariance between response and predictor. The gain of MLE enhances with stronger true relationship between response and predictor and with lower precision in the predictor measurements. We present a real data example on the relationship between fasting insulin, a surrogate marker, and true insulin sensitivity measured by a gold-standard euglycaemic insulin clamp, and simulations, where the behavior of profile-likelihood-based confidence intervals is examined. MLE was shown to be a robust estimator for non-normal distributions and efficient for small sample situations. Copyright (c) 2008 John Wiley & Sons, Ltd.

The role of chemometrics in single and sequential extraction assays: a review. Part II. Cluster analysis, multiple linear regression, mixture resolution, experimental design and other techniques.

PubMed

Giacomino, Agnese; Abollino, Ornella; Malandrino, Mery; Mentasti, Edoardo

2011-03-04

Single and sequential extraction procedures are used for studying element mobility and availability in solid matrices, like soils, sediments, sludge, and airborne particulate matter. In the first part of this review we reported an overview on these procedures and described the applications of chemometric uni- and bivariate techniques and of multivariate pattern recognition techniques based on variable reduction to the experimental results obtained. The second part of the review deals with the use of chemometrics not only for the visualization and interpretation of data, but also for the investigation of the effects of experimental conditions on the response, the optimization of their values and the calculation of element fractionation. We will describe the principles of the multivariate chemometric techniques considered, the aims for which they were applied and the key findings obtained. The following topics will be critically addressed: pattern recognition by cluster analysis (CA), linear discriminant analysis (LDA) and other less common techniques; modelling by multiple linear regression (MLR); investigation of spatial distribution of variables by geostatistics; calculation of fractionation patterns by a mixture resolution method (Chemometric Identification of Substrates and Element Distributions, CISED); optimization and characterization of extraction procedures by experimental design; other multivariate techniques less commonly applied. Copyright © 2010 Elsevier B.V. All rights reserved.

Using a Linear Regression Method to Detect Outliers in IRT Common Item Equating

ERIC Educational Resources Information Center

He, Yong; Cui, Zhongmin; Fang, Yu; Chen, Hanwei

2013-01-01

Common test items play an important role in equating alternate test forms under the common item nonequivalent groups design. When the item response theory (IRT) method is applied in equating, inconsistent item parameter estimates among common items can lead to large bias in equated scores. It is prudent to evaluate inconsistency in parameter…

A Multilevel Study of Students' Motivations of Studying Accounting: Implications for Employers

ERIC Educational Resources Information Center

Law, Philip; Yuen, Desmond

2012-01-01

Purpose: The purpose of this study is to examine the influence of factors affecting students' choice of accounting as a study major in Hong Kong. Design/methodology/approach: Multinomial logistic regression and Hierarchical Generalized Linear Modeling (HGLM) are used to analyze the survey data for the level one and level two data, which is the…

The associations between diet quality, body mass index (BMI) and health and activity limitation index (HALEX) in the Geisinger Rural Aging Study (GRAS)

USDA-ARS?s Scientific Manuscript database

Objectives To determine the associations between diet quality, body mass index (BMI), and health-related quality of life (HRQOL) as assessed by the health and activity limitation index (HALex) in older adults. Design Multivariate linear regression models were used to analyze associations between Di...

Parenting Styles as Predicators of Anxiety and Depression of In-School Adolescents in Nigeria

ERIC Educational Resources Information Center

Adubale, Andrew A.

2017-01-01

The study investigates parenting styles as predictors of anxiety and depression in secondary school students in Edo State, Nigeria. It employed a correlation research design. Two hundred and forty students constituted the sample for the study. Parenting Style Scale questionnaire was used to collect data for the study. Linear regression was used to…

Stagnation in Mortality Decline among Elders in the Netherlands

ERIC Educational Resources Information Center

Janssen, Fanny; Nusselder, Wilma J.; Looman, Caspar W. N.; Mackenbach, Johan P.; Kunst, Anton E.

2003-01-01

Purpose: This study assesses whether the stagnation of old-age (80+) mortality decline observed in The Netherlands in the 1980s continued in the 1990s and determines which factors contributed to this stagnation. Emphasis is on the role of smoking. Design and Methods: Poisson regression analysis with linear splines was applied to total and…

The Relationship between Teachers' and Principals' Perceptions of the Working Conditions in North Carolina Elementary Schools and Student Achievement

ERIC Educational Resources Information Center

Mizzelle, Sylvia Jean

2012-01-01

The purpose of this study was to examine the relationship between teachers' and principals' perceptions on the North Carolina Teacher Working Conditions Survey (TWC) and the influence this relationship had on student achievement. A quantitative research design using a Multiple Linear Regression investigated the relationship between teachers' and…

Secondary Students' Considerations of Variability in Measurement Activities Based on Authentic Practices

ERIC Educational Resources Information Center

Dierdorp, Adri; Bakker, Arthur; Ben-Zvi, Dani; Makar, Katie

2017-01-01

Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17-18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities?…

Quantitative structure-activity relationship of the curcumin-related compounds using various regression methods

NASA Astrophysics Data System (ADS)

Khazaei, Ardeshir; Sarmasti, Negin; Seyf, Jaber Yousefi

2016-03-01

Quantitative structure activity relationship were used to study a series of curcumin-related compounds with inhibitory effect on prostate cancer PC-3 cells, pancreas cancer Panc-1 cells, and colon cancer HT-29 cells. Sphere exclusion method was used to split data set in two categories of train and test set. Multiple linear regression, principal component regression and partial least squares were used as the regression methods. In other hand, to investigate the effect of feature selection methods, stepwise, Genetic algorithm, and simulated annealing were used. In two cases (PC-3 cells and Panc-1 cells), the best models were generated by a combination of multiple linear regression and stepwise (PC-3 cells: r2 = 0.86, q2 = 0.82, pred_r2 = 0.93, and r2m (test) = 0.43, Panc-1 cells: r2 = 0.85, q2 = 0.80, pred_r2 = 0.71, and r2m (test) = 0.68). For the HT-29 cells, principal component regression with stepwise (r2 = 0.69, q2 = 0.62, pred_r2 = 0.54, and r2m (test) = 0.41) is the best method. The QSAR study reveals descriptors which have crucial role in the inhibitory property of curcumin-like compounds. 6ChainCount, T_C_C_1, and T_O_O_7 are the most important descriptors that have the greatest effect. With a specific end goal to design and optimization of novel efficient curcumin-related compounds it is useful to introduce heteroatoms such as nitrogen, oxygen, and sulfur atoms in the chemical structure (reduce the contribution of T_C_C_1 descriptor) and increase the contribution of 6ChainCount and T_O_O_7 descriptors. Models can be useful in the better design of some novel curcumin-related compounds that can be used in the treatment of prostate, pancreas, and colon cancers.

FPGA implementation of predictive degradation model for engine oil lifetime

NASA Astrophysics Data System (ADS)

Idros, M. F. M.; Razak, A. H. A.; Junid, S. A. M. Al; Suliman, S. I.; Halim, A. K.

2018-03-01

This paper presents the implementation of linear regression model for degradation prediction on Register Transfer Logic (RTL) using QuartusII. A stationary model had been identified in the degradation trend for the engine oil in a vehicle in time series method. As for RTL implementation, the degradation model is written in Verilog HDL and the data input are taken at a certain time. Clock divider had been designed to support the timing sequence of input data. At every five data, a regression analysis is adapted for slope variation determination and prediction calculation. Here, only the negative value are taken as the consideration for the prediction purposes for less number of logic gate. Least Square Method is adapted to get the best linear model based on the mean values of time series data. The coded algorithm has been implemented on FPGA for validation purposes. The result shows the prediction time to change the engine oil.

Compound Identification Using Penalized Linear Regression on Metabolomics

PubMed Central

Liu, Ruiqi; Wu, Dongfeng; Zhang, Xiang; Kim, Seongho

2014-01-01

Compound identification is often achieved by matching the experimental mass spectra to the mass spectra stored in a reference library based on mass spectral similarity. Because the number of compounds in the reference library is much larger than the range of mass-to-charge ratio (m/z) values so that the data become high dimensional data suffering from singularity. For this reason, penalized linear regressions such as ridge regression and the lasso are used instead of the ordinary least squares regression. Furthermore, two-step approaches using the dot product and Pearson’s correlation along with the penalized linear regression are proposed in this study. PMID:27212894

Control Variate Selection for Multiresponse Simulation.

DTIC Science & Technology

1987-05-01

M. H. Knuter, Applied Linear Regression Mfodels, Richard D. Erwin, Inc., Homewood, Illinois, 1983. Neuts, Marcel F., Probability, Allyn and Bacon...1982. Neter, J., V. Wasserman, and M. H. Knuter, Applied Linear Regression .fodels, Richard D. Erwin, Inc., Homewood, Illinois, 1983. Neuts, Marcel F...Aspects of J%,ultivariate Statistical Theory, John Wiley and Sons, New York, New York, 1982. dY Neter, J., W. Wasserman, and M. H. Knuter, Applied Linear Regression Mfodels

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…

High correlations between MRI brain volume measurements based on NeuroQuant® and FreeSurfer.

PubMed

Ross, David E; Ochs, Alfred L; Tate, David F; Tokac, Umit; Seabaugh, John; Abildskov, Tracy J; Bigler, Erin D

2018-05-30

NeuroQuant ® (NQ) and FreeSurfer (FS) are commonly used computer-automated programs for measuring MRI brain volume. Previously they were reported to have high intermethod reliabilities but often large intermethod effect size differences. We hypothesized that linear transformations could be used to reduce the large effect sizes. This study was an extension of our previously reported study. We performed NQ and FS brain volume measurements on 60 subjects (including normal controls, patients with traumatic brain injury, and patients with Alzheimer's disease). We used two statistical approaches in parallel to develop methods for transforming FS volumes into NQ volumes: traditional linear regression, and Bayesian linear regression. For both methods, we used regression analyses to develop linear transformations of the FS volumes to make them more similar to the NQ volumes. The FS-to-NQ transformations based on traditional linear regression resulted in effect sizes which were small to moderate. The transformations based on Bayesian linear regression resulted in all effect sizes being trivially small. To our knowledge, this is the first report describing a method for transforming FS to NQ data so as to achieve high reliability and low effect size differences. Machine learning methods like Bayesian regression may be more useful than traditional methods. Copyright © 2018 Elsevier B.V. All rights reserved.

Quantile Regression in the Study of Developmental Sciences

PubMed Central

Petscher, Yaacov; Logan, Jessica A. R.

2014-01-01

Linear regression analysis is one of the most common techniques applied in developmental research, but only allows for an estimate of the average relations between the predictor(s) and the outcome. This study describes quantile regression, which provides estimates of the relations between the predictor(s) and outcome, but across multiple points of the outcome’s distribution. Using data from the High School and Beyond and U.S. Sustained Effects Study databases, quantile regression is demonstrated and contrasted with linear regression when considering models with: (a) one continuous predictor, (b) one dichotomous predictor, (c) a continuous and a dichotomous predictor, and (d) a longitudinal application. Results from each example exhibited the differential inferences which may be drawn using linear or quantile regression. PMID:24329596

Data mining for materials design: A computational study of single molecule magnet

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

Dam, Hieu Chi; Faculty of Physics, Vietnam National University, 334 Nguyen Trai, Hanoi; Pham, Tien Lam

2014-01-28

We develop a method that combines data mining and first principles calculation to guide the designing of distorted cubane Mn{sup 4+} Mn {sub 3}{sup 3+} single molecule magnets. The essential idea of the method is a process consisting of sparse regressions and cross-validation for analyzing calculated data of the materials. The method allows us to demonstrate that the exchange coupling between Mn{sup 4+} and Mn{sup 3+} ions can be predicted from the electronegativities of constituent ligands and the structural features of the molecule by a linear regression model with high accuracy. The relations between the structural features and magnetic propertiesmore » of the materials are quantitatively and consistently evaluated and presented by a graph. We also discuss the properties of the materials and guide the material design basing on the obtained results.« less

Improving validation methods for molecular diagnostics: application of Bland-Altman, Deming and simple linear regression analyses in assay comparison and evaluation for next-generation sequencing

PubMed Central

Misyura, Maksym; Sukhai, Mahadeo A; Kulasignam, Vathany; Zhang, Tong; Kamel-Reid, Suzanne; Stockley, Tracy L

2018-01-01

Aims A standard approach in test evaluation is to compare results of the assay in validation to results from previously validated methods. For quantitative molecular diagnostic assays, comparison of test values is often performed using simple linear regression and the coefficient of determination (R2), using R2 as the primary metric of assay agreement. However, the use of R2 alone does not adequately quantify constant or proportional errors required for optimal test evaluation. More extensive statistical approaches, such as Bland-Altman and expanded interpretation of linear regression methods, can be used to more thoroughly compare data from quantitative molecular assays. Methods We present the application of Bland-Altman and linear regression statistical methods to evaluate quantitative outputs from next-generation sequencing assays (NGS). NGS-derived data sets from assay validation experiments were used to demonstrate the utility of the statistical methods. Results Both Bland-Altman and linear regression were able to detect the presence and magnitude of constant and proportional error in quantitative values of NGS data. Deming linear regression was used in the context of assay comparison studies, while simple linear regression was used to analyse serial dilution data. Bland-Altman statistical approach was also adapted to quantify assay accuracy, including constant and proportional errors, and precision where theoretical and empirical values were known. Conclusions The complementary application of the statistical methods described in this manuscript enables more extensive evaluation of performance characteristics of quantitative molecular assays, prior to implementation in the clinical molecular laboratory. PMID:28747393

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

NASA Technical Reports Server (NTRS)

Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.

1998-01-01

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth; Sivanesan, S

2006-08-25

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.

Convert a low-cost sensor to a colorimeter using an improved regression method

NASA Astrophysics Data System (ADS)

Wu, Yifeng

2008-01-01

Closed loop color calibration is a process to maintain consistent color reproduction for color printers. To perform closed loop color calibration, a pre-designed color target should be printed, and automatically measured by a color measuring instrument. A low cost sensor has been embedded to the printer to perform the color measurement. A series of sensor calibration and color conversion methods have been developed. The purpose is to get accurate colorimetric measurement from the data measured by the low cost sensor. In order to get high accuracy colorimetric measurement, we need carefully calibrate the sensor, and minimize all possible errors during the color conversion. After comparing several classical color conversion methods, a regression based color conversion method has been selected. The regression is a powerful method to estimate the color conversion functions. But the main difficulty to use this method is to find an appropriate function to describe the relationship between the input and the output data. In this paper, we propose to use 1D pre-linearization tables to improve the linearity between the input sensor measuring data and the output colorimetric data. Using this method, we can increase the accuracy of the regression method, so as to improve the accuracy of the color conversion.

Comparison of Neural Network and Linear Regression Models in Statistically Predicting Mental and Physical Health Status of Breast Cancer Survivors

DTIC Science & Technology

2015-07-15

Long-term effects on cancer survivors’ quality of life of physical training versus physical training combined with cognitive-behavioral therapy ...COMPARISON OF NEURAL NETWORK AND LINEAR REGRESSION MODELS IN STATISTICALLY PREDICTING MENTAL AND PHYSICAL HEALTH STATUS OF BREAST...34Comparison of Neural Network and Linear Regression Models in Statistically Predicting Mental and Physical Health Status of Breast Cancer Survivors

Estimation of Standard Error of Regression Effects in Latent Regression Models Using Binder's Linearization. Research Report. ETS RR-07-09

ERIC Educational Resources Information Center

Li, Deping; Oranje, Andreas

2007-01-01

Two versions of a general method for approximating standard error of regression effect estimates within an IRT-based latent regression model are compared. The general method is based on Binder's (1983) approach, accounting for complex samples and finite populations by Taylor series linearization. In contrast, the current National Assessment of…

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.

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

Optimal experimental designs for estimating Henry's law constants via the method of phase ratio variation.

PubMed

Kapelner, Adam; Krieger, Abba; Blanford, William J

2016-10-14

When measuring Henry's law constants (k H ) using the phase ratio variation (PRV) method via headspace gas chromatography (G C ), the value of k H of the compound under investigation is calculated from the ratio of the slope to the intercept of a linear regression of the inverse G C response versus the ratio of gas to liquid volumes of a series of vials drawn from the same parent solution. Thus, an experimenter collects measurements consisting of the independent variable (the gas/liquid volume ratio) and dependent variable (the G C -1 peak area). A review of the literature found that the common design is a simple uniform spacing of liquid volumes. We present an optimal experimental design which estimates k H with minimum error and provides multiple means for building confidence intervals for such estimates. We illustrate performance improvements of our design with an example measuring the k H for Naphthalene in aqueous solution as well as simulations on previous studies. Our designs are most applicable after a trial run defines the linear G C response and the linear phase ratio to the G C -1 region (where the PRV method is suitable) after which a practitioner can collect measurements in bulk. The designs can be easily computed using our open source software optDesignSlopeInt, an R package on CRAN. Copyright © 2016 Elsevier B.V. All rights reserved.

Estimating linear temporal trends from aggregated environmental monitoring data

USGS Publications Warehouse

Erickson, Richard A.; Gray, Brian R.; Eager, Eric A.

2017-01-01

Trend estimates are often used as part of environmental monitoring programs. These trends inform managers (e.g., are desired species increasing or undesired species decreasing?). Data collected from environmental monitoring programs is often aggregated (i.e., averaged), which confounds sampling and process variation. State-space models allow sampling variation and process variations to be separated. We used simulated time-series to compare linear trend estimations from three state-space models, a simple linear regression model, and an auto-regressive model. We also compared the performance of these five models to estimate trends from a long term monitoring program. We specifically estimated trends for two species of fish and four species of aquatic vegetation from the Upper Mississippi River system. We found that the simple linear regression had the best performance of all the given models because it was best able to recover parameters and had consistent numerical convergence. Conversely, the simple linear regression did the worst job estimating populations in a given year. The state-space models did not estimate trends well, but estimated population sizes best when the models converged. We found that a simple linear regression performed better than more complex autoregression and state-space models when used to analyze aggregated environmental monitoring data.

Making Curriculum Decisions in K-8 Science: The Relationship between Teacher Dispositions and Curriculum Content

ERIC Educational Resources Information Center

Eidietis, L.; Jewkes, A. M.

2011-01-01

This study examined teachers' dispositions toward and choices to teach ocean science using a survey design. A sample of 89 in-service K-8 teachers in the United States reported their (1) feelings of preparedness to teach about ocean literacy and (2) attitudes toward ocean science on three measures. Results of multiple linear regression showed that…

Characterizing trends in fruit and vegetable intake in the US by self-report and by supply-and-disappearance data: 2001-2014

USDA-ARS?s Scientific Manuscript database

Objective: To examine the comparability of fruit and vegetable (F&V) intake data in the US from 2001-2014 between data acquired from two national data collection programs. Design: Cross-sectional analysis. Linear regression models estimated trends in daily per-capita intake of total F&V. Pooled di...

Subjective Health and Mental Well-Being of Adolescents and the Health Promoting School: A Cross-Sectional Multilevel Analysis

ERIC Educational Resources Information Center

Levin, Kate; Inchley, Jo; Currie, Dorothy; Currie, Candace

2012-01-01

Purpose: The aim of this paper is to examine the impact of the health promoting school (HPS) on adolescent well-being. Design/methodology/approach: Data from the 2006 Health Behaviour in School-aged Children: WHO-collaborative Study in Scotland were analysed using multilevel linear regression analyses for outcome measures: happiness, confidence,…

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

Correlation and simple linear regression.

PubMed

Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G

2003-06-01

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.

Improving validation methods for molecular diagnostics: application of Bland-Altman, Deming and simple linear regression analyses in assay comparison and evaluation for next-generation sequencing.

PubMed

Misyura, Maksym; Sukhai, Mahadeo A; Kulasignam, Vathany; Zhang, Tong; Kamel-Reid, Suzanne; Stockley, Tracy L

2018-02-01

A standard approach in test evaluation is to compare results of the assay in validation to results from previously validated methods. For quantitative molecular diagnostic assays, comparison of test values is often performed using simple linear regression and the coefficient of determination (R 2 ), using R 2 as the primary metric of assay agreement. However, the use of R 2 alone does not adequately quantify constant or proportional errors required for optimal test evaluation. More extensive statistical approaches, such as Bland-Altman and expanded interpretation of linear regression methods, can be used to more thoroughly compare data from quantitative molecular assays. We present the application of Bland-Altman and linear regression statistical methods to evaluate quantitative outputs from next-generation sequencing assays (NGS). NGS-derived data sets from assay validation experiments were used to demonstrate the utility of the statistical methods. Both Bland-Altman and linear regression were able to detect the presence and magnitude of constant and proportional error in quantitative values of NGS data. Deming linear regression was used in the context of assay comparison studies, while simple linear regression was used to analyse serial dilution data. Bland-Altman statistical approach was also adapted to quantify assay accuracy, including constant and proportional errors, and precision where theoretical and empirical values were known. The complementary application of the statistical methods described in this manuscript enables more extensive evaluation of performance characteristics of quantitative molecular assays, prior to implementation in the clinical molecular laboratory. © 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.

Linear regression in astronomy. II

NASA Technical Reports Server (NTRS)

Feigelson, Eric D.; Babu, Gutti J.

1992-01-01

A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.

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…

Subsonic Aircraft With Regression and Neural-Network Approximators Designed

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.

2004-01-01

At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics, Inc., Mountainview, CA), the regression training required a fraction of a CPU second, whereas neural network training was between 1 and 9 min, as given. For a single analysis cycle, the 3-sec CPU time required by the FLOPS code was reduced to milliseconds by the approximators. For design calculations, the time with the FLOPS code was 34 min. It was reduced to 2 sec with the regression method and to 4 min by the neural network technique. The performance of the regression and neural network methods was found to be satisfactory for the analysis and design optimization of the subsonic aircraft.

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.

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.

Spatially resolved regression analysis of pre-treatment FDG, FLT and Cu-ATSM PET from post-treatment FDG PET: an exploratory study

PubMed Central

Bowen, Stephen R; Chappell, Richard J; Bentzen, Søren M; Deveau, Michael A; Forrest, Lisa J; Jeraj, Robert

2012-01-01

Purpose To quantify associations between pre-radiotherapy and post-radiotherapy PET parameters via spatially resolved regression. Materials and methods Ten canine sinonasal cancer patients underwent PET/CT scans of [18F]FDG (FDGpre), [18F]FLT (FLTpre), and [61Cu]Cu-ATSM (Cu-ATSMpre). Following radiotherapy regimens of 50 Gy in 10 fractions, veterinary patients underwent FDG PET/CT scans at three months (FDGpost). Regression of standardized uptake values in baseline FDGpre, FLTpre and Cu-ATSMpre tumour voxels to those in FDGpost images was performed for linear, log-linear, generalized-linear and mixed-fit linear models. Goodness-of-fit in regression coefficients was assessed by R2. Hypothesis testing of coefficients over the patient population was performed. Results Multivariate linear model fits of FDGpre to FDGpost were significantly positive over the population (FDGpost~0.17 FDGpre, p=0.03), and classified slopes of RECIST non-responders and responders to be different (0.37 vs. 0.07, p=0.01). Generalized-linear model fits related FDGpre to FDGpost by a linear power law (FDGpost~FDGpre0.93, p<0.001). Univariate mixture model fits of FDGpre improved R2 from 0.17 to 0.52. Neither baseline FLT PET nor Cu-ATSM PET uptake contributed statistically significant multivariate regression coefficients. Conclusions Spatially resolved regression analysis indicates that pre-treatment FDG PET uptake is most strongly associated with three-month post-treatment FDG PET uptake in this patient population, though associations are histopathology-dependent. PMID:22682748

Linear regression analysis of survival data with missing censoring indicators.

PubMed

Wang, Qihua; Dinse, Gregg E

2011-04-01

Linear regression analysis has been studied extensively in a random censorship setting, but typically all of the censoring indicators are assumed to be observed. In this paper, we develop synthetic data methods for estimating regression parameters in a linear model when some censoring indicators are missing. We define estimators based on regression calibration, imputation, and inverse probability weighting techniques, and we prove all three estimators are asymptotically normal. The finite-sample performance of each estimator is evaluated via simulation. We illustrate our methods by assessing the effects of sex and age on the time to non-ambulatory progression for patients in a brain cancer clinical trial.

An Analysis of COLA (Cost of Living Adjustment) Allocation within the United States Coast Guard.

DTIC Science & Technology

1983-09-01

books Applied Linear Regression [Ref. 39], and Statistical Methods in Research and Production [Ref. 40], or any other book on regression. In the event...Indexes, Master’s Thesis, Air Force Institute of Technology, Wright-Patterson AFB, 1976. 39. Weisberg, Stanford, Applied Linear Regression , Wiley, 1980. 40

Testing hypotheses for differences between linear regression lines

Treesearch

Stanley J. Zarnoch

2009-01-01

Five hypotheses are identified for testing differences between simple linear regression lines. The distinctions between these hypotheses are based on a priori assumptions and illustrated with full and reduced models. The contrast approach is presented as an easy and complete method for testing for overall differences between the regressions and for making pairwise...

Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.

ERIC Educational Resources Information Center

Schafer, William D.; Wang, Yuh-Yin

A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…

Teaching the Concept of Breakdown Point in Simple Linear Regression.

ERIC Educational Resources Information Center

Chan, Wai-Sum

2001-01-01

Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…

Estimating monotonic rates from biological data using local linear regression.

PubMed

Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R

2017-03-01

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.

HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION

PubMed Central

Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong

2015-01-01

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a function of two components: a design matrix sparsity index and signal strength, each of which is a function of the sparsity of the alternative. For any alternative, if the design matrix sparsity index is too high, any test is asymptotically powerless irrespective of the magnitude of signal strength. For binary design matrices with the sparsity index that is not too high, our results are parallel to those in the Gaussian case. In this context, we derive detection boundaries for both dense and sparse regimes. For the dense regime, we show that the generalized likelihood ratio is rate optimal; for the sparse regime, we propose an extended Higher Criticism Test and show it is rate optimal and sharp. We illustrate the finite sample properties of the theoretical results using simulation studies. PMID:26246645

Locally linear regression for pose-invariant face recognition.

PubMed

Chai, Xiujuan; Shan, Shiguang; Chen, Xilin; Gao, Wen

2007-07-01

The variation of facial appearance due to the viewpoint (/pose) degrades face recognition systems considerably, which is one of the bottlenecks in face recognition. One of the possible solutions is generating virtual frontal view from any given nonfrontal view to obtain a virtual gallery/probe face. Following this idea, this paper proposes a simple, but efficient, novel locally linear regression (LLR) method, which generates the virtual frontal view from a given nonfrontal face image. We first justify the basic assumption of the paper that there exists an approximate linear mapping between a nonfrontal face image and its frontal counterpart. Then, by formulating the estimation of the linear mapping as a prediction problem, we present the regression-based solution, i.e., globally linear regression. To improve the prediction accuracy in the case of coarse alignment, LLR is further proposed. In LLR, we first perform dense sampling in the nonfrontal face image to obtain many overlapped local patches. Then, the linear regression technique is applied to each small patch for the prediction of its virtual frontal patch. Through the combination of all these patches, the virtual frontal view is generated. The experimental results on the CMU PIE database show distinct advantage of the proposed method over Eigen light-field method.

A Systematic Review and Meta-Regression Analysis of Lung Cancer Risk and Inorganic Arsenic in Drinking Water.

PubMed

Lamm, Steven H; Ferdosi, Hamid; Dissen, Elisabeth K; Li, Ji; Ahn, Jaeil

2015-12-07

High levels (> 200 µg/L) of inorganic arsenic in drinking water are known to be a cause of human lung cancer, but the evidence at lower levels is uncertain. We have sought the epidemiological studies that have examined the dose-response relationship between arsenic levels in drinking water and the risk of lung cancer over a range that includes both high and low levels of arsenic. Regression analysis, based on six studies identified from an electronic search, examined the relationship between the log of the relative risk and the log of the arsenic exposure over a range of 1-1000 µg/L. The best-fitting continuous meta-regression model was sought and found to be a no-constant linear-quadratic analysis where both the risk and the exposure had been logarithmically transformed. This yielded both a statistically significant positive coefficient for the quadratic term and a statistically significant negative coefficient for the linear term. Sub-analyses by study design yielded results that were similar for both ecological studies and non-ecological studies. Statistically significant X-intercepts consistently found no increased level of risk at approximately 100-150 µg/L arsenic.

A Systematic Review and Meta-Regression Analysis of Lung Cancer Risk and Inorganic Arsenic in Drinking Water

PubMed Central

Lamm, Steven H.; Ferdosi, Hamid; Dissen, Elisabeth K.; Li, Ji; Ahn, Jaeil

2015-01-01

High levels (> 200 µg/L) of inorganic arsenic in drinking water are known to be a cause of human lung cancer, but the evidence at lower levels is uncertain. We have sought the epidemiological studies that have examined the dose-response relationship between arsenic levels in drinking water and the risk of lung cancer over a range that includes both high and low levels of arsenic. Regression analysis, based on six studies identified from an electronic search, examined the relationship between the log of the relative risk and the log of the arsenic exposure over a range of 1–1000 µg/L. The best-fitting continuous meta-regression model was sought and found to be a no-constant linear-quadratic analysis where both the risk and the exposure had been logarithmically transformed. This yielded both a statistically significant positive coefficient for the quadratic term and a statistically significant negative coefficient for the linear term. Sub-analyses by study design yielded results that were similar for both ecological studies and non-ecological studies. Statistically significant X-intercepts consistently found no increased level of risk at approximately 100–150 µg/L arsenic. PMID:26690190

Evaluation of force-velocity and power-velocity relationship of arm muscles.

PubMed

Sreckovic, Sreten; Cuk, Ivan; Djuric, Sasa; Nedeljkovic, Aleksandar; Mirkov, Dragan; Jaric, Slobodan

2015-08-01

A number of recent studies have revealed an approximately linear force-velocity (F-V) and, consequently, a parabolic power-velocity (P-V) relationship of multi-joint tasks. However, the measurement characteristics of their parameters have been neglected, particularly those regarding arm muscles, which could be a problem for using the linear F-V model in both research and routine testing. Therefore, the aims of the present study were to evaluate the strength, shape, reliability, and concurrent validity of the F-V relationship of arm muscles. Twelve healthy participants performed maximum bench press throws against loads ranging from 20 to 70 % of their maximum strength, and linear regression model was applied on the obtained range of F and V data. One-repetition maximum bench press and medicine ball throw tests were also conducted. The observed individual F-V relationships were exceptionally strong (r = 0.96-0.99; all P < 0.05) and fairly linear, although it remains unresolved whether a polynomial fit could provide even stronger relationships. The reliability of parameters obtained from the linear F-V regressions proved to be mainly high (ICC > 0.80), while their concurrent validity regarding directly measured F, P, and V ranged from high (for maximum F) to medium-to-low (for maximum P and V). The findings add to the evidence that the linear F-V and, consequently, parabolic P-V models could be used to study the mechanical properties of muscular systems, as well as to design a relatively simple, reliable, and ecologically valid routine test of the muscle ability of force, power, and velocity production.

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

Effect of Malmquist bias on correlation studies with IRAS data base

NASA Technical Reports Server (NTRS)

Verter, Frances

1993-01-01

The relationships between galaxy properties in the sample of Trinchieri et al. (1989) are reexamined with corrections for Malmquist bias. The linear correlations are tested and linear regressions are fit for log-log plots of L(FIR), L(H-alpha), and L(B) as well as ratios of these quantities. The linear correlations for Malmquist bias are corrected using the method of Verter (1988), in which each galaxy observation is weighted by the inverse of its sampling volume. The linear regressions are corrected for Malmquist bias by a new method invented here in which each galaxy observation is weighted by its sampling volume. The results of correlation and regressions among the sample are significantly changed in the anticipated sense that the corrected correlation confidences are lower and the corrected slopes of the linear regressions are lower. The elimination of Malmquist bias eliminates the nonlinear rise in luminosity that has caused some authors to hypothesize additional components of FIR emission.

A primer for biomedical scientists on how to execute model II linear regression analysis.

PubMed

Ludbrook, John

2012-04-01

1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions. © 2011 The Author. Clinical and Experimental Pharmacology and Physiology. © 2011 Blackwell Publishing Asia Pty Ltd.

Analyzing Multilevel Data: Comparing Findings from Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2013-01-01

This study examined the differing conclusions one may come to depending upon the type of analysis chosen, hierarchical linear modeling or ordinary least squares (OLS) regression. To illustrate this point, this study examined the influences of seniors' self-reported critical thinking abilities three ways: (1) an OLS regression with the student…

Non-stationary hydrologic frequency analysis using B-spline quantile regression

NASA Astrophysics Data System (ADS)

Nasri, B.; Bouezmarni, T.; St-Hilaire, A.; Ouarda, T. B. M. J.

2017-11-01

Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, it is possible that the assumption of stationarity, which is prerequisite for traditional frequency analysis and hence, the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extremes based on B-Spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates with linear and non-linear dependence. A Markov Chain Monte Carlo (MCMC) algorithm was used to estimate quantiles and their posterior distributions. A coefficient of determination and Bayesian information criterion (BIC) for quantile regression are used in order to select the best model, i.e. for each quantile, we choose the degree and number of knots of the adequate B-spline quantile regression model. The method is applied to annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in the variable of interest and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for an annual maximum and minimum discharge with high annual non-exceedance probabilities.

Analyzing Multilevel Data: An Empirical Comparison of Parameter Estimates of Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2011-01-01

Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

Computational Tools for Probing Interactions in Multiple Linear Regression, Multilevel Modeling, and Latent Curve Analysis

ERIC Educational Resources Information Center

Preacher, Kristopher J.; Curran, Patrick J.; Bauer, Daniel J.

2006-01-01

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

Classical Testing in Functional Linear Models.

PubMed

Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

2016-01-01

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

Classical Testing in Functional Linear Models

PubMed Central

Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

2016-01-01

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications. PMID:28955155

Quantitative structure-activity relationships by neural networks and inductive logic programming. I. The inhibition of dihydrofolate reductase by pyrimidines

NASA Astrophysics Data System (ADS)

Hirst, Jonathan D.; King, Ross D.; Sternberg, Michael J. E.

1994-08-01

Neural networks and inductive logic programming (ILP) have been compared to linear regression for modelling the QSAR of the inhibition of E. coli dihydrofolate reductase (DHFR) by 2,4-diamino-5-(substitured benzyl)pyrimidines, and, in the subsequent paper [Hirst, J.D., King, R.D. and Sternberg, M.J.E., J. Comput.-Aided Mol. Design, 8 (1994) 421], the inhibition of rodent DHFR by 2,4-diamino-6,6-dimethyl-5-phenyl-dihydrotriazines. Cross-validation trials provide a statistically rigorous assessment of the predictive capabilities of the methods, with training and testing data selected randomly and all the methods developed using identical training data. For the ILP analysis, molecules are represented by attributes other than Hansch parameters. Neural networks and ILP perform better than linear regression using the attribute representation, but the difference is not statistically significant. The major benefit from the ILP analysis is the formulation of understandable rules relating the activity of the inhibitors to their chemical structure.

Comparison of two-concentration with multi-concentration linear regressions: Retrospective data analysis of multiple regulated LC-MS bioanalytical projects.

PubMed

Musuku, Adrien; Tan, Aimin; Awaiye, Kayode; Trabelsi, Fethi

2013-09-01

Linear calibration is usually performed using eight to ten calibration concentration levels in regulated LC-MS bioanalysis because a minimum of six are specified in regulatory guidelines. However, we have previously reported that two-concentration linear calibration is as reliable as or even better than using multiple concentrations. The purpose of this research is to compare two-concentration with multiple-concentration linear calibration through retrospective data analysis of multiple bioanalytical projects that were conducted in an independent regulated bioanalytical laboratory. A total of 12 bioanalytical projects were randomly selected: two validations and two studies for each of the three most commonly used types of sample extraction methods (protein precipitation, liquid-liquid extraction, solid-phase extraction). When the existing data were retrospectively linearly regressed using only the lowest and the highest concentration levels, no extra batch failure/QC rejection was observed and the differences in accuracy and precision between the original multi-concentration regression and the new two-concentration linear regression are negligible. Specifically, the differences in overall mean apparent bias (square root of mean individual bias squares) are within the ranges of -0.3% to 0.7% and 0.1-0.7% for the validations and studies, respectively. The differences in mean QC concentrations are within the ranges of -0.6% to 1.8% and -0.8% to 2.5% for the validations and studies, respectively. The differences in %CV are within the ranges of -0.7% to 0.9% and -0.3% to 0.6% for the validations and studies, respectively. The average differences in study sample concentrations are within the range of -0.8% to 2.3%. With two-concentration linear regression, an average of 13% of time and cost could have been saved for each batch together with 53% of saving in the lead-in for each project (the preparation of working standard solutions, spiking, and aliquoting). Furthermore, examples are given as how to evaluate the linearity over the entire concentration range when only two concentration levels are used for linear regression. To conclude, two-concentration linear regression is accurate and robust enough for routine use in regulated LC-MS bioanalysis and it significantly saves time and cost as well. Copyright © 2013 Elsevier B.V. All rights reserved.

A Linear Regression and Markov Chain Model for the Arabian Horse Registry

DTIC Science & Technology

1993-04-01

as a tax deduction? Yes No T-4367 68 26. Regardless of previous equine tax deductions, do you consider your current horse activities to be... (Mark one...E L T-4367 A Linear Regression and Markov Chain Model For the Arabian Horse Registry Accesion For NTIS CRA&I UT 7 4:iC=D 5 D-IC JA" LI J:13tjlC,3 lO...the Arabian Horse Registry, which needed to forecast its future registration of purebred Arabian horses . A linear regression model was utilized to

Extending local canonical correlation analysis to handle general linear contrasts for FMRI data.

PubMed

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

Extending Local Canonical Correlation Analysis to Handle General Linear Contrasts for fMRI Data

PubMed Central

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic. PMID:22461786

An improved multiple linear regression and data analysis computer program package

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-07-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach was justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatland sites in Finland and a tundra site in Siberia. The flux measurements were performed using transparent chambers on vegetated surfaces and opaque chambers on bare peat surfaces. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes and even lower for longer closure times. The degree of underestimation increased with increasing CO2 flux strength and is dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

Statistical Tutorial | Center for Cancer Research

Cancer.gov

Recent advances in cancer biology have resulted in the need for increased statistical analysis of research data.  ST is designed as a follow up to Statistical Analysis of Research Data (SARD) held in April 2018.  The tutorial will apply the general principles of statistical analysis of research data including descriptive statistics, z- and t-tests of means and mean differences, simple and multiple linear regression, ANOVA tests, and Chi-Squared distribution.

An approach to checking case-crossover analyses based on equivalence with time-series methods.

PubMed

Lu, Yun; Symons, James Morel; Geyh, Alison S; Zeger, Scott L

2008-03-01

The case-crossover design has been increasingly applied to epidemiologic investigations of acute adverse health effects associated with ambient air pollution. The correspondence of the design to that of matched case-control studies makes it inferentially appealing for epidemiologic studies. Case-crossover analyses generally use conditional logistic regression modeling. This technique is equivalent to time-series log-linear regression models when there is a common exposure across individuals, as in air pollution studies. Previous methods for obtaining unbiased estimates for case-crossover analyses have assumed that time-varying risk factors are constant within reference windows. In this paper, we rely on the connection between case-crossover and time-series methods to illustrate model-checking procedures from log-linear model diagnostics for time-stratified case-crossover analyses. Additionally, we compare the relative performance of the time-stratified case-crossover approach to time-series methods under 3 simulated scenarios representing different temporal patterns of daily mortality associated with air pollution in Chicago, Illinois, during 1995 and 1996. Whenever a model-be it time-series or case-crossover-fails to account appropriately for fluctuations in time that confound the exposure, the effect estimate will be biased. It is therefore important to perform model-checking in time-stratified case-crossover analyses rather than assume the estimator is unbiased.

Biostatistics Series Module 6: Correlation and Linear Regression.

PubMed

Hazra, Avijit; Gogtay, Nithya

2016-01-01

Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient ( r ). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P < 0.05. A 95% confidence interval of the correlation coefficient can also be calculated for an idea of the correlation in the population. The value r 2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation ( y = a + bx ), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.

Biostatistics Series Module 6: Correlation and Linear Regression

PubMed Central

Hazra, Avijit; Gogtay, Nithya

2016-01-01

Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient (r). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P < 0.05. A 95% confidence interval of the correlation coefficient can also be calculated for an idea of the correlation in the population. The value r2 denotes the proportion of the variability of the dependent variable y that can be attributed to its linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation (y = a + bx), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous. PMID:27904175

The weighted priors approach for combining expert opinions in logistic regression experiments

DOE PAGES

Quinlan, Kevin R.; Anderson-Cook, Christine M.; Myers, Kary L.

2017-04-24

When modeling the reliability of a system or component, it is not uncommon for more than one expert to provide very different prior estimates of the expected reliability as a function of an explanatory variable such as age or temperature. Our goal in this paper is to incorporate all information from the experts when choosing a design about which units to test. Bayesian design of experiments has been shown to be very successful for generalized linear models, including logistic regression models. We use this approach to develop methodology for the case where there are several potentially non-overlapping priors under consideration.more » While multiple priors have been used for analysis in the past, they have never been used in a design context. The Weighted Priors method performs well for a broad range of true underlying model parameter choices and is more robust when compared to other reasonable design choices. Finally, we illustrate the method through multiple scenarios and a motivating example. Additional figures for this article are available in the online supplementary information.« less

The weighted priors approach for combining expert opinions in logistic regression experiments

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

Quinlan, Kevin R.; Anderson-Cook, Christine M.; Myers, Kary L.

When modeling the reliability of a system or component, it is not uncommon for more than one expert to provide very different prior estimates of the expected reliability as a function of an explanatory variable such as age or temperature. Our goal in this paper is to incorporate all information from the experts when choosing a design about which units to test. Bayesian design of experiments has been shown to be very successful for generalized linear models, including logistic regression models. We use this approach to develop methodology for the case where there are several potentially non-overlapping priors under consideration.more » While multiple priors have been used for analysis in the past, they have never been used in a design context. The Weighted Priors method performs well for a broad range of true underlying model parameter choices and is more robust when compared to other reasonable design choices. Finally, we illustrate the method through multiple scenarios and a motivating example. Additional figures for this article are available in the online supplementary information.« less

Using the Coefficient of Determination "R"[superscript 2] to Test the Significance of Multiple Linear Regression

ERIC Educational Resources Information Center

Quinino, Roberto C.; Reis, Edna A.; Bessegato, Lupercio F.

2013-01-01

This article proposes the use of the coefficient of determination as a statistic for hypothesis testing in multiple linear regression based on distributions acquired by beta sampling. (Contains 3 figures.)

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.

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.

CO2 flux determination by closed-chamber methods can be seriously biased by inappropriate application of linear regression

NASA Astrophysics Data System (ADS)

Kutzbach, L.; Schneider, J.; Sachs, T.; Giebels, M.; Nykänen, H.; Shurpali, N. J.; Martikainen, P. J.; Alm, J.; Wilmking, M.

2007-11-01

Closed (non-steady state) chambers are widely used for quantifying carbon dioxide (CO2) fluxes between soils or low-stature canopies and the atmosphere. It is well recognised that covering a soil or vegetation by a closed chamber inherently disturbs the natural CO2 fluxes by altering the concentration gradients between the soil, the vegetation and the overlying air. Thus, the driving factors of CO2 fluxes are not constant during the closed chamber experiment, and no linear increase or decrease of CO2 concentration over time within the chamber headspace can be expected. Nevertheless, linear regression has been applied for calculating CO2 fluxes in many recent, partly influential, studies. This approach has been justified by keeping the closure time short and assuming the concentration change over time to be in the linear range. Here, we test if the application of linear regression is really appropriate for estimating CO2 fluxes using closed chambers over short closure times and if the application of nonlinear regression is necessary. We developed a nonlinear exponential regression model from diffusion and photosynthesis theory. This exponential model was tested with four different datasets of CO2 flux measurements (total number: 1764) conducted at three peatlands sites in Finland and a tundra site in Siberia. Thorough analyses of residuals demonstrated that linear regression was frequently not appropriate for the determination of CO2 fluxes by closed-chamber methods, even if closure times were kept short. The developed exponential model was well suited for nonlinear regression of the concentration over time c(t) evolution in the chamber headspace and estimation of the initial CO2 fluxes at closure time for the majority of experiments. However, a rather large percentage of the exponential regression functions showed curvatures not consistent with the theoretical model which is considered to be caused by violations of the underlying model assumptions. Especially the effects of turbulence and pressure disturbances by the chamber deployment are suspected to have caused unexplainable curvatures. CO2 flux estimates by linear regression can be as low as 40% of the flux estimates of exponential regression for closure times of only two minutes. The degree of underestimation increased with increasing CO2 flux strength and was dependent on soil and vegetation conditions which can disturb not only the quantitative but also the qualitative evaluation of CO2 flux dynamics. The underestimation effect by linear regression was observed to be different for CO2 uptake and release situations which can lead to stronger bias in the daily, seasonal and annual CO2 balances than in the individual fluxes. To avoid serious bias of CO2 flux estimates based on closed chamber experiments, we suggest further tests using published datasets and recommend the use of nonlinear regression models for future closed chamber studies.

A comparison of regression methods for model selection in individual-based landscape genetic analysis.

PubMed

Shirk, Andrew J; Landguth, Erin L; Cushman, Samuel A

2018-01-01

Anthropogenic migration barriers fragment many populations and limit the ability of species to respond to climate-induced biome shifts. Conservation actions designed to conserve habitat connectivity and mitigate barriers are needed to unite fragmented populations into larger, more viable metapopulations, and to allow species to track their climate envelope over time. Landscape genetic analysis provides an empirical means to infer landscape factors influencing gene flow and thereby inform such conservation actions. However, there are currently many methods available for model selection in landscape genetics, and considerable uncertainty as to which provide the greatest accuracy in identifying the true landscape model influencing gene flow among competing alternative hypotheses. In this study, we used population genetic simulations to evaluate the performance of seven regression-based model selection methods on a broad array of landscapes that varied by the number and type of variables contributing to resistance, the magnitude and cohesion of resistance, as well as the functional relationship between variables and resistance. We also assessed the effect of transformations designed to linearize the relationship between genetic and landscape distances. We found that linear mixed effects models had the highest accuracy in every way we evaluated model performance; however, other methods also performed well in many circumstances, particularly when landscape resistance was high and the correlation among competing hypotheses was limited. Our results provide guidance for which regression-based model selection methods provide the most accurate inferences in landscape genetic analysis and thereby best inform connectivity conservation actions. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

Computation of nonlinear least squares estimator and maximum likelihood using principles in matrix calculus

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi; Balasiddamuni, P.

2017-11-01

This paper uses matrix calculus techniques to obtain Nonlinear Least Squares Estimator (NLSE), Maximum Likelihood Estimator (MLE) and Linear Pseudo model for nonlinear regression model. David Pollard and Peter Radchenko [1] explained analytic techniques to compute the NLSE. However the present research paper introduces an innovative method to compute the NLSE using principles in multivariate calculus. This study is concerned with very new optimization techniques used to compute MLE and NLSE. Anh [2] derived NLSE and MLE of a heteroscedatistic regression model. Lemcoff [3] discussed a procedure to get linear pseudo model for nonlinear regression model. In this research article a new technique is developed to get the linear pseudo model for nonlinear regression model using multivariate calculus. The linear pseudo model of Edmond Malinvaud [4] has been explained in a very different way in this paper. David Pollard et.al used empirical process techniques to study the asymptotic of the LSE (Least-squares estimation) for the fitting of nonlinear regression function in 2006. In Jae Myung [13] provided a go conceptual for Maximum likelihood estimation in his work “Tutorial on maximum likelihood estimation

A Model for Oil-Gas Pipelines Cost Prediction Based on a Data Mining Process

NASA Astrophysics Data System (ADS)

Batzias, Fragiskos A.; Spanidis, Phillip-Mark P.

2009-08-01

This paper addresses the problems associated with the cost estimation of oil/gas pipelines during the elaboration of feasibility assessments. Techno-economic parameters, i.e., cost, length and diameter, are critical for such studies at the preliminary design stage. A methodology for the development of a cost prediction model based on Data Mining (DM) process is proposed. The design and implementation of a Knowledge Base (KB), maintaining data collected from various disciplines of the pipeline industry, are presented. The formulation of a cost prediction equation is demonstrated by applying multiple regression analysis using data sets extracted from the KB. Following the methodology proposed, a learning context is inductively developed as background pipeline data are acquired, grouped and stored in the KB, and through a linear regression model provide statistically substantial results, useful for project managers or decision makers.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

GIS Tools to Estimate Average Annual Daily Traffic

DOT National Transportation Integrated Search

2012-06-01

This project presents five tools that were created for a geographical information system to estimate Annual Average Daily : Traffic using linear regression. Three of the tools can be used to prepare spatial data for linear regression. One tool can be...

Estimating extent of mortality associated with the Douglas-fir beetle in the Central and Northern Rockies

Treesearch

Jose F. Negron; Willis C. Schaupp; Kenneth E. Gibson; John Anhold; Dawn Hansen; Ralph Thier; Phil Mocettini

1999-01-01

Data collected from Douglas-fir stands infected by the Douglas-fir beetle in Wyoming, Montana, Idaho, and Utah, were used to develop models to estimate amount of mortality in terms of basal area killed. Models were built using stepwise linear regression and regression tree approaches. Linear regression models using initial Douglas-fir basal area were built for all...

[Prediction model of health workforce and beds in county hospitals of Hunan by multiple linear regression].

PubMed

Ling, Ru; Liu, Jiawang

2011-12-01

To construct prediction model for health workforce and hospital beds in county hospitals of Hunan by multiple linear regression. We surveyed 16 counties in Hunan with stratified random sampling according to uniform questionnaires,and multiple linear regression analysis with 20 quotas selected by literature view was done. Independent variables in the multiple linear regression model on medical personnels in county hospitals included the counties' urban residents' income, crude death rate, medical beds, business occupancy, professional equipment value, the number of devices valued above 10 000 yuan, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, and utilization rate of hospital beds. Independent variables in the multiple linear regression model on county hospital beds included the the population of aged 65 and above in the counties, disposable income of urban residents, medical personnel of medical institutions in county area, business occupancy, the total value of professional equipment, fixed assets, long-term debt, medical income, medical expenses, outpatient and emergency visits, hospital visits, actual available bed days, utilization rate of hospital beds, and length of hospitalization. The prediction model shows good explanatory and fitting, and may be used for short- and mid-term forecasting.

A new approach to correct the QT interval for changes in heart rate using a nonparametric regression model in beagle dogs.

PubMed

Watanabe, Hiroyuki; Miyazaki, Hiroyasu

2006-01-01

Over- and/or under-correction of QT intervals for changes in heart rate may lead to misleading conclusions and/or masking the potential of a drug to prolong the QT interval. This study examines a nonparametric regression model (Loess Smoother) to adjust the QT interval for differences in heart rate, with an improved fitness over a wide range of heart rates. 240 sets of (QT, RR) observations collected from each of 8 conscious and non-treated beagle dogs were used as the materials for investigation. The fitness of the nonparametric regression model to the QT-RR relationship was compared with four models (individual linear regression, common linear regression, and Bazett's and Fridericia's correlation models) with reference to Akaike's Information Criterion (AIC). Residuals were visually assessed. The bias-corrected AIC of the nonparametric regression model was the best of the models examined in this study. Although the parametric models did not fit, the nonparametric regression model improved the fitting at both fast and slow heart rates. The nonparametric regression model is the more flexible method compared with the parametric method. The mathematical fit for linear regression models was unsatisfactory at both fast and slow heart rates, while the nonparametric regression model showed significant improvement at all heart rates in beagle dogs.

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.

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.

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.

Geodesic regression for image time-series.

PubMed

Niethammer, Marc; Huang, Yang; Vialard, François-Xavier

2011-01-01

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

Influenza detection and prediction algorithms: comparative accuracy trial in Östergötland county, Sweden, 2008-2012.

PubMed

Spreco, A; Eriksson, O; Dahlström, Ö; Timpka, T

2017-07-01

Methods for the detection of influenza epidemics and prediction of their progress have seldom been comparatively evaluated using prospective designs. This study aimed to perform a prospective comparative trial of algorithms for the detection and prediction of increased local influenza activity. Data on clinical influenza diagnoses recorded by physicians and syndromic data from a telenursing service were used. Five detection and three prediction algorithms previously evaluated in public health settings were calibrated and then evaluated over 3 years. When applied on diagnostic data, only detection using the Serfling regression method and prediction using the non-adaptive log-linear regression method showed acceptable performances during winter influenza seasons. For the syndromic data, none of the detection algorithms displayed a satisfactory performance, while non-adaptive log-linear regression was the best performing prediction method. We conclude that evidence was found for that available algorithms for influenza detection and prediction display satisfactory performance when applied on local diagnostic data during winter influenza seasons. When applied on local syndromic data, the evaluated algorithms did not display consistent performance. Further evaluations and research on combination of methods of these types in public health information infrastructures for 'nowcasting' (integrated detection and prediction) of influenza activity are warranted.

Cellulose microfibril orientation of Picea abies and its variability at the micron-level determined by Raman imaging.

PubMed

Gierlinger, Notburga; Luss, Saskia; König, Christian; Konnerth, Johannes; Eder, Michaela; Fratzl, Peter

2010-01-01

The functional characteristics of plant cell walls depend on the composition of the cell wall polymers, as well as on their highly ordered architecture at scales from a few nanometres to several microns. Raman spectra of wood acquired with linear polarized laser light include information about polymer composition as well as the alignment of cellulose microfibrils with respect to the fibre axis (microfibril angle). By changing the laser polarization direction in 3 degrees steps, the dependency between cellulose and laser orientation direction was investigated. Orientation-dependent changes of band height ratios and spectra were described by quadratic linear regression and partial least square regressions, respectively. Using the models and regressions with high coefficients of determination (R(2) > 0.99) microfibril orientation was predicted in the S1 and S2 layers distinguished by the Raman imaging approach in cross-sections of spruce normal, opposite, and compression wood. The determined microfibril angle (MFA) in the different S2 layers ranged from 0 degrees to 49.9 degrees and was in coincidence with X-ray diffraction determination. With the prerequisite of geometric sample and laser alignment, exact MFA prediction can complete the picture of the chemical cell wall design gained by the Raman imaging approach at the micron level in all plant tissues.

A rotor optimization using regression analysis

NASA Technical Reports Server (NTRS)

Giansante, N.

1984-01-01

The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

Scoring and staging systems using cox linear regression modeling and recursive partitioning.

PubMed

Lee, J W; Um, S H; Lee, J B; Mun, J; Cho, H

2006-01-01

Scoring and staging systems are used to determine the order and class of data according to predictors. Systems used for medical data, such as the Child-Turcotte-Pugh scoring and staging systems for ordering and classifying patients with liver disease, are often derived strictly from physicians' experience and intuition. We construct objective and data-based scoring/staging systems using statistical methods. We consider Cox linear regression modeling and recursive partitioning techniques for censored survival data. In particular, to obtain a target number of stages we propose cross-validation and amalgamation algorithms. We also propose an algorithm for constructing scoring and staging systems by integrating local Cox linear regression models into recursive partitioning, so that we can retain the merits of both methods such as superior predictive accuracy, ease of use, and detection of interactions between predictors. The staging system construction algorithms are compared by cross-validation evaluation of real data. The data-based cross-validation comparison shows that Cox linear regression modeling is somewhat better than recursive partitioning when there are only continuous predictors, while recursive partitioning is better when there are significant categorical predictors. The proposed local Cox linear recursive partitioning has better predictive accuracy than Cox linear modeling and simple recursive partitioning. This study indicates that integrating local linear modeling into recursive partitioning can significantly improve prediction accuracy in constructing scoring and staging systems.

"Mad or bad?": burden on caregivers of patients with personality disorders.

PubMed

Bauer, Rita; Döring, Antje; Schmidt, Tanja; Spießl, Hermann

2012-12-01

The burden on caregivers of patients with personality disorders is often greatly underestimated or completely disregarded. Possibilities for caregiver support have rarely been assessed. Thirty interviews were conducted with caregivers of such patients to assess illness-related burden. Responses were analyzed with a mixed method of qualitative and quantitative analysis in a sequential design. Patient and caregiver data, including sociodemographic and disease-related variables, were evaluated with regression analysis and regression trees. Caregiver statements (n = 404) were summarized into 44 global statements. The most frequent global statements were worries about the burden on other family members (70.0%), poor cooperation with clinical centers and other institutions (60.0%), financial burden (56.7%), worry about the patient's future (53.3%), and dissatisfaction with the patient's treatment and rehabilitation (53.3%). Linear regression and regression tree analysis identified predictors for more burdened caregivers. Caregivers of patients with personality disorders experience a variety of burdens, some disorder specific. Yet these caregivers often receive little attention or support.

Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism.

PubMed

Scarneciu, Camelia C; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D; Varciu, Mihai S; Andreescu, Oana; Scarneciu, Ioan

2017-01-01

This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is given by a polynomial equation of second degree where the parabola is its graphical representation.

A simplified calculation procedure for mass isotopomer distribution analysis (MIDA) based on multiple linear regression.

PubMed

Fernández-Fernández, Mario; Rodríguez-González, Pablo; García Alonso, J Ignacio

2016-10-01

We have developed a novel, rapid and easy calculation procedure for Mass Isotopomer Distribution Analysis based on multiple linear regression which allows the simultaneous calculation of the precursor pool enrichment and the fraction of newly synthesized labelled proteins (fractional synthesis) using linear algebra. To test this approach, we used the peptide RGGGLK as a model tryptic peptide containing three subunits of glycine. We selected glycine labelled in two 13 C atoms ( 13 C 2 -glycine) as labelled amino acid to demonstrate that spectral overlap is not a problem in the proposed methodology. The developed methodology was tested first in vitro by changing the precursor pool enrichment from 10 to 40% of 13 C 2 -glycine. Secondly, a simulated in vivo synthesis of proteins was designed by combining the natural abundance RGGGLK peptide and 10 or 20% 13 C 2 -glycine at 1 : 1, 1 : 3 and 3 : 1 ratios. Precursor pool enrichments and fractional synthesis values were calculated with satisfactory precision and accuracy using a simple spreadsheet. This novel approach can provide a relatively rapid and easy means to measure protein turnover based on stable isotope tracers. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Prediction of accommodative optical response in prepresbyopic patients using ultrasound biomicroscopy

PubMed Central

Ramasubramanian, Viswanathan; Glasser, Adrian

2015-01-01

PURPOSE To determine whether relatively low-resolution ultrasound biomicroscopy (UBM) can predict the accommodative optical response in prepresbyopic eyes as well as in a previous study of young phakic subjects, despite lower accommodative amplitudes. SETTING College of Optometry, University of Houston, Houston, USA. DESIGN Observational cross-sectional study. METHODS Static accommodative optical response was measured with infrared photorefraction and an autorefractor (WR-5100K) in subjects aged 36 to 46 years. A 35 MHz UBM device (Vumax, Sonomed Escalon) was used to image the left eye, while the right eye viewed accommodative stimuli. Custom-developed Matlab image-analysis software was used to perform automated analysis of UBM images to measure the ocular biometry parameters. The accommodative optical response was predicted from biometry parameters using linear regression, 95% confidence intervals (CIs), and 95% prediction intervals. RESULTS The study evaluated 25 subjects. Per-diopter (D) accommodative changes in anterior chamber depth (ACD), lens thickness, anterior and posterior lens radii of curvature, and anterior segment length were similar to previous values from young subjects. The standard deviations (SDs) of accommodative optical response predicted from linear regressions for UBM-measured biometry parameters were ACD, 0.15 D; lens thickness, 0.25 D; anterior lens radii of curvature, 0.09 D; posterior lens radii of curvature, 0.37 D; and anterior segment length, 0.42 D. CONCLUSIONS Ultrasound biomicroscopy parameters can, on average, predict accommodative optical response with SDs of less than 0.55 D using linear regressions and 95% CIs. Ultrasound biomicroscopy can be used to visualize and quantify accommodative biometric changes and predict accommodative optical response in prepresbyopic eyes. PMID:26049831

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...

A simplified competition data analysis for radioligand specific activity determination.

PubMed

Venturino, A; Rivera, E S; Bergoc, R M; Caro, R A

1990-01-01

Non-linear regression and two-step linear fit methods were developed to determine the actual specific activity of 125I-ovine prolactin by radioreceptor self-displacement analysis. The experimental results obtained by the different methods are superposable. The non-linear regression method is considered to be the most adequate procedure to calculate the specific activity, but if its software is not available, the other described methods are also suitable.

Height and Weight Estimation From Anthropometric Measurements Using Machine Learning Regressions

PubMed Central

Fernandes, Bruno J. T.; Roque, Alexandre

2018-01-01

Height and weight are measurements explored to tracking nutritional diseases, energy expenditure, clinical conditions, drug dosages, and infusion rates. Many patients are not ambulant or may be unable to communicate, and a sequence of these factors may not allow accurate estimation or measurements; in those cases, it can be estimated approximately by anthropometric means. Different groups have proposed different linear or non-linear equations which coefficients are obtained by using single or multiple linear regressions. In this paper, we present a complete study of the application of different learning models to estimate height and weight from anthropometric measurements: support vector regression, Gaussian process, and artificial neural networks. The predicted values are significantly more accurate than that obtained with conventional linear regressions. In all the cases, the predictions are non-sensitive to ethnicity, and to gender, if more than two anthropometric parameters are analyzed. The learning model analysis creates new opportunities for anthropometric applications in industry, textile technology, security, and health care. PMID:29651366

Electricity Consumption in the Industrial Sector of Jordan: Application of Multivariate Linear Regression and Adaptive Neuro-Fuzzy Techniques

NASA Astrophysics Data System (ADS)

Samhouri, M.; Al-Ghandoor, A.; Fouad, R. H.

2009-08-01

In this study two techniques, for modeling electricity consumption of the Jordanian industrial sector, are presented: (i) multivariate linear regression and (ii) neuro-fuzzy models. Electricity consumption is modeled as function of different variables such as number of establishments, number of employees, electricity tariff, prevailing fuel prices, production outputs, capacity utilizations, and structural effects. It was found that industrial production and capacity utilization are the most important variables that have significant effect on future electrical power demand. The results showed that both the multivariate linear regression and neuro-fuzzy models are generally comparable and can be used adequately to simulate industrial electricity consumption. However, comparison that is based on the square root average squared error of data suggests that the neuro-fuzzy model performs slightly better for future prediction of electricity consumption than the multivariate linear regression model. Such results are in full agreement with similar work, using different methods, for other countries.

Improving Prediction Accuracy for WSN Data Reduction by Applying Multivariate Spatio-Temporal Correlation

PubMed Central

Carvalho, Carlos; Gomes, Danielo G.; Agoulmine, Nazim; de Souza, José Neuman

2011-01-01

This paper proposes a method based on multivariate spatial and temporal correlation to improve prediction accuracy in data reduction for Wireless Sensor Networks (WSN). Prediction of data not sent to the sink node is a technique used to save energy in WSNs by reducing the amount of data traffic. However, it may not be very accurate. Simulations were made involving simple linear regression and multiple linear regression functions to assess the performance of the proposed method. The results show a higher correlation between gathered inputs when compared to time, which is an independent variable widely used for prediction and forecasting. Prediction accuracy is lower when simple linear regression is used, whereas multiple linear regression is the most accurate one. In addition to that, our proposal outperforms some current solutions by about 50% in humidity prediction and 21% in light prediction. To the best of our knowledge, we believe that we are probably the first to address prediction based on multivariate correlation for WSN data reduction. PMID:22346626

Using the Ridge Regression Procedures to Estimate the Multiple Linear Regression Coefficients

NASA Astrophysics Data System (ADS)

Gorgees, HazimMansoor; Mahdi, FatimahAssim

2018-05-01

This article concerns with comparing the performance of different types of ordinary ridge regression estimators that have been already proposed to estimate the regression parameters when the near exact linear relationships among the explanatory variables is presented. For this situations we employ the data obtained from tagi gas filling company during the period (2008-2010). The main result we reached is that the method based on the condition number performs better than other methods since it has smaller mean square error (MSE) than the other stated methods.

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.

Alzheimer's Disease Detection by Pseudo Zernike Moment and Linear Regression Classification.

PubMed

Wang, Shui-Hua; Du, Sidan; Zhang, Yin; Phillips, Preetha; Wu, Le-Nan; Chen, Xian-Qing; Zhang, Yu-Dong

2017-01-01

This study presents an improved method based on "Gorji et al. Neuroscience. 2015" by introducing a relatively new classifier-linear regression classification. Our method selects one axial slice from 3D brain image, and employed pseudo Zernike moment with maximum order of 15 to extract 256 features from each image. Finally, linear regression classification was harnessed as the classifier. The proposed approach obtains an accuracy of 97.51%, a sensitivity of 96.71%, and a specificity of 97.73%. Our method performs better than Gorji's approach and five other state-of-the-art approaches. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Statistical power for the comparative regression discontinuity design with a nonequivalent comparison group.

PubMed

Tang, Yang; Cook, Thomas D; Kisbu-Sakarya, Yasemin

2018-03-01

In the "sharp" regression discontinuity design (RD), all units scoring on one side of a designated score on an assignment variable receive treatment, whereas those scoring on the other side become controls. Thus the continuous assignment variable and binary treatment indicator are measured on the same scale. Because each must be in the impact model, the resulting multi-collinearity reduces the efficiency of the RD design. However, untreated comparison data can be added along the assignment variable, and a comparative regression discontinuity design (CRD) is then created. When the untreated data come from a non-equivalent comparison group, we call this CRD-CG. Assuming linear functional forms, we show that power in CRD-CG is (a) greater than in basic RD; (b) less sensitive to the location of the cutoff and the distribution of the assignment variable; and that (c) fewer treated units are needed in the basic RD component within the CRD-CG so that savings can result from having fewer treated cases. The theory we develop is used to make numerical predictions about the efficiency of basic RD and CRD-CG relative to each other and to a randomized control trial. Data from the National Head Start Impact study are used to test these predictions. The obtained estimates are closer to the predicted parameters for CRD-CG than for basic RD and are generally quite close to the parameter predictions, supporting the emerging argument that CRD should be the design of choice in many applications for which basic RD is now used. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

A simple bias correction in linear regression for quantitative trait association under two-tail extreme selection.

PubMed

Kwan, Johnny S H; Kung, Annie W C; Sham, Pak C

2011-09-01

Selective genotyping can increase power in quantitative trait association. One example of selective genotyping is two-tail extreme selection, but simple linear regression analysis gives a biased genetic effect estimate. Here, we present a simple correction for the bias.

Ridge Regression Signal Processing

NASA Technical Reports Server (NTRS)

Kuhl, Mark R.

1990-01-01

The introduction of the Global Positioning System (GPS) into the National Airspace System (NAS) necessitates the development of Receiver Autonomous Integrity Monitoring (RAIM) techniques. In order to guarantee a certain level of integrity, a thorough understanding of modern estimation techniques applied to navigational problems is required. The extended Kalman filter (EKF) is derived and analyzed under poor geometry conditions. It was found that the performance of the EKF is difficult to predict, since the EKF is designed for a Gaussian environment. A novel approach is implemented which incorporates ridge regression to explain the behavior of an EKF in the presence of dynamics under poor geometry conditions. The basic principles of ridge regression theory are presented, followed by the derivation of a linearized recursive ridge estimator. Computer simulations are performed to confirm the underlying theory and to provide a comparative analysis of the EKF and the recursive ridge estimator.

A Common Mechanism for Resistance to Oxime Reactivation of Acetylcholinesterase Inhibited by Organophosphorus Compounds

DTIC Science & Technology

2013-01-01

application of the Hammett equation with the constants rph in the chemistry of organophosphorus compounds, Russ. Chem. Rev. 38 (1969) 795–811. [13...of oximes and OP compounds and the ability of oximes to reactivate OP- inhibited AChE. Multiple linear regression equations were analyzed using...phosphonate pairs, 21 oxime/ phosphoramidate pairs and 12 oxime/phosphate pairs. The best linear regression equation resulting from multiple regression anal

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

Deep Wavelet Scattering for Quantum Energy Regression

NASA Astrophysics Data System (ADS)

Hirn, Matthew

Physical functionals are usually computed as solutions of variational problems or from solutions of partial differential equations, which may require huge computations for complex systems. Quantum chemistry calculations of ground state molecular energies is such an example. Indeed, if x is a quantum molecular state, then the ground state energy E0 (x) is the minimum eigenvalue solution of the time independent Schrödinger Equation, which is computationally intensive for large systems. Machine learning algorithms do not simulate the physical system but estimate solutions by interpolating values provided by a training set of known examples {(xi ,E0 (xi) } i <= n . However, precise interpolations may require a number of examples that is exponential in the system dimension, and are thus intractable. This curse of dimensionality may be circumvented by computing interpolations in smaller approximation spaces, which take advantage of physical invariants. Linear regressions of E0 over a dictionary Φ ={ϕk } k compute an approximation E 0 as: E 0 (x) =∑kwkϕk (x) , where the weights {wk } k are selected to minimize the error between E0 and E 0 on the training set. The key to such a regression approach then lies in the design of the dictionary Φ. It must be intricate enough to capture the essential variability of E0 (x) over the molecular states x of interest, while simple enough so that evaluation of Φ (x) is significantly less intensive than a direct quantum mechanical computation (or approximation) of E0 (x) . In this talk we present a novel dictionary Φ for the regression of quantum mechanical energies based on the scattering transform of an intermediate, approximate electron density representation ρx of the state x. The scattering transform has the architecture of a deep convolutional network, composed of an alternating sequence of linear filters and nonlinear maps. Whereas in many deep learning tasks the linear filters are learned from the training data, here the physical properties of E0 (invariance to isometric transformations of the state x, stable to deformations of x) are leveraged to design a collection of linear filters ρx *ψλ for an appropriate wavelet ψ. These linear filters are composed with the nonlinear modulus operator, and the process is iterated upon so that at each layer stable, invariant features are extracted: ϕk (x) = ∥ | | ρx *ψλ1 | * ψλ2 | * ... *ψλm ∥ , k = (λ1 , ... ,λm) , m = 1 , 2 , ... The scattering transform thus encodes not only interactions at multiple scales (in the first layer, m = 1), but also features that encode complex phenomena resulting from a cascade of interactions across scales (in subsequent layers, m >= 2). Numerical experiments give state of the art accuracy over data bases of organic molecules, while theoretical results guarantee performance for the component of the ground state energy resulting from Coulombic interactions. Supported by the ERC InvariantClass 320959 Grant.

Specialization Agreements in the Council for Mutual Economic Assistance

DTIC Science & Technology

1988-02-01

proportions to stabilize variance (S. Weisberg, Applied Linear Regression , 2nd ed., John Wiley & Sons, New York, 1985, p. 134). If the dependent...27, 1986, p. 3. Weisberg, S., Applied Linear Regression , 2nd ed., John Wiley & Sons, New York, 1985, p. 134. Wiles, P. J., Communist International

Radio Propagation Prediction Software for Complex Mixed Path Physical Channels

DTIC Science & Technology

2006-08-14

63 4.4.6. Applied Linear Regression Analysis in the Frequency Range 1-50 MHz 69 4.4.7. Projected Scaling to...4.4.6. Applied Linear Regression Analysis in the Frequency Range 1-50 MHz In order to construct a comprehensive numerical algorithm capable of

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...

Data Transformations for Inference with Linear Regression: Clarifications and Recommendations

ERIC Educational Resources Information Center

Pek, Jolynn; Wong, Octavia; Wong, C. M.

2017-01-01

Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…

USING LINEAR AND POLYNOMIAL MODELS TO EXAMINE THE ENVIRONMENTAL STABILITY OF VIRUSES

EPA Science Inventory

The article presents the development of model equations for describing the fate of viral infectivity in environmental samples. Most of the models were based upon the use of a two-step linear regression approach. The first step employs regression of log base 10 transformed viral t...

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…

Simple and multiple linear regression: sample size considerations.

PubMed

Hanley, James A

2016-11-01

The suggested "two subjects per variable" (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression. This article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing "exposure" (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or "profiles." It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates. By drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres. Copyright © 2016 Elsevier Inc. All rights reserved.

A Cross-Domain Collaborative Filtering Algorithm Based on Feature Construction and Locally Weighted Linear Regression

PubMed Central

Jiang, Feng; Han, Ji-zhong

2018-01-01

Cross-domain collaborative filtering (CDCF) solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR). We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR) model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods. PMID:29623088

A Cross-Domain Collaborative Filtering Algorithm Based on Feature Construction and Locally Weighted Linear Regression.

PubMed

Yu, Xu; Lin, Jun-Yu; Jiang, Feng; Du, Jun-Wei; Han, Ji-Zhong

2018-01-01

Cross-domain collaborative filtering (CDCF) solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR). We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR) model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods.

Nonparametric regression applied to quantitative structure-activity relationships

PubMed

Constans; Hirst

2000-03-01

Several nonparametric regressors have been applied to modeling quantitative structure-activity relationship (QSAR) data. The simplest regressor, the Nadaraya-Watson, was assessed in a genuine multivariate setting. Other regressors, the local linear and the shifted Nadaraya-Watson, were implemented within additive models--a computationally more expedient approach, better suited for low-density designs. Performances were benchmarked against the nonlinear method of smoothing splines. A linear reference point was provided by multilinear regression (MLR). Variable selection was explored using systematic combinations of different variables and combinations of principal components. For the data set examined, 47 inhibitors of dopamine beta-hydroxylase, the additive nonparametric regressors have greater predictive accuracy (as measured by the mean absolute error of the predictions or the Pearson correlation in cross-validation trails) than MLR. The use of principal components did not improve the performance of the nonparametric regressors over use of the original descriptors, since the original descriptors are not strongly correlated. It remains to be seen if the nonparametric regressors can be successfully coupled with better variable selection and dimensionality reduction in the context of high-dimensional QSARs.

Teaching High School Students Machine Learning Algorithms to Analyze Flood Risk Factors in River Deltas

NASA Astrophysics Data System (ADS)

Rose, R.; Aizenman, H.; Mei, E.; Choudhury, N.

2013-12-01

High School students interested in the STEM fields benefit most when actively participating, so I created a series of learning modules on how to analyze complex systems using machine-learning that give automated feedback to students. The automated feedbacks give timely responses that will encourage the students to continue testing and enhancing their programs. I have designed my modules to take the tactical learning approach in conveying the concepts behind correlation, linear regression, and vector distance based classification and clustering. On successful completion of these modules, students will learn how to calculate linear regression, Pearson's correlation, and apply classification and clustering techniques to a dataset. Working on these modules will allow the students to take back to the classroom what they've learned and then apply it to the Earth Science curriculum. During my research this summer, we applied these lessons to analyzing river deltas; we looked at trends in the different variables over time, looked for similarities in NDVI, precipitation, inundation, runoff and discharge, and attempted to predict floods based on the precipitation, waves mean, area of discharge, NDVI, and inundation.

Multi-Axis Identifiability Using Single-Surface Parameter Estimation Maneuvers on the X-48B Blended Wing Body

NASA Technical Reports Server (NTRS)

Ratnayake, Nalin A.; Koshimoto, Ed T.; Taylor, Brian R.

2011-01-01

The problem of parameter estimation on hybrid-wing-body type aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aero- dynamic control effectors that act in coplanar motion. This fact adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of system inputs must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, asymmetric, single-surface maneuvers are used to excite multiple axes of aircraft motion simultaneously. Time history reconstructions of the moment coefficients computed by the solved regression models are then compared to each other in order to assess relative model accuracy. The reduced flight-test time required for inner surface parameter estimation using multi-axis methods was found to come at the cost of slightly reduced accuracy and statistical confidence for linear regression methods. Since the multi-axis maneuvers captured parameter estimates similar to both longitudinal and lateral-directional maneuvers combined, the number of test points required for the inner, aileron-like surfaces could in theory have been reduced by 50%. While trends were similar, however, individual parameters as estimated by a multi-axis model were typically different by an average absolute difference of roughly 15-20%, with decreased statistical significance, than those estimated by a single-axis model. The multi-axis model exhibited an increase in overall fit error of roughly 1-5% for the linear regression estimates with respect to the single-axis model, when applied to flight data designed for each, respectively.

Cassava dreg as replacement of corn in goat kid diets.

PubMed

Ferraz, Lucíola Vilarim; Guim, Adriana; Véras, Robson Magno Liberal; de Carvalho, Francisco Fernando Ramos; de Freitas, Marciela Thais Dino

2018-02-01

The effects of corn replacement by cassava dreg in diets of crossbred goat kids were evaluated. We tested the impacts of 0, 33, 66 and 100% replacement on intake, digestibility, feeding behaviour, performance and carcass characteristics. Thirty-six goat kids, aged between 4 and 5 months and with initial body weights of 17.61 ± 1.98 kg, were used in a completely randomised design. Analysis of regression revealed a negative linear effect on neutral detergent fibre (NDF) intake and a positive linear effect on non-fibrous carbohydrates (NFC) and hydrocyanic acids (HCN) intake. Cassava dreg use had a positive linear effect on organic matter digestibility and non-fibrous carbohydrates. Based on our results, cassava dreg use did not negatively impact animal performance, feeding behaviour and carcass characteristics, suggesting that it may replace corn up to 100% in the diets of confined goat kids.

Destination bedside: using research findings to visualize optimal unit layouts and health information technology in support of bedside care.

PubMed

Watkins, Nicholas; Kennedy, Mary; Lee, Nelson; O'Neill, Michael; Peavey, Erin; Ducharme, Maria; Padula, Cynthia

2012-05-01

This study explored the impact of unit design and healthcare information technology (HIT) on nursing workflow and patient-centered care (PCC). Healthcare information technology and unit layout-related predictors of nursing workflow and PCC were measured during a 3-phase study involving questionnaires and work sampling methods. Stepwise multiple linear regressions demonstrated several HIT and unit layout-related factors that impact nursing workflow and PCC.

Determination of the minimal clinically important difference for seven fatigue measures in rheumatoid arthritis

PubMed Central

Pouchot, Jacques; Kherani, Raheem B.; Brant, Rollin; Lacaille, Diane; Lehman, Allen J.; Ensworth, Stephanie; Kopec, Jacek; Esdaile, John M.; Liang, Matthew H.

2008-01-01

Objective To estimate the minimal clinically important difference (MCID) of seven measures of fatigue in rheumatoid arthritis. Study Design and Setting A cross-sectional study design based on inter-individual comparisons was used. Six to eight subjects participated in a single meeting and completed seven fatigue questionnaires (nine sessions were organized and 61 subjects participated). After completion of the questionnaires, the subjects had five one-on-one 10-minute conversations with different people in the group to discuss their fatigue. After each conversation, each patient compared their fatigue to their conversational partner’s on a global rating. Ratings were compared to the scores of the fatigue measures to estimate the MCID. Both non-parametric and linear regression analyses were used. Results Non-parametric estimates for the MCID relative to “little more fatigue” tended to be smaller than those for “little less fatigue”. The global MCIDs estimated by linear regression were: FSS 20.2, VT 14.8, MAF 18.7, MFI 16.6, FACIT–F 15.9, CFS 9.9, RS 19.7, for normalized scores (0 to 100). The standardized MCIDs for the seven measures were roughly similar (0.67 to 0.76). Conclusion These estimates of MCID will help to interpret changes observed in a fatigue score and will be critical in estimating sample size requirements. PMID:18359189

Site-specific estimation of peak-streamflow frequency using generalized least-squares regression for natural basins in Texas

USGS Publications Warehouse

Asquith, William H.; Slade, R.M.

1999-01-01

The U.S. Geological Survey, in cooperation with the Texas Department of Transportation, has developed a computer program to estimate peak-streamflow frequency for ungaged sites in natural basins in Texas. Peak-streamflow frequency refers to the peak streamflows for recurrence intervals of 2, 5, 10, 25, 50, and 100 years. Peak-streamflow frequency estimates are needed by planners, managers, and design engineers for flood-plain management; for objective assessment of flood risk; for cost-effective design of roads and bridges; and also for the desin of culverts, dams, levees, and other flood-control structures. The program estimates peak-streamflow frequency using a site-specific approach and a multivariate generalized least-squares linear regression. A site-specific approach differs from a traditional regional regression approach by developing unique equations to estimate peak-streamflow frequency specifically for the ungaged site. The stations included in the regression are selected using an informal cluster analysis that compares the basin characteristics of the ungaged site to the basin characteristics of all the stations in the data base. The program provides several choices for selecting the stations. Selecting the stations using cluster analysis ensures that the stations included in the regression will have the most pertinent information about flooding characteristics of the ungaged site and therefore provide the basis for potentially improved peak-streamflow frequency estimation. An evaluation of the site-specific approach in estimating peak-streamflow frequency for gaged sites indicates that the site-specific approach is at least as accurate as a traditional regional regression approach.

Analysis of Binary Adherence Data in the Setting of Polypharmacy: A Comparison of Different Approaches

PubMed Central

Esserman, Denise A.; Moore, Charity G.; Roth, Mary T.

2009-01-01

Older community dwelling adults often take multiple medications for numerous chronic diseases. Non-adherence to these medications can have a large public health impact. Therefore, the measurement and modeling of medication adherence in the setting of polypharmacy is an important area of research. We apply a variety of different modeling techniques (standard linear regression; weighted linear regression; adjusted linear regression; naïve logistic regression; beta-binomial (BB) regression; generalized estimating equations (GEE)) to binary medication adherence data from a study in a North Carolina based population of older adults, where each medication an individual was taking was classified as adherent or non-adherent. In addition, through simulation we compare these different methods based on Type I error rates, bias, power, empirical 95% coverage, and goodness of fit. We find that estimation and inference using GEE is robust to a wide variety of scenarios and we recommend using this in the setting of polypharmacy when adherence is dichotomously measured for multiple medications per person. PMID:20414358

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.

Multivariate Linear Regression and CART Regression Analysis of TBM Performance at Abu Hamour Phase-I Tunnel

NASA Astrophysics Data System (ADS)

Jakubowski, J.; Stypulkowski, J. B.; Bernardeau, F. G.

2017-12-01

The first phase of the Abu Hamour drainage and storm tunnel was completed in early 2017. The 9.5 km long, 3.7 m diameter tunnel was excavated with two Earth Pressure Balance (EPB) Tunnel Boring Machines from Herrenknecht. TBM operation processes were monitored and recorded by Data Acquisition and Evaluation System. The authors coupled collected TBM drive data with available information on rock mass properties, cleansed, completed with secondary variables and aggregated by weeks and shifts. Correlations and descriptive statistics charts were examined. Multivariate Linear Regression and CART regression tree models linking TBM penetration rate (PR), penetration per revolution (PPR) and field penetration index (FPI) with TBM operational and geotechnical characteristics were performed for the conditions of the weak/soft rock of Doha. Both regression methods are interpretable and the data were screened with different computational approaches allowing enriched insight. The primary goal of the analysis was to investigate empirical relations between multiple explanatory and responding variables, to search for best subsets of explanatory variables and to evaluate the strength of linear and non-linear relations. For each of the penetration indices, a predictive model coupling both regression methods was built and validated. The resultant models appeared to be stronger than constituent ones and indicated an opportunity for more accurate and robust TBM performance predictions.

Design Process for High Speed Civil Transport Aircraft Improved by Neural Network and Regression Methods

NASA Technical Reports Server (NTRS)

Hopkins, Dale A.

1998-01-01

A key challenge in designing the new High Speed Civil Transport (HSCT) aircraft is determining a good match between the airframe and engine. Multidisciplinary design optimization can be used to solve the problem by adjusting parameters of both the engine and the airframe. Earlier, an example problem was presented of an HSCT aircraft with four mixed-flow turbofan engines and a baseline mission to carry 305 passengers 5000 nautical miles at a cruise speed of Mach 2.4. The problem was solved by coupling NASA Lewis Research Center's design optimization testbed (COMETBOARDS) with NASA Langley Research Center's Flight Optimization System (FLOPS). The computing time expended in solving the problem was substantial, and the instability of the FLOPS analyzer at certain design points caused difficulties. In an attempt to alleviate both of these limitations, we explored the use of two approximation concepts in the design optimization process. The two concepts, which are based on neural network and linear regression approximation, provide the reanalysis capability and design sensitivity analysis information required for the optimization process. The HSCT aircraft optimization problem was solved by using three alternate approaches; that is, the original FLOPS analyzer and two approximate (derived) analyzers. The approximate analyzers were calibrated and used in three different ranges of the design variables; narrow (interpolated), standard, and wide (extrapolated).

Guidance for the utility of linear models in meta-analysis of genetic association studies of binary phenotypes.

PubMed

Cook, James P; Mahajan, Anubha; Morris, Andrew P

2017-02-01

Linear mixed models are increasingly used for the analysis of genome-wide association studies (GWAS) of binary phenotypes because they can efficiently and robustly account for population stratification and relatedness through inclusion of random effects for a genetic relationship matrix. However, the utility of linear (mixed) models in the context of meta-analysis of GWAS of binary phenotypes has not been previously explored. In this investigation, we present simulations to compare the performance of linear and logistic regression models under alternative weighting schemes in a fixed-effects meta-analysis framework, considering designs that incorporate variable case-control imbalance, confounding factors and population stratification. Our results demonstrate that linear models can be used for meta-analysis of GWAS of binary phenotypes, without loss of power, even in the presence of extreme case-control imbalance, provided that one of the following schemes is used: (i) effective sample size weighting of Z-scores or (ii) inverse-variance weighting of allelic effect sizes after conversion onto the log-odds scale. Our conclusions thus provide essential recommendations for the development of robust protocols for meta-analysis of binary phenotypes with linear models.

Association of daily asthma emergency department visits and hospital admissions with ambient air pollutants among the pediatric Medicaid population in Detroit: time-series and time-stratified case-crossover analyses with threshold effects.

PubMed

Li, Shi; Batterman, Stuart; Wasilevich, Elizabeth; Wahl, Robert; Wirth, Julie; Su, Feng-Chiao; Mukherjee, Bhramar

2011-11-01

Asthma morbidity has been associated with ambient air pollutants in time-series and case-crossover studies. In such study designs, threshold effects of air pollutants on asthma outcomes have been relatively unexplored, which are of potential interest for exploring concentration-response relationships. This study analyzes daily data on the asthma morbidity experienced by the pediatric Medicaid population (ages 2-18 years) of Detroit, Michigan and concentrations of pollutants fine particles (PM2.5), CO, NO2 and SO2 for the 2004-2006 period, using both time-series and case-crossover designs. We use a simple, testable and readily implementable profile likelihood-based approach to estimate threshold parameters in both designs. Evidence of significant increases in daily acute asthma events was found for SO2 and PM2.5, and a significant threshold effect was estimated for PM2.5 at 13 and 11 μg m(-3) using generalized additive models and conditional logistic regression models, respectively. Stronger effect sizes above the threshold were typically noted compared to standard linear relationship, e.g., in the time series analysis, an interquartile range increase (9.2 μg m(-3)) in PM2.5 (5-day-moving average) had a risk ratio of 1.030 (95% CI: 1.001, 1.061) in the generalized additive models, and 1.066 (95% CI: 1.031, 1.102) in the threshold generalized additive models. The corresponding estimates for the case-crossover design were 1.039 (95% CI: 1.013, 1.066) in the conditional logistic regression, and 1.054 (95% CI: 1.023, 1.086) in the threshold conditional logistic regression. This study indicates that the associations of SO2 and PM2.5 concentrations with asthma emergency department visits and hospitalizations, as well as the estimated PM2.5 threshold were fairly consistent across time-series and case-crossover analyses, and suggests that effect estimates based on linear models (without thresholds) may underestimate the true risk. Copyright © 2011 Elsevier Inc. All rights reserved.

Abdominal girth and vertebral column length can adjust spinal anesthesia for lower limb surgery, a prospective, observational study.

PubMed

Zhou, Qing-he; Zhu, Bo; Wei, Chang-na; Yan, Min

2016-03-24

Studies have shown that abdominal girth and vertebral column length have high predictive value for spinal spread after administering a dose of plain bupivacaine. we designed a study to identify the specific correlations between abdominal girth, vertebral column length and a 0.5% dosage of plain bupivacaine, which should provide a minimum upper block level (T12) and a suitable upper block level (T10) for lower limb surgeries. A suitable dose of 0.5% plain bupivacaine was administered intrathecally between the L3 and L4 vertebrae for lower limb surgeries. If the upper cephalad spread of the patient by loss of pinprick discrimination was T12 or T10, the patient was enrolled in this study. Five patient variables and intrathecal plain bupivacaine dose were recorded. Linear regression and multiple regression analyses were performed. Totals of 111 patients and 121 patients who lost pinprick discrimination at T12 and T10, respectively, were analyzed in this study. Linear regression analysis showed that only abdominal girth and plain bupivacaine dose were strongly correlated (r =-0.827 for T12, r = -0.806 for T10; both p < 0.0001). Multiple linear regression analysis showed that both abdominal girth and vertebral column length were the key determinants of plain bupivacaine dose (both p < 0.0001). R(2) was 0.874 and 0.860 for the loss of pinprick discrimination at T12 and T10, respectively. Our data indicated that vertebral column length and abdominal girth were strongly correlated with the dosage of intrathecal plain bupivacaine for the loss of pinprick discrimination at T12 and T10. The two regression equations were YT12 = 3.547 + 0.045X1-0.044X2 and YT10 = 3.848 + 0.047X1- 0.046X2 (Y, 0.5% plain bupivacaine volume; X1, vertebral column length;and X 2, abdominal girth), which can accurately predict the minimum and suitable intrathecal bupivacaine dose for lower limb surgery to a great extent, separately.

Spectral-Spatial Shared Linear Regression for Hyperspectral Image Classification.

PubMed

Haoliang Yuan; Yuan Yan Tang

2017-04-01

Classification of the pixels in hyperspectral image (HSI) is an important task and has been popularly applied in many practical applications. Its major challenge is the high-dimensional small-sized problem. To deal with this problem, lots of subspace learning (SL) methods are developed to reduce the dimension of the pixels while preserving the important discriminant information. Motivated by ridge linear regression (RLR) framework for SL, we propose a spectral-spatial shared linear regression method (SSSLR) for extracting the feature representation. Comparing with RLR, our proposed SSSLR has the following two advantages. First, we utilize a convex set to explore the spatial structure for computing the linear projection matrix. Second, we utilize a shared structure learning model, which is formed by original data space and a hidden feature space, to learn a more discriminant linear projection matrix for classification. To optimize our proposed method, an efficient iterative algorithm is proposed. Experimental results on two popular HSI data sets, i.e., Indian Pines and Salinas demonstrate that our proposed methods outperform many SL methods.

Lateral-Directional Parameter Estimation on the X-48B Aircraft Using an Abstracted, Multi-Objective Effector Model

NASA Technical Reports Server (NTRS)

Ratnayake, Nalin A.; Waggoner, Erin R.; Taylor, Brian R.

2011-01-01

The problem of parameter estimation on hybrid-wing-body aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aerodynamic control effectors that act in coplanar motion. This adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of flight and simulation data must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, time-decorrelation techniques are applied to a model structure selected through stepwise regression for simulated and flight-generated lateral-directional parameter estimation data. A virtual effector model that uses mathematical abstractions to describe the multi-axis effects of clamshell surfaces is developed and applied. Comparisons are made between time history reconstructions and observed data in order to assess the accuracy of the regression model. The Cram r-Rao lower bounds of the estimated parameters are used to assess the uncertainty of the regression model relative to alternative models. Stepwise regression was found to be a useful technique for lateral-directional model design for hybrid-wing-body aircraft, as suggested by available flight data. Based on the results of this study, linear regression parameter estimation methods using abstracted effectors are expected to perform well for hybrid-wing-body aircraft properly equipped for the task.

Advanced Statistical Analyses to Reduce Inconsistency of Bond Strength Data.

PubMed

Minamino, T; Mine, A; Shintani, A; Higashi, M; Kawaguchi-Uemura, A; Kabetani, T; Hagino, R; Imai, D; Tajiri, Y; Matsumoto, M; Yatani, H

2017-11-01

This study was designed to clarify the interrelationship of factors that affect the value of microtensile bond strength (µTBS), focusing on nondestructive testing by which information of the specimens can be stored and quantified. µTBS test specimens were prepared from 10 noncarious human molars. Six factors of µTBS test specimens were evaluated: presence of voids at the interface, X-ray absorption coefficient of resin, X-ray absorption coefficient of dentin, length of dentin part, size of adhesion area, and individual differences of teeth. All specimens were observed nondestructively by optical coherence tomography and micro-computed tomography before µTBS testing. After µTBS testing, the effect of these factors on µTBS data was analyzed by the general linear model, linear mixed effects regression model, and nonlinear regression model with 95% confidence intervals. By the general linear model, a significant difference in individual differences of teeth was observed ( P < 0.001). A significantly positive correlation was shown between µTBS and length of dentin part ( P < 0.001); however, there was no significant nonlinearity ( P = 0.157). Moreover, a significantly negative correlation was observed between µTBS and size of adhesion area ( P = 0.001), with significant nonlinearity ( P = 0.014). No correlation was observed between µTBS and X-ray absorption coefficient of resin ( P = 0.147), and there was no significant nonlinearity ( P = 0.089). Additionally, a significantly positive correlation was observed between µTBS and X-ray absorption coefficient of dentin ( P = 0.022), with significant nonlinearity ( P = 0.036). A significant difference was also observed between the presence and absence of voids by linear mixed effects regression analysis. Our results showed correlations between various parameters of tooth specimens and µTBS data. To evaluate the performance of the adhesive more precisely, the effect of tooth variability and a method to reduce variation in bond strength values should also be considered.

Simple linear and multivariate regression models.

PubMed

Rodríguez del Águila, M M; Benítez-Parejo, N

2011-01-01

In biomedical research it is common to find problems in which we wish to relate a response variable to one or more variables capable of describing the behaviour of the former variable by means of mathematical models. Regression techniques are used to this effect, in which an equation is determined relating the two variables. While such equations can have different forms, linear equations are the most widely used form and are easy to interpret. The present article describes simple and multiple linear regression models, how they are calculated, and how their applicability assumptions are checked. Illustrative examples are provided, based on the use of the freely accessible R program. Copyright © 2011 SEICAP. Published by Elsevier Espana. All rights reserved.

Optimization of isotherm models for pesticide sorption on biopolymer-nanoclay composite by error analysis.

PubMed

Narayanan, Neethu; Gupta, Suman; Gajbhiye, V T; Manjaiah, K M

2017-04-01

A carboxy methyl cellulose-nano organoclay (nano montmorillonite modified with 35-45 wt % dimethyl dialkyl (C 14 -C 18 ) amine (DMDA)) composite was prepared by solution intercalation method. The prepared composite was characterized by infrared spectroscopy (FTIR), X-Ray diffraction spectroscopy (XRD) and scanning electron microscopy (SEM). The composite was utilized for its pesticide sorption efficiency for atrazine, imidacloprid and thiamethoxam. The sorption data was fitted into Langmuir and Freundlich isotherms using linear and non linear methods. The linear regression method suggested best fitting of sorption data into Type II Langmuir and Freundlich isotherms. In order to avoid the bias resulting from linearization, seven different error parameters were also analyzed by non linear regression method. The non linear error analysis suggested that the sorption data fitted well into Langmuir model rather than in Freundlich model. The maximum sorption capacity, Q 0 (μg/g) was given by imidacloprid (2000) followed by thiamethoxam (1667) and atrazine (1429). The study suggests that the degree of determination of linear regression alone cannot be used for comparing the best fitting of Langmuir and Freundlich models and non-linear error analysis needs to be done to avoid inaccurate results. Copyright © 2017 Elsevier Ltd. All rights reserved.

London Measure of Unplanned Pregnancy: guidance for its use as an outcome measure

PubMed Central

Hall, Jennifer A; Barrett, Geraldine; Copas, Andrew; Stephenson, Judith

2017-01-01

Background The London Measure of Unplanned Pregnancy (LMUP) is a psychometrically validated measure of the degree of intention of a current or recent pregnancy. The LMUP is increasingly being used worldwide, and can be used to evaluate family planning or preconception care programs. However, beyond recommending the use of the full LMUP scale, there is no published guidance on how to use the LMUP as an outcome measure. Ordinal logistic regression has been recommended informally, but studies published to date have all used binary logistic regression and dichotomized the scale at different cut points. There is thus a need for evidence-based guidance to provide a standardized methodology for multivariate analysis and to enable comparison of results. This paper makes recommendations for the regression method for analysis of the LMUP as an outcome measure. Materials and methods Data collected from 4,244 pregnant women in Malawi were used to compare five regression methods: linear, logistic with two cut points, and ordinal logistic with either the full or grouped LMUP score. The recommendations were then tested on the original UK LMUP data. Results There were small but no important differences in the findings across the regression models. Logistic regression resulted in the largest loss of information, and assumptions were violated for the linear and ordinal logistic regression. Consequently, robust standard errors were used for linear regression and a partial proportional odds ordinal logistic regression model attempted. The latter could only be fitted for grouped LMUP score. Conclusion We recommend the linear regression model with robust standard errors to make full use of the LMUP score when analyzed as an outcome measure. Ordinal logistic regression could be considered, but a partial proportional odds model with grouped LMUP score may be required. Logistic regression is the least-favored option, due to the loss of information. For logistic regression, the cut point for un/planned pregnancy should be between nine and ten. These recommendations will standardize the analysis of LMUP data and enhance comparability of results across studies. PMID:28435343

Using Parametric Cost Models to Estimate Engineering and Installation Costs of Selected Electronic Communications Systems

DTIC Science & Technology

1994-09-01

Institute of Technology, Wright- Patterson AFB OH, January 1994. 4. Neter, John and others. Applied Linear Regression Models. Boston: Irwin, 1989. 5...Technology, Wright-Patterson AFB OH 5 April 1994. 29. Neter, John and others. Applied Linear Regression Models. Boston: Irwin, 1989. 30. Office of

An Evaluation of the Automated Cost Estimating Integrated Tools (ACEIT) System

DTIC Science & Technology

1989-09-01

residual and it is described as the residual divided by its standard deviation (13:App A,17). Neter, Wasserman, and Kutner, in Applied Linear Regression Models...others. Applied Linear Regression Models. Homewood IL: Irwin, 1983. 19. Raduchel, William J. "A Professional’s Perspective on User-Friendliness," Byte

A Simple and Convenient Method of Multiple Linear Regression to Calculate Iodine Molecular Constants

ERIC Educational Resources Information Center

Cooper, Paul D.

2010-01-01

A new procedure using a student-friendly least-squares multiple linear-regression technique utilizing a function within Microsoft Excel is described that enables students to calculate molecular constants from the vibronic spectrum of iodine. This method is advantageous pedagogically as it calculates molecular constants for ground and excited…

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…

Fitting program for linear regressions according to Mahon (1996)

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

Trappitsch, Reto G.

2018-01-09

This program takes the users' Input data and fits a linear regression to it using the prescription presented by Mahon (1996). Compared to the commonly used York fit, this method has the correct prescription for measurement error propagation. This software should facilitate the proper fitting of measurements with a simple Interface.

How Robust Is Linear Regression with Dummy Variables?

ERIC Educational Resources Information Center

Blankmeyer, Eric

2006-01-01

Researchers in education and the social sciences make extensive use of linear regression models in which the dependent variable is continuous-valued while the explanatory variables are a combination of continuous-valued regressors and dummy variables. The dummies partition the sample into groups, some of which may contain only a few observations.…

Revisiting the Scale-Invariant, Two-Dimensional Linear Regression Method

ERIC Educational Resources Information Center

Patzer, A. Beate C.; Bauer, Hans; Chang, Christian; Bolte, Jan; Su¨lzle, Detlev

2018-01-01

The scale-invariant way to analyze two-dimensional experimental and theoretical data with statistical errors in both the independent and dependent variables is revisited by using what we call the triangular linear regression method. This is compared to the standard least-squares fit approach by applying it to typical simple sets of example data…

An Introduction to Graphical and Mathematical Methods for Detecting Heteroscedasticity in Linear Regression.

ERIC Educational Resources Information Center

Thompson, Russel L.

Homoscedasticity is an important assumption of linear regression. This paper explains what it is and why it is important to the researcher. Graphical and mathematical methods for testing the homoscedasticity assumption are demonstrated. Sources of homoscedasticity and types of homoscedasticity are discussed, and methods for correction are…

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

Common pitfalls in statistical analysis: Linear regression analysis

PubMed Central

Aggarwal, Rakesh; Ranganathan, Priya

2017-01-01

In a previous article in this series, we explained correlation analysis which describes the strength of relationship between two continuous variables. In this article, we deal with linear regression analysis which predicts the value of one continuous variable from another. We also discuss the assumptions and pitfalls associated with this analysis. PMID:28447022

Ranking of factors determining potassium mass balance in bicarbonate haemodialysis.

PubMed

Basile, Carlo; Libutti, Pasquale; Lisi, Piero; Teutonico, Annalisa; Vernaglione, Luigi; Casucci, Francesco; Lomonte, Carlo

2015-03-01

One of the most important pathogenetic factors involved in the onset of intradialysis arrhytmias is the alteration in electrolyte concentration, particularly potassium (K(+)). Two studies were performed: Study A was designed to investigate above all the isolated effect of the factor time t on intradialysis K(+) mass balance (K(+)MB): 11 stable prevalent Caucasian anuric patients underwent one standard (∼4 h) and one long-hour (∼8 h) bicarbonate haemodialysis (HD) session. The latter were pair-matched as far as the dialysate and blood volume processed (90 L) and volume of ultrafiltration are concerned. Study B was designed to identify and rank the other factors determining intradialysis K(+)MB: 63 stable prevalent Caucasian anuric patients underwent one 4-h standard bicarbonate HD session. Dialysate K(+) concentration was 2.0 mmol/L in both studies. Blood samples were obtained from the inlet blood tubing immediately before the onset of dialysis and at t60, t120, t180 min and at end of the 4- and 8-h sessions for the measurement of plasma K(+), blood bicarbonates and blood pH. Additional blood samples were obtained at t360 min for the 8 h sessions. Direct dialysate quantification was utilized for K(+)MBs. Direct potentiometry with an ion-selective electrode was used for K(+) measurements. Study A: mean K(+)MBs were significantly higher in the 8-h sessions (4 h: -88.4 ± 23.2 SD mmol versus 8 h: -101.9 ± 32.2 mmol; P = 0.02). Bivariate linear regression analyses showed that only mean plasma K(+), area under the curve (AUC) of the hourly inlet dialyser diffusion concentration gradient of K(+) (hcgAUCK(+)) and AUC of blood bicarbonates and mean blood bicarbonates were significantly related to K(+)MB in both 4- and 8-h sessions. A multiple linear regression output with K(+)MB as dependent variable showed that only mean plasma K(+), hcgAUCK(+) and duration of HD sessions per se remained statistically significant. Study B: mean K(+)MBs were -86.7 ± 22.6 mmol. Bivariate linear regression analyses showed that only mean plasma K(+), hcgAUCK(+) and mean blood bicarbonates were significantly related to K(+)MB. Again, only mean plasma K(+) and hcgAUCK(+) predicted K(+)MB at the multiple linear regression analysis. Our studies enabled to establish the ranking of factors determining intradialysis K(+)MB: plasma K(+) → dialysate K(+) gradient is the main determinant; acid-base balance plays a much less important role. The duration of HD session per se is an independent determinant of K(+)MB. © The Author 2014. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting

NASA Astrophysics Data System (ADS)

Wu, Cheng; Zhen Yu, Jian

2018-03-01

Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.

A novel simple QSAR model for the prediction of anti-HIV activity using multiple linear regression analysis.

PubMed

Afantitis, Antreas; Melagraki, Georgia; Sarimveis, Haralambos; Koutentis, Panayiotis A; Markopoulos, John; Igglessi-Markopoulou, Olga

2006-08-01

A quantitative-structure activity relationship was obtained by applying Multiple Linear Regression Analysis to a series of 80 1-[2-hydroxyethoxy-methyl]-6-(phenylthio) thymine (HEPT) derivatives with significant anti-HIV activity. For the selection of the best among 37 different descriptors, the Elimination Selection Stepwise Regression Method (ES-SWR) was utilized. The resulting QSAR model (R (2) (CV) = 0.8160; S (PRESS) = 0.5680) proved to be very accurate both in training and predictive stages.

Wavelet regression model in forecasting crude oil price

NASA Astrophysics Data System (ADS)

Hamid, Mohd Helmie; Shabri, Ani

2017-05-01

This study presents the performance of wavelet multiple linear regression (WMLR) technique in daily crude oil forecasting. WMLR model was developed by integrating the discrete wavelet transform (DWT) and multiple linear regression (MLR) model. The original time series was decomposed to sub-time series with different scales by wavelet theory. Correlation analysis was conducted to assist in the selection of optimal decomposed components as inputs for the WMLR model. The daily WTI crude oil price series has been used in this study to test the prediction capability of the proposed model. The forecasting performance of WMLR model were also compared with regular multiple linear regression (MLR), Autoregressive Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) using root mean square errors (RMSE) and mean absolute errors (MAE). Based on the experimental results, it appears that the WMLR model performs better than the other forecasting technique tested in this study.

Advances in simultaneous atmospheric profile and cloud parameter regression based retrieval from high-spectral resolution radiance measurements

NASA Astrophysics Data System (ADS)

Weisz, Elisabeth; Smith, William L.; Smith, Nadia

2013-06-01

The dual-regression (DR) method retrieves information about the Earth surface and vertical atmospheric conditions from measurements made by any high-spectral resolution infrared sounder in space. The retrieved information includes temperature and atmospheric gases (such as water vapor, ozone, and carbon species) as well as surface and cloud top parameters. The algorithm was designed to produce a high-quality product with low latency and has been demonstrated to yield accurate results in real-time environments. The speed of the retrieval is achieved through linear regression, while accuracy is achieved through a series of classification schemes and decision-making steps. These steps are necessary to account for the nonlinearity of hyperspectral retrievals. In this work, we detail the key steps that have been developed in the DR method to advance accuracy in the retrieval of nonlinear parameters, specifically cloud top pressure. The steps and their impact on retrieval results are discussed in-depth and illustrated through relevant case studies. In addition to discussing and demonstrating advances made in addressing nonlinearity in a linear geophysical retrieval method, advances toward multi-instrument geophysical analysis by applying the DR to three different operational sounders in polar orbit are also noted. For any area on the globe, the DR method achieves consistent accuracy and precision, making it potentially very valuable to both the meteorological and environmental user communities.

Cellulose microfibril orientation of Picea abies and its variability at the micron-level determined by Raman imaging

PubMed Central

Gierlinger, Notburga; Luss, Saskia; König, Christian; Konnerth, Johannes; Eder, Michaela; Fratzl, Peter

2010-01-01

The functional characteristics of plant cell walls depend on the composition of the cell wall polymers, as well as on their highly ordered architecture at scales from a few nanometres to several microns. Raman spectra of wood acquired with linear polarized laser light include information about polymer composition as well as the alignment of cellulose microfibrils with respect to the fibre axis (microfibril angle). By changing the laser polarization direction in 3° steps, the dependency between cellulose and laser orientation direction was investigated. Orientation-dependent changes of band height ratios and spectra were described by quadratic linear regression and partial least square regressions, respectively. Using the models and regressions with high coefficients of determination (R2 > 0.99) microfibril orientation was predicted in the S1 and S2 layers distinguished by the Raman imaging approach in cross-sections of spruce normal, opposite, and compression wood. The determined microfibril angle (MFA) in the different S2 layers ranged from 0° to 49.9° and was in coincidence with X-ray diffraction determination. With the prerequisite of geometric sample and laser alignment, exact MFA prediction can complete the picture of the chemical cell wall design gained by the Raman imaging approach at the micron level in all plant tissues. PMID:20007198

Prevalence and correlates of cognitive impairment in kidney transplant recipients.

PubMed

Gupta, Aditi; Mahnken, Jonathan D; Johnson, David K; Thomas, Tashra S; Subramaniam, Dipti; Polshak, Tyler; Gani, Imran; John Chen, G; Burns, Jeffrey M; Sarnak, Mark J

2017-05-12

There is a high prevalence of cognitive impairment in dialysis patients. The prevalence of cognitive impairment after kidney transplantation is unknown. Study Design: Cross-sectional study. Single center study of prevalent kidney transplant recipients from a transplant clinic in a large academic center. Assessment of cognition using the Montreal Cognitive Assessment (MoCA). Demographic and clinical variables associated with cognitive impairment were also examined. Outcomes and Measurements: a) Prevalence of cognitive impairment defined by a MoCA score of <26. b) Multivariable linear and logistic regression to examine the association of demographic and clinical factors with cognitive impairment. Data from 226 patients were analyzed. Mean (SD) age was 54 (13.4) years, 73% were white, 60% were male, 37% had diabetes, 58% had an education level of college or above, and the mean (SD) time since kidney transplant was 3.4 (4.1) years. The prevalence of cognitive impairment was 58.0%. Multivariable linear regression demonstrated that older age, male gender and absence of diabetes were associated with lower MoCA scores (p < 0.01 for all). Estimated glomerular filtration rate (eGFR) was not associated with level of cognition. The logistic regression analysis confirmed the association of older age with cognitive impairment. Cognitive impairment is common in prevalent kidney transplant recipients, at a younger age compared to general population, and is associated with certain demographic variables, but not level of eGFR.

Order-constrained linear optimization.

PubMed

Tidwell, Joe W; Dougherty, Michael R; Chrabaszcz, Jeffrey S; Thomas, Rick P

2017-11-01

Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties. In this paper, we develop an order-constrained linear least-squares (OCLO) optimization algorithm that maximizes the linear least-squares fit to the data conditional on maximizing the ordinal fit based on Kendall's τ. The algorithm builds on the maximum rank correlation estimator (Han, 1987, Journal of Econometrics, 35, 303) and the general monotone model (Dougherty & Thomas, 2012, Psychological Review, 119, 321). Analyses of simulated data indicate that when modelling data that adhere to the assumptions of ordinary least squares, OCLO shows minimal bias, little increase in variance, and almost no loss in out-of-sample predictive accuracy. In contrast, under conditions in which data include a small number of extreme scores (fat-tailed distributions), OCLO shows less bias and variance, and substantially better out-of-sample predictive accuracy, even when the outliers are removed. We show that the advantages of OCLO over ordinary least squares in predicting new observations hold across a variety of scenarios in which researchers must decide to retain or eliminate extreme scores when fitting data. © 2017 The British Psychological Society.

Job stress models, depressive disorders and work performance of engineers in microelectronics industry.

PubMed

Chen, Sung-Wei; Wang, Po-Chuan; Hsin, Ping-Lung; Oates, Anthony; Sun, I-Wen; Liu, Shen-Ing

2011-01-01

Microelectronic engineers are considered valuable human capital contributing significantly toward economic development, but they may encounter stressful work conditions in the context of a globalized industry. The study aims at identifying risk factors of depressive disorders primarily based on job stress models, the Demand-Control-Support and Effort-Reward Imbalance models, and at evaluating whether depressive disorders impair work performance in microelectronics engineers in Taiwan. The case-control study was conducted among 678 microelectronics engineers, 452 controls and 226 cases with depressive disorders which were defined by a score 17 or more on the Beck Depression Inventory and a psychiatrist's diagnosis. The self-administered questionnaires included the Job Content Questionnaire, Effort-Reward Imbalance Questionnaire, demography, psychosocial factors, health behaviors and work performance. Hierarchical logistic regression was applied to identify risk factors of depressive disorders. Multivariate linear regressions were used to determine factors affecting work performance. By hierarchical logistic regression, risk factors of depressive disorders are high demands, low work social support, high effort/reward ratio and low frequency of physical exercise. Combining the two job stress models may have better predictive power for depressive disorders than adopting either model alone. Three multivariate linear regressions provide similar results indicating that depressive disorders are associated with impaired work performance in terms of absence, role limitation and social functioning limitation. The results may provide insight into the applicability of job stress models in a globalized high-tech industry considerably focused in non-Western countries, and the design of workplace preventive strategies for depressive disorders in Asian electronics engineering population.

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.

A field trial of ethyl hexanediol against Aedes dorsalis in Sonoma County, California.

PubMed

Rutledge, L C; Hooper, R L; Wirtz, R A; Gupta, R K

1989-09-01

The repellent ethyl hexanediol (2-ethyl-1,3-hexanediol) was tested against the mosquito Aedes dorsalis in a coastal salt marsh in California. The experimental design incorporated a linear regression model, sequential treatments and a proportional end point (95%) for protection time. The protection time of 0.10 mg/cm2 ethyl hexanediol was estimated at 0.8 h. This time is shorter than that obtained previously for deet (N,N-diethyl-3-methylbenzamide) against Ae. dorsalis (4.4 h).

Multilevel Vehicle Design: Fuel Economy, Mobility and Safety Considerations, Part B. Ground Vehicle Weight and Occupant Safety Under Blast Loading

DTIC Science & Technology

2010-05-11

UNCLASSIFIED 11 Occupant Model Inputs: Blast Pulse (apeak) Seat Cushion Foam Stiffness (sc) Seat EA System Stiffness (sEA) Outputs: Upper Neck Axial Force...Floor Pad Surrogate model from linear regression on 300 data points: Inputs: Blast Pulse (apeak) Seat Cushion Foam Stiffness (sc) Seat EA System...B Ground Vehicle Weight and Occupant Safety Under Blast Loading Steven Hoffenson, presenter (U of M) Panos Papalambros, PI (U of M) Michael

Post-processing through linear regression

NASA Astrophysics Data System (ADS)

van Schaeybroeck, B.; Vannitsem, S.

2011-03-01

Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred.

The Relationship between Religious Coping and Self-Care Behaviors in Iranian Medical Students.

PubMed

Sharif Nia, Hamid; Pahlevan Sharif, Saeed; Goudarzian, Amir Hossein; Allen, Kelly A; Jamali, Saman; Heydari Gorji, Mohammad Ali

2017-12-01

In recent years, researchers have identified that coping strategies are an important contributor to an individual's life satisfaction and ability to manage stress. The positive relationship between religious copings, specifically, with physical and mental health has also been identified in some studies. Spirituality and religion have been discussed rigorously in research, but very few studies exist on religious coping. The aim of this study was to determine the relationship between religious coping methods (i.e., positive and negative religious coping) and self-care behaviors in Iranian medical students. This study used a cross-sectional design of 335 randomly selected students from Mazandaran University of Medical Sciences, Iran. A data collection tool comprised of the standard questionnaire of religious coping methods and questionnaire of self-care behaviors assessment was utilized. Data were analyzed using a two-sample t test assuming equal variances. Adjusted linear regression was used to evaluate the independent association of religious copings with self-care. Adjusted linear regression model indicated an independent significant association between positive (b = 4.616, 95% CI 4.234-4.999) and negative (b = -3.726, 95% CI -4.311 to -3.141) religious coping with self-care behaviors. Findings showed a linear relationship between religious coping and self-care behaviors. Further research with larger sample sizes in diverse populations is recommended.

Structure-function relationships using spectral-domain optical coherence tomography: comparison with scanning laser polarimetry.

PubMed

Aptel, Florent; Sayous, Romain; Fortoul, Vincent; Beccat, Sylvain; Denis, Philippe

2010-12-01

To evaluate and compare the regional relationships between visual field sensitivity and retinal nerve fiber layer (RNFL) thickness as measured by spectral-domain optical coherence tomography (OCT) and scanning laser polarimetry. Prospective cross-sectional study. One hundred and twenty eyes of 120 patients (40 with healthy eyes, 40 with suspected glaucoma, and 40 with glaucoma) were tested on Cirrus-OCT, GDx VCC, and standard automated perimetry. Raw data on RNFL thickness were extracted for 256 peripapillary sectors of 1.40625 degrees each for the OCT measurement ellipse and 64 peripapillary sectors of 5.625 degrees each for the GDx VCC measurement ellipse. Correlations between peripapillary RNFL thickness in 6 sectors and visual field sensitivity in the 6 corresponding areas were evaluated using linear and logarithmic regression analysis. Receiver operating curve areas were calculated for each instrument. With spectral-domain OCT, the correlations (r(2)) between RNFL thickness and visual field sensitivity ranged from 0.082 (nasal RNFL and corresponding visual field area, linear regression) to 0.726 (supratemporal RNFL and corresponding visual field area, logarithmic regression). By comparison, with GDx-VCC, the correlations ranged from 0.062 (temporal RNFL and corresponding visual field area, linear regression) to 0.362 (supratemporal RNFL and corresponding visual field area, logarithmic regression). In pairwise comparisons, these structure-function correlations were generally stronger with spectral-domain OCT than with GDx VCC and with logarithmic regression than with linear regression. The largest areas under the receiver operating curve were seen for OCT superior thickness (0.963 ± 0.022; P < .001) in eyes with glaucoma and for OCT average thickness (0.888 ± 0.072; P < .001) in eyes with suspected glaucoma. The structure-function relationship was significantly stronger with spectral-domain OCT than with scanning laser polarimetry, and was better expressed logarithmically than linearly. Measurements with these 2 instruments should not be considered to be interchangeable. Copyright © 2010 Elsevier Inc. All rights reserved.

A Simulation-Based Comparison of Several Stochastic Linear Regression Methods in the Presence of Outliers.

ERIC Educational Resources Information Center

Rule, David L.

Several regression methods were examined within the framework of weighted structural regression (WSR), comparing their regression weight stability and score estimation accuracy in the presence of outlier contamination. The methods compared are: (1) ordinary least squares; (2) WSR ridge regression; (3) minimum risk regression; (4) minimum risk 2;…

Unit Cohesion and the Surface Navy: Does Cohesion Affect Performance

DTIC Science & Technology

1989-12-01

v. 68, 1968. Neter, J., Wasserman, W., and Kutner, M. H., Applied Linear Regression Models, 2d ed., Boston, MA: Irwin, 1989. Rand Corporation R-2607...Neter, J., Wasserman, W., and Kutner, M. H., Applied Linear Regression Models, 2d ed., Boston, MA: Irwin, 1989. SAS User’s Guide: Basics, Version 5 ed

Comparison of Selection Procedures and Validation of Criterion Used in Selection of Significant Control Variates of a Simulation Model

DTIC Science & Technology

1990-03-01

and M.H. Knuter. Applied Linear Regression Models. Homewood IL: Richard D. Erwin Inc., 1983. Pritsker, A. Alan B. Introduction to Simulation and SLAM...Control Variates in Simulation," European Journal of Operational Research, 42: (1989). Neter, J., W. Wasserman, and M.H. Xnuter. Applied Linear Regression Models

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…

Calibrated Peer Review for Interpreting Linear Regression Parameters: Results from a Graduate Course

ERIC Educational Resources Information Center

Enders, Felicity B.; Jenkins, Sarah; Hoverman, Verna

2010-01-01

Biostatistics is traditionally a difficult subject for students to learn. While the mathematical aspects are challenging, it can also be demanding for students to learn the exact language to use to correctly interpret statistical results. In particular, correctly interpreting the parameters from linear regression is both a vital tool and a…

What Is Wrong with ANOVA and Multiple Regression? Analyzing Sentence Reading Times with Hierarchical Linear Models

ERIC Educational Resources Information Center

Richter, Tobias

2006-01-01

Most reading time studies using naturalistic texts yield data sets characterized by a multilevel structure: Sentences (sentence level) are nested within persons (person level). In contrast to analysis of variance and multiple regression techniques, hierarchical linear models take the multilevel structure of reading time data into account. They…

Some Applied Research Concerns Using Multiple Linear Regression Analysis.

ERIC Educational Resources Information Center

Newman, Isadore; Fraas, John W.

The intention of this paper is to provide an overall reference on how a researcher can apply multiple linear regression in order to utilize the advantages that it has to offer. The advantages and some concerns expressed about the technique are examined. A number of practical ways by which researchers can deal with such concerns as…

Using Simple Linear Regression to Assess the Success of the Montreal Protocol in Reducing Atmospheric Chlorofluorocarbons

ERIC Educational Resources Information Center

Nelson, Dean

2009-01-01

Following the Guidelines for Assessment and Instruction in Statistics Education (GAISE) recommendation to use real data, an example is presented in which simple linear regression is used to evaluate the effect of the Montreal Protocol on atmospheric concentration of chlorofluorocarbons. This simple set of data, obtained from a public archive, can…

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

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.

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.

Performance and strategy comparisons of human listeners and logistic regression in discriminating underwater targets.

PubMed

Yang, Lixue; Chen, Kean

2015-11-01

To improve the design of underwater target recognition systems based on auditory perception, this study compared human listeners with automatic classifiers. Performances measures and strategies in three discrimination experiments, including discriminations between man-made and natural targets, between ships and submarines, and among three types of ships, were used. In the experiments, the subjects were asked to assign a score to each sound based on how confident they were about the category to which it belonged, and logistic regression, which represents linear discriminative models, also completed three similar tasks by utilizing many auditory features. The results indicated that the performances of logistic regression improved as the ratio between inter- and intra-class differences became larger, whereas the performances of the human subjects were limited by their unfamiliarity with the targets. Logistic regression performed better than the human subjects in all tasks but the discrimination between man-made and natural targets, and the strategies employed by excellent human subjects were similar to that of logistic regression. Logistic regression and several human subjects demonstrated similar performances when discriminating man-made and natural targets, but in this case, their strategies were not similar. An appropriate fusion of their strategies led to further improvement in recognition accuracy.

QSRR modeling for diverse drugs using different feature selection methods coupled with linear and nonlinear regressions.

PubMed

Goodarzi, Mohammad; Jensen, Richard; Vander Heyden, Yvan

2012-12-01

A Quantitative Structure-Retention Relationship (QSRR) is proposed to estimate the chromatographic retention of 83 diverse drugs on a Unisphere poly butadiene (PBD) column, using isocratic elutions at pH 11.7. Previous work has generated QSRR models for them using Classification And Regression Trees (CART). In this work, Ant Colony Optimization is used as a feature selection method to find the best molecular descriptors from a large pool. In addition, several other selection methods have been applied, such as Genetic Algorithms, Stepwise Regression and the Relief method, not only to evaluate Ant Colony Optimization as a feature selection method but also to investigate its ability to find the important descriptors in QSRR. Multiple Linear Regression (MLR) and Support Vector Machines (SVMs) were applied as linear and nonlinear regression methods, respectively, giving excellent correlation between the experimental, i.e. extrapolated to a mobile phase consisting of pure water, and predicted logarithms of the retention factors of the drugs (logk(w)). The overall best model was the SVM one built using descriptors selected by ACO. Copyright © 2012 Elsevier B.V. All rights reserved.

Timeline trend profile and seasonal variations in nicotine present in ambient PM10 samples: A four year investigation from Delhi region, India

NASA Astrophysics Data System (ADS)

Yadav, Shweta; Tandon, Ankit; Attri, Arun K.

2014-12-01

The detection of nicotine, an organic tracer for Environmental Tobacco Smoke (ETS), in the collected PM10 samples from Delhi region's ambient environment, in a appropriately designed investigation was initiated over four years (2006-2009) to: (1) Comprehend seasonal and inter-annual variations in the nicotine present in PM10; (2) Extract regression based linear trend profile manifested by nicotine in PM10; (3) Determine the non-linear trend timeline from the nicotine data, and compare it with the obtained linear trend; (4) Suggest the possible use of the designed experiment and analysis to have a qualitative appraisal of Tobacco Smoking activity in the sampling region. The PM10 samples were collected in a monthly time-series sequence at a known receptor site. Quantitative estimates of nicotine (ng m-3) were made by using a Thermal Desorption Gas Chromatography Mass Spectrometry (TD-GC/MS). The annual average concentrations of nicotine (ng m-3) were 516 ± 302 (2008) > 494 ± 301 (2009) > 438 ± 250 (2007) > 325 ± 149 (2006). The estimated linear trend of 5.4 ng m-3 month-1 corresponded to 16.3% per annum increase in the PM10 associated nicotine. The industrial production of India's tobacco index normalized to Delhi region's consumption, pegged an increase at 10.5% per annum over this period.

Evaluating Differential Effects Using Regression Interactions and Regression Mixture Models

ERIC Educational Resources Information Center

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 article focuses on understanding regression mixture models, which are 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…

SEMIPARAMETRIC QUANTILE REGRESSION WITH HIGH-DIMENSIONAL COVARIATES

PubMed Central

Zhu, Liping; Huang, Mian; Li, Runze

2012-01-01

This paper is concerned with quantile regression for a semiparametric regression model, in which both the conditional mean and conditional variance function of the response given the covariates admit a single-index structure. This semiparametric regression model enables us to reduce the dimension of the covariates and simultaneously retains the flexibility of nonparametric regression. Under mild conditions, we show that the simple linear quantile regression offers a consistent estimate of the index parameter vector. This is a surprising and interesting result because the single-index model is possibly misspecified under the linear quantile regression. With a root-n consistent estimate of the index vector, one may employ a local polynomial regression technique to estimate the conditional quantile function. This procedure is computationally efficient, which is very appealing in high-dimensional data analysis. We show that the resulting estimator of the quantile function performs asymptotically as efficiently as if the true value of the index vector were known. The methodologies are demonstrated through comprehensive simulation studies and an application to a real dataset. PMID:24501536

Predictive and mechanistic multivariate linear regression models for reaction development

PubMed Central

Santiago, Celine B.; Guo, Jing-Yao

2018-01-01

Multivariate Linear Regression (MLR) models utilizing computationally-derived and empirically-derived physical organic molecular descriptors are described in this review. Several reports demonstrating the effectiveness of this methodological approach towards reaction optimization and mechanistic interrogation are discussed. A detailed protocol to access quantitative and predictive MLR models is provided as a guide for model development and parameter analysis. PMID:29719711

Adding a Parameter Increases the Variance of an Estimated Regression Function

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2011-01-01

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

Using nonlinear quantile regression to estimate the self-thinning boundary curve

Treesearch

Quang V. Cao; Thomas J. Dean

2015-01-01

The relationship between tree size (quadratic mean diameter) and tree density (number of trees per unit area) has been a topic of research and discussion for many decades. Starting with Reineke in 1933, the maximum size-density relationship, on a log-log scale, has been assumed to be linear. Several techniques, including linear quantile regression, have been employed...

Simultaneous spectrophotometric determination of salbutamol and bromhexine in tablets.

PubMed

Habib, I H I; Hassouna, M E M; Zaki, G A

2005-03-01

Typical anti-mucolytic drugs called salbutamol hydrochloride and bromhexine sulfate encountered in tablets were determined simultaneously either by using linear regression at zero-crossing wavelengths of the first derivation of UV-spectra or by application of multiple linear partial least squares regression method. The results obtained by the two proposed mathematical methods were compared with those obtained by the HPLC technique.

High-throughput quantitative biochemical characterization of algal biomass by NIR spectroscopy; multiple linear regression and multivariate linear regression analysis.

PubMed

Laurens, L M L; Wolfrum, E J

2013-12-18

One of the challenges associated with microalgal biomass characterization and the comparison of microalgal strains and conversion processes is the rapid determination of the composition of algae. We have developed and applied a high-throughput screening technology based on near-infrared (NIR) spectroscopy for the rapid and accurate determination of algal biomass composition. We show that NIR spectroscopy can accurately predict the full composition using multivariate linear regression analysis of varying lipid, protein, and carbohydrate content of algal biomass samples from three strains. We also demonstrate a high quality of predictions of an independent validation set. A high-throughput 96-well configuration for spectroscopy gives equally good prediction relative to a ring-cup configuration, and thus, spectra can be obtained from as little as 10-20 mg of material. We found that lipids exhibit a dominant, distinct, and unique fingerprint in the NIR spectrum that allows for the use of single and multiple linear regression of respective wavelengths for the prediction of the biomass lipid content. This is not the case for carbohydrate and protein content, and thus, the use of multivariate statistical modeling approaches remains necessary.

Modeling the frequency of opposing left-turn conflicts at signalized intersections using generalized linear regression models.

PubMed

Zhang, Xin; Liu, Pan; Chen, Yuguang; Bai, Lu; Wang, Wei

2014-01-01

The primary objective of this study was to identify whether the frequency of traffic conflicts at signalized intersections can be modeled. The opposing left-turn conflicts were selected for the development of conflict predictive models. Using data collected at 30 approaches at 20 signalized intersections, the underlying distributions of the conflicts under different traffic conditions were examined. Different conflict-predictive models were developed to relate the frequency of opposing left-turn conflicts to various explanatory variables. The models considered include a linear regression model, a negative binomial model, and separate models developed for four traffic scenarios. The prediction performance of different models was compared. The frequency of traffic conflicts follows a negative binominal distribution. The linear regression model is not appropriate for the conflict frequency data. In addition, drivers behaved differently under different traffic conditions. Accordingly, the effects of conflicting traffic volumes on conflict frequency vary across different traffic conditions. The occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The use of conflict predictive models has potential to expand the uses of surrogate safety measures in safety estimation and evaluation.

Standards for Standardized Logistic Regression Coefficients

ERIC Educational Resources Information Center

Menard, Scott

2011-01-01

Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…

Treatment of dyeing wastewater by TiO2/H2O2/UV process: experimental design approach for evaluating total organic carbon (TOC) removal efficiency.

PubMed

Lee, Seung-Mok; Kim, Young-Gyu; Cho, Il-Hyoung

2005-01-01

Optimal operating conditions in order to treat dyeing wastewater were investigated by using the factorial design and responses surface methodology (RSM). The experiment was statistically designed and carried out according to a 22 full factorial design with four factorial points, three center points, and four axial points. Then, the linear and nonlinear regression was applied on the data by using SAS package software. The independent variables were TiO2 dosage, H2O2 concentration and total organic carbon (TOC) removal efficiency of dyeing wastewater was dependent variable. From the factorial design and responses surface methodology (RSM), maximum removal efficiency (85%) of dyeing wastewater was obtained at TiO2 dosage (1.82 gL(-1)), H2O2 concentration (980 mgL(-1)) for oxidation reaction (20 min).

Comparing Machine Learning Classifiers and Linear/Logistic Regression to Explore the Relationship between Hand Dimensions and Demographic Characteristics

PubMed Central

2016-01-01

Understanding the relationship between physiological measurements from human subjects and their demographic data is important within both the biometric and forensic domains. In this paper we explore the relationship between measurements of the human hand and a range of demographic features. We assess the ability of linear regression and machine learning classifiers to predict demographics from hand features, thereby providing evidence on both the strength of relationship and the key features underpinning this relationship. Our results show that we are able to predict sex, height, weight and foot size accurately within various data-range bin sizes, with machine learning classification algorithms out-performing linear regression in most situations. In addition, we identify the features used to provide these relationships applicable across multiple applications. PMID:27806075

Comparing Machine Learning Classifiers and Linear/Logistic Regression to Explore the Relationship between Hand Dimensions and Demographic Characteristics.

PubMed

Miguel-Hurtado, Oscar; Guest, Richard; Stevenage, Sarah V; Neil, Greg J; Black, Sue

2016-01-01

Understanding the relationship between physiological measurements from human subjects and their demographic data is important within both the biometric and forensic domains. In this paper we explore the relationship between measurements of the human hand and a range of demographic features. We assess the ability of linear regression and machine learning classifiers to predict demographics from hand features, thereby providing evidence on both the strength of relationship and the key features underpinning this relationship. Our results show that we are able to predict sex, height, weight and foot size accurately within various data-range bin sizes, with machine learning classification algorithms out-performing linear regression in most situations. In addition, we identify the features used to provide these relationships applicable across multiple applications.

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

PubMed

Kumar, K Vasanth; Porkodi, K; Rocha, F

2008-01-15

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Revisiting the Relationship between Managed Care and Hospital Consolidation

PubMed Central

Town, Robert J; Wholey, Douglas; Feldman, Roger; Burns, Lawton R

2007-01-01

Objective This paper analyzes whether the rise in managed care during the 1990s caused the increase in hospital concentration. Data Sources We assemble data from the American Hospital Association, InterStudy and government censuses from 1990 to 2000. Study Design We employ linear regression analyses on long differenced data to estimate the impact of managed care penetration on hospital consolidation. Instrumental variable analogs of these regressions are also analyzed to control for potential endogeneity. Data Collection All data are from secondary sources merged at the level of the Health Care Services Area. Principle Findings In 1990, the mean population-weighted hospital Herfindahl–Hirschman index (HHI) in a Health Services Area was .19. By 2000, the HHI had risen to .26. Most of this increase in hospital concentration is due to hospital consolidation. Over the same time frame HMO penetration increased three fold. However, our regression analysis strongly implies that the rise of managed care did not cause the hospital consolidation wave. This finding is robust to a number of different specifications. PMID:17355590

Estimate the contribution of incubation parameters influence egg hatchability using multiple linear regression analysis

PubMed Central

Khalil, Mohamed H.; Shebl, Mostafa K.; Kosba, Mohamed A.; El-Sabrout, Karim; Zaki, Nesma

2016-01-01

Aim: This research was conducted to determine the most affecting parameters on hatchability of indigenous and improved local chickens’ eggs. Materials and Methods: Five parameters were studied (fertility, early and late embryonic mortalities, shape index, egg weight, and egg weight loss) on four strains, namely Fayoumi, Alexandria, Matrouh, and Montazah. Multiple linear regression was performed on the studied parameters to determine the most influencing one on hatchability. Results: The results showed significant differences in commercial and scientific hatchability among strains. Alexandria strain has the highest significant commercial hatchability (80.70%). Regarding the studied strains, highly significant differences in hatching chick weight among strains were observed. Using multiple linear regression analysis, fertility made the greatest percent contribution (71.31%) to hatchability, and the lowest percent contributions were made by shape index and egg weight loss. Conclusion: A prediction of hatchability using multiple regression analysis could be a good tool to improve hatchability percentage in chickens. PMID:27651666

Predicting recycling behaviour: Comparison of a linear regression model and a fuzzy logic model.

PubMed

Vesely, Stepan; Klöckner, Christian A; Dohnal, Mirko

2016-03-01

In this paper we demonstrate that fuzzy logic can provide a better tool for predicting recycling behaviour than the customarily used linear regression. To show this, we take a set of empirical data on recycling behaviour (N=664), which we randomly divide into two halves. The first half is used to estimate a linear regression model of recycling behaviour, and to develop a fuzzy logic model of recycling behaviour. As the first comparison, the fit of both models to the data included in estimation of the models (N=332) is evaluated. As the second comparison, predictive accuracy of both models for "new" cases (hold-out data not included in building the models, N=332) is assessed. In both cases, the fuzzy logic model significantly outperforms the regression model in terms of fit. To conclude, when accurate predictions of recycling and possibly other environmental behaviours are needed, fuzzy logic modelling seems to be a promising technique. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Nearest-neighbor thermodynamics of deoxyinosine pairs in DNA duplexes

PubMed Central

Watkins, Norman E.; SantaLucia, John

2005-01-01

Nearest-neighbor thermodynamic parameters of the ‘universal pairing base’ deoxyinosine were determined for the pairs I·C, I·A, I·T, I·G and I·I adjacent to G·C and A·T pairs. Ultraviolet absorbance melting curves were measured and non-linear regression performed on 84 oligonucleotide duplexes with 9 or 12 bp lengths. These data were combined with data for 13 inosine containing duplexes from the literature. Multiple linear regression was used to solve for the 32 nearest-neighbor unknowns. The parameters predict the Tm for all sequences within 1.2°C on average. The general trend in decreasing stability is I·C > I·A > I·T ≈ I· G > I·I. The stability trend for the base pair 5′ of the I·X pair is G·C > C·G > A·T > T·A. The stability trend for the base pair 3′ of I·X is the same. These trends indicate a complex interplay between H-bonding, nearest-neighbor stacking, and mismatch geometry. A survey of 14 tandem inosine pairs and 8 tandem self-complementary inosine pairs is also provided. These results may be used in the design of degenerate PCR primers and for degenerate microarray probes. PMID:16264087

Analysis of Sequence Data Under Multivariate Trait-Dependent Sampling.

PubMed

Tao, Ran; Zeng, Donglin; Franceschini, Nora; North, Kari E; Boerwinkle, Eric; Lin, Dan-Yu

2015-06-01

High-throughput DNA sequencing allows for the genotyping of common and rare variants for genetic association studies. At the present time and for the foreseeable future, it is not economically feasible to sequence all individuals in a large cohort. A cost-effective strategy is to sequence those individuals with extreme values of a quantitative trait. We consider the design under which the sampling depends on multiple quantitative traits. Under such trait-dependent sampling, standard linear regression analysis can result in bias of parameter estimation, inflation of type I error, and loss of power. We construct a likelihood function that properly reflects the sampling mechanism and utilizes all available data. We implement a computationally efficient EM algorithm and establish the theoretical properties of the resulting maximum likelihood estimators. Our methods can be used to perform separate inference on each trait or simultaneous inference on multiple traits. We pay special attention to gene-level association tests for rare variants. We demonstrate the superiority of the proposed methods over standard linear regression through extensive simulation studies. We provide applications to the Cohorts for Heart and Aging Research in Genomic Epidemiology Targeted Sequencing Study and the National Heart, Lung, and Blood Institute Exome Sequencing Project.

An Application to the Prediction of LOD Change Based on General Regression Neural Network

NASA Astrophysics Data System (ADS)

Zhang, X. H.; Wang, Q. J.; Zhu, J. J.; Zhang, H.

2011-07-01

Traditional prediction of the LOD (length of day) change was based on linear models, such as the least square model and the autoregressive technique, etc. Due to the complex non-linear features of the LOD variation, the performances of the linear model predictors are not fully satisfactory. This paper applies a non-linear neural network - general regression neural network (GRNN) model to forecast the LOD change, and the results are analyzed and compared with those obtained with the back propagation neural network and other models. The comparison shows that the performance of the GRNN model in the prediction of the LOD change is efficient and feasible.

Solving a mixture of many random linear equations by tensor decomposition and alternating minimization.

DOT National Transportation Integrated Search

2016-09-01

We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample...

Linear regression techniques for use in the EC tracer method of secondary organic aerosol estimation

NASA Astrophysics Data System (ADS)

Saylor, Rick D.; Edgerton, Eric S.; Hartsell, Benjamin E.

A variety of linear regression techniques and simple slope estimators are evaluated for use in the elemental carbon (EC) tracer method of secondary organic carbon (OC) estimation. Linear regression techniques based on ordinary least squares are not suitable for situations where measurement uncertainties exist in both regressed variables. In the past, regression based on the method of Deming [1943. Statistical Adjustment of Data. Wiley, London] has been the preferred choice for EC tracer method parameter estimation. In agreement with Chu [2005. Stable estimate of primary OC/EC ratios in the EC tracer method. Atmospheric Environment 39, 1383-1392], we find that in the limited case where primary non-combustion OC (OC non-comb) is assumed to be zero, the ratio of averages (ROA) approach provides a stable and reliable estimate of the primary OC-EC ratio, (OC/EC) pri. In contrast with Chu [2005. Stable estimate of primary OC/EC ratios in the EC tracer method. Atmospheric Environment 39, 1383-1392], however, we find that the optimal use of Deming regression (and the more general York et al. [2004. Unified equations for the slope, intercept, and standard errors of the best straight line. American Journal of Physics 72, 367-375] regression) provides excellent results as well. For the more typical case where OC non-comb is allowed to obtain a non-zero value, we find that regression based on the method of York is the preferred choice for EC tracer method parameter estimation. In the York regression technique, detailed information on uncertainties in the measurement of OC and EC is used to improve the linear best fit to the given data. If only limited information is available on the relative uncertainties of OC and EC, then Deming regression should be used. On the other hand, use of ROA in the estimation of secondary OC, and thus the assumption of a zero OC non-comb value, generally leads to an overestimation of the contribution of secondary OC to total measured OC.

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.

Development of non-linear models predicting daily fine particle concentrations using aerosol optical depth retrievals and ground-based measurements at a municipality in the Brazilian Amazon region

NASA Astrophysics Data System (ADS)

Gonçalves, Karen dos Santos; Winkler, Mirko S.; Benchimol-Barbosa, Paulo Roberto; de Hoogh, Kees; Artaxo, Paulo Eduardo; de Souza Hacon, Sandra; Schindler, Christian; Künzli, Nino

2018-07-01

Epidemiological studies generally use particulate matter measurements with diameter less 2.5 μm (PM2.5) from monitoring networks. Satellite aerosol optical depth (AOD) data has considerable potential in predicting PM2.5 concentrations, and thus provides an alternative method for producing knowledge regarding the level of pollution and its health impact in areas where no ground PM2.5 measurements are available. This is the case in the Brazilian Amazon rainforest region where forest fires are frequent sources of high pollution. In this study, we applied a non-linear model for predicting PM2.5 concentration from AOD retrievals using interaction terms between average temperature, relative humidity, sine, cosine of date in a period of 365,25 days and the square of the lagged relative residual. Regression performance statistics were tested comparing the goodness of fit and R2 based on results from linear regression and non-linear regression for six different models. The regression results for non-linear prediction showed the best performance, explaining on average 82% of the daily PM2.5 concentrations when considering the whole period studied. In the context of Amazonia, it was the first study predicting PM2.5 concentrations using the latest high-resolution AOD products also in combination with the testing of a non-linear model performance. Our results permitted a reliable prediction considering the AOD-PM2.5 relationship and set the basis for further investigations on air pollution impacts in the complex context of Brazilian Amazon Region.

Impact of the Japanese 5S management method on patients’ and caretakers’ satisfaction: a quasi-experimental study in Senegal

PubMed Central

Kanamori, Shogo; Castro, Marcia C.; Sow, Seydou; Matsuno, Rui; Cissokho, Alioune; Jimba, Masamine

2016-01-01

Background The 5S method is a lean management tool for workplace organization, with 5S being an abbreviation for five Japanese words that translate to English as Sort, Set in Order, Shine, Standardize, and Sustain. In Senegal, the 5S intervention program was implemented in 10 health centers in two regions between 2011 and 2014. Objective To identify the impact of the 5S intervention program on the satisfaction of clients (patients and caretakers) who visited the health centers. Design A standardized 5S intervention protocol was implemented in the health centers using a quasi-experimental separate pre-post samples design (four intervention and three control health facilities). A questionnaire with 10 five-point Likert items was used to measure client satisfaction. Linear regression analysis was conducted to identify the intervention's effect on the client satisfaction scores, represented by an equally weighted average of the 10 Likert items (Cronbach's alpha=0.83). Additional regression analyses were conducted to identify the intervention's effect on the scores of each Likert item. Results Backward stepwise linear regression (n=1,928) indicated a statistically significant effect of the 5S intervention, represented by an increase of 0.19 points in the client satisfaction scores in the intervention group, 6 to 8 months after the intervention (p=0.014). Additional regression analyses showed significant score increases of 0.44 (p=0.002), 0.14 (p=0.002), 0.06 (p=0.019), and 0.17 (p=0.044) points on four items, which, respectively were healthcare staff members’ communication, explanations about illnesses or cases, and consultation duration, and clients’ overall satisfaction. Conclusions The 5S has the potential to improve client satisfaction at resource-poor health facilities and could therefore be recommended as a strategic option for improving the quality of healthcare service in low- and middle-income countries. To explore more effective intervention modalities, further studies need to address the mechanisms by which 5S leads to attitude changes in healthcare staff. PMID:27900932

Stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure.

PubMed

Senn, Stephen; Graf, Erika; Caputo, Angelika

2007-12-30

Stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure. A more traditional alternative technique is the direct adjustment for confounding in regression models. This paper discusses fundamental differences between the two approaches, with a focus on linear regression and propensity score stratification, and identifies points to be considered for an adequate comparison. The treatment estimators are examined for unbiasedness and efficiency. This is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models. We demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model, even if it is built on coarser covariate strata than the linear model. As a consequence the coarsening property of the propensity score-adjustment for a one-dimensional confounder instead of a high-dimensional covariate-may be viewed as a way to implement a pre-specified, richly parametrized linear model. We conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome. Copyright (c) 2007 John Wiley & Sons, Ltd.

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

Coping Styles in Heart Failure Patients with Depressive Symptoms

PubMed Central

Trivedi, Ranak B.; Blumenthal, James A.; O'Connor, Christopher; Adams, Kirkwood; Hinderliter, Alan; Sueta-Dupree, Carla; Johnson, Kristy; Sherwood, Andrew

2009-01-01

Objective Elevated depressive symptoms have been linked to poorer prognosis in heart failure (HF) patients. Our objective was to identify coping styles associated with depressive symptoms in HF patients. Methods 222 stable HF patients (32.75% female, 45.4% non-Hispanic Black) completed multiple questionnaires. Beck Depression Inventory (BDI) assessed depressive symptoms, Life Orientation Test (LOT-R) assessed optimism, ENRICHD Social Support Inventory (ESSI) and Perceived Social Support Scale (PSSS) assessed social support, and COPE assessed coping styles. Linear regression analyses were employed to assess the association of coping styles with continuous BDI scores. Logistic regression analyses were performed using BDI scores dichotomized into BDI<10 versus BDI≥10, to identify coping styles accompanying clinically significant depressive symptoms. Results In linear regression models, higher BDI scores were associated with lower scores on the acceptance (β=-.14), humor (β=-.15), planning (β=-.15), and emotional support (β=-.14) subscales of the COPE, and higher scores on the behavioral disengagement (β=.41), denial (β=.33), venting (β=.25), and mental disengagement (β=.22) subscales. Higher PSSS and ESSI scores were associated with lower BDI scores (β=-.32 and -.25, respectively). Higher LOT-R scores were associated with higher BDI scores (β=.39, p<.001). In logistical regression models, BDI≥10 was associated with greater likelihood of behavioral disengagement (OR=1.3), denial (OR=1.2), mental disengagement (OR=1.3), venting (OR=1.2), and pessimism (OR=1.2), and lower perceived social support measured by PSSS (OR=.92) and ESSI (OR=.92). Conclusion Depressive symptoms in HF patients are associated with avoidant coping, lower perceived social support, and pessimism. Results raise the possibility that interventions designed to improve coping may reduce depressive symptoms. PMID:19773027

Plant leaf chlorophyll content retrieval based on a field imaging spectroscopy system.

PubMed

Liu, Bo; Yue, Yue-Min; Li, Ru; Shen, Wen-Jing; Wang, Ke-Lin

2014-10-23

A field imaging spectrometer system (FISS; 380-870 nm and 344 bands) was designed for agriculture applications. In this study, FISS was used to gather spectral information from soybean leaves. The chlorophyll content was retrieved using a multiple linear regression (MLR), partial least squares (PLS) regression and support vector machine (SVM) regression. Our objective was to verify the performance of FISS in a quantitative spectral analysis through the estimation of chlorophyll content and to determine a proper quantitative spectral analysis method for processing FISS data. The results revealed that the derivative reflectance was a more sensitive indicator of chlorophyll content and could extract content information more efficiently than the spectral reflectance, which is more significant for FISS data compared to ASD (analytical spectral devices) data, reducing the corresponding RMSE (root mean squared error) by 3.3%-35.6%. Compared with the spectral features, the regression methods had smaller effects on the retrieval accuracy. A multivariate linear model could be the ideal model to retrieve chlorophyll information with a small number of significant wavelengths used. The smallest RMSE of the chlorophyll content retrieved using FISS data was 0.201 mg/g, a relative reduction of more than 30% compared with the RMSE based on a non-imaging ASD spectrometer, which represents a high estimation accuracy compared with the mean chlorophyll content of the sampled leaves (4.05 mg/g). Our study indicates that FISS could obtain both spectral and spatial detailed information of high quality. Its image-spectrum-in-one merit promotes the good performance of FISS in quantitative spectral analyses, and it can potentially be widely used in the agricultural sector.

Plant Leaf Chlorophyll Content Retrieval Based on a Field Imaging Spectroscopy System

PubMed Central

Liu, Bo; Yue, Yue-Min; Li, Ru; Shen, Wen-Jing; Wang, Ke-Lin

2014-01-01

A field imaging spectrometer system (FISS; 380–870 nm and 344 bands) was designed for agriculture applications. In this study, FISS was used to gather spectral information from soybean leaves. The chlorophyll content was retrieved using a multiple linear regression (MLR), partial least squares (PLS) regression and support vector machine (SVM) regression. Our objective was to verify the performance of FISS in a quantitative spectral analysis through the estimation of chlorophyll content and to determine a proper quantitative spectral analysis method for processing FISS data. The results revealed that the derivative reflectance was a more sensitive indicator of chlorophyll content and could extract content information more efficiently than the spectral reflectance, which is more significant for FISS data compared to ASD (analytical spectral devices) data, reducing the corresponding RMSE (root mean squared error) by 3.3%–35.6%. Compared with the spectral features, the regression methods had smaller effects on the retrieval accuracy. A multivariate linear model could be the ideal model to retrieve chlorophyll information with a small number of significant wavelengths used. The smallest RMSE of the chlorophyll content retrieved using FISS data was 0.201 mg/g, a relative reduction of more than 30% compared with the RMSE based on a non-imaging ASD spectrometer, which represents a high estimation accuracy compared with the mean chlorophyll content of the sampled leaves (4.05 mg/g). Our study indicates that FISS could obtain both spectral and spatial detailed information of high quality. Its image-spectrum-in-one merit promotes the good performance of FISS in quantitative spectral analyses, and it can potentially be widely used in the agricultural sector. PMID:25341439

Coping styles in heart failure patients with depressive symptoms.

PubMed

Trivedi, Ranak B; Blumenthal, James A; O'Connor, Christopher; Adams, Kirkwood; Hinderliter, Alan; Dupree, Carla; Johnson, Kristy; Sherwood, Andrew

2009-10-01

Elevated depressive symptoms have been linked to poorer prognosis in heart failure (HF) patients. Our objective was to identify coping styles associated with depressive symptoms in HF patients. A total of 222 stable HF patients (32.75% female, 45.4% non-Hispanic black) completed multiple questionnaires. Beck Depression Inventory (BDI) assessed depressive symptoms, Life Orientation Test (LOT-R) assessed optimism, ENRICHD Social Support Inventory (ESSI) and Perceived Social Support Scale (PSSS) assessed social support, and COPE assessed coping styles. Linear regression analyses were employed to assess the association of coping styles with continuous BDI scores. Logistic regression analyses were performed using BDI scores dichotomized into BDI<10 vs. BDI> or =10, to identify coping styles accompanying clinically significant depressive symptoms. In linear regression models, higher BDI scores were associated with lower scores on the acceptance (beta=-.14), humor (beta=-.15), planning (beta=-.15), and emotional support (beta=-.14) subscales of the COPE, and higher scores on the behavioral disengagement (beta=.41), denial (beta=.33), venting (beta=.25), and mental disengagement (beta=.22) subscales. Higher PSSS and ESSI scores were associated with lower BDI scores (beta=-.32 and -.25, respectively). Higher LOT-R scores were associated with higher BDI scores (beta=.39, P<.001). In logistical regression models, BDI> or =10 was associated with greater likelihood of behavioral disengagement (OR=1.3), denial (OR=1.2), mental disengagement (OR=1.3), venting (OR=1.2), and pessimism (OR=1.2), and lower perceived social support measured by PSSS (OR=.92) and ESSI (OR=.92). Depressive symptoms in HF patients are associated with avoidant coping, lower perceived social support, and pessimism. Results raise the possibility that interventions designed to improve coping may reduce depressive symptoms.

Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

Understanding child stunting in India: a comprehensive analysis of socio-economic, nutritional and environmental determinants using additive quantile regression.

PubMed

Fenske, Nora; Burns, Jacob; Hothorn, Torsten; Rehfuess, Eva A

2013-01-01

Most attempts to address undernutrition, responsible for one third of global child deaths, have fallen behind expectations. This suggests that the assumptions underlying current modelling and intervention practices should be revisited. We undertook a comprehensive analysis of the determinants of child stunting in India, and explored whether the established focus on linear effects of single risks is appropriate. Using cross-sectional data for children aged 0-24 months from the Indian National Family Health Survey for 2005/2006, we populated an evidence-based diagram of immediate, intermediate and underlying determinants of stunting. We modelled linear, non-linear, spatial and age-varying effects of these determinants using additive quantile regression for four quantiles of the Z-score of standardized height-for-age and logistic regression for stunting and severe stunting. At least one variable within each of eleven groups of determinants was significantly associated with height-for-age in the 35% Z-score quantile regression. The non-modifiable risk factors child age and sex, and the protective factors household wealth, maternal education and BMI showed the largest effects. Being a twin or multiple birth was associated with dramatically decreased height-for-age. Maternal age, maternal BMI, birth order and number of antenatal visits influenced child stunting in non-linear ways. Findings across the four quantile and two logistic regression models were largely comparable. Our analysis confirms the multifactorial nature of child stunting. It emphasizes the need to pursue a systems-based approach and to consider non-linear effects, and suggests that differential effects across the height-for-age distribution do not play a major role.

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.

An hourly PM10 diagnosis model for the Bilbao metropolitan area using a linear regression methodology.

PubMed

González-Aparicio, I; Hidalgo, J; Baklanov, A; Padró, A; Santa-Coloma, O

2013-07-01

There is extensive evidence of the negative impacts on health linked to the rise of the regional background of particulate matter (PM) 10 levels. These levels are often increased over urban areas becoming one of the main air pollution concerns. This is the case on the Bilbao metropolitan area, Spain. This study describes a data-driven model to diagnose PM10 levels in Bilbao at hourly intervals. The model is built with a training period of 7-year historical data covering different urban environments (inland, city centre and coastal sites). The explanatory variables are quantitative-log [NO2], temperature, short-wave incoming radiation, wind speed and direction, specific humidity, hour and vehicle intensity-and qualitative-working days/weekends, season (winter/summer), the hour (from 00 to 23 UTC) and precipitation/no precipitation. Three different linear regression models are compared: simple linear regression; linear regression with interaction terms (INT); and linear regression with interaction terms following the Sawa's Bayesian Information Criteria (INT-BIC). Each type of model is calculated selecting two different periods: the training (it consists of 6 years) and the testing dataset (it consists of 1 year). The results of each type of model show that the INT-BIC-based model (R(2) = 0.42) is the best. Results were R of 0.65, 0.63 and 0.60 for the city centre, inland and coastal sites, respectively, a level of confidence similar to the state-of-the art methodology. The related error calculated for longer time intervals (monthly or seasonal means) diminished significantly (R of 0.75-0.80 for monthly means and R of 0.80 to 0.98 at seasonally means) with respect to shorter periods.

Visual field progression in glaucoma: estimating the overall significance of deterioration with permutation analyses of pointwise linear regression (PoPLR).

PubMed

O'Leary, Neil; Chauhan, Balwantray C; Artes, Paul H

2012-10-01

To establish a method for estimating the overall statistical significance of visual field deterioration from an individual patient's data, and to compare its performance to pointwise linear regression. The Truncated Product Method was used to calculate a statistic S that combines evidence of deterioration from individual test locations in the visual field. The overall statistical significance (P value) of visual field deterioration was inferred by comparing S with its permutation distribution, derived from repeated reordering of the visual field series. Permutation of pointwise linear regression (PoPLR) and pointwise linear regression were evaluated in data from patients with glaucoma (944 eyes, median mean deviation -2.9 dB, interquartile range: -6.3, -1.2 dB) followed for more than 4 years (median 10 examinations over 8 years). False-positive rates were estimated from randomly reordered series of this dataset, and hit rates (proportion of eyes with significant deterioration) were estimated from the original series. The false-positive rates of PoPLR were indistinguishable from the corresponding nominal significance levels and were independent of baseline visual field damage and length of follow-up. At P < 0.05, the hit rates of PoPLR were 12, 29, and 42%, at the fifth, eighth, and final examinations, respectively, and at matching specificities they were consistently higher than those of pointwise linear regression. In contrast to population-based progression analyses, PoPLR provides a continuous estimate of statistical significance for visual field deterioration individualized to a particular patient's data. This allows close control over specificity, essential for monitoring patients in clinical practice and in clinical trials.

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…

Use of AMMI and linear regression models to analyze genotype-environment interaction in durum wheat.

PubMed

Nachit, M M; Nachit, G; Ketata, H; Gauch, H G; Zobel, R W

1992-03-01

The joint durum wheat (Triticum turgidum L var 'durum') breeding program of the International Maize and Wheat Improvement Center (CIMMYT) and the International Center for Agricultural Research in the Dry Areas (ICARDA) for the Mediterranean region employs extensive multilocation testing. Multilocation testing produces significant genotype-environment (GE) interaction that reduces the accuracy for estimating yield and selecting appropriate germ plasm. The sum of squares (SS) of GE interaction was partitioned by linear regression techniques into joint, genotypic, and environmental regressions, and by Additive Main effects and the Multiplicative Interactions (AMMI) model into five significant Interaction Principal Component Axes (IPCA). The AMMI model was more effective in partitioning the interaction SS than the linear regression technique. The SS contained in the AMMI model was 6 times higher than the SS for all three regressions. Postdictive assessment recommended the use of the first five IPCA axes, while predictive assessment AMMI1 (main effects plus IPCA1). After elimination of random variation, AMMI1 estimates for genotypic yields within sites were more precise than unadjusted means. This increased precision was equivalent to increasing the number of replications by a factor of 3.7.

FIRE: an SPSS program for variable selection in multiple linear regression analysis via the relative importance of predictors.

PubMed

Lorenzo-Seva, Urbano; Ferrando, Pere J

2011-03-01

We provide an SPSS program that implements currently recommended techniques and recent developments for selecting variables in multiple linear regression analysis via the relative importance of predictors. The approach consists of: (1) optimally splitting the data for cross-validation, (2) selecting the final set of predictors to be retained in the equation regression, and (3) assessing the behavior of the chosen model using standard indices and procedures. The SPSS syntax, a short manual, and data files related to this article are available as supplemental materials from brm.psychonomic-journals.org/content/supplemental.

Linear regression based on Minimum Covariance Determinant (MCD) and TELBS methods on the productivity of phytoplankton

NASA Astrophysics Data System (ADS)

Gusriani, N.; Firdaniza

2018-03-01

The existence of outliers on multiple linear regression analysis causes the Gaussian assumption to be unfulfilled. If the Least Square method is forcedly used on these data, it will produce a model that cannot represent most data. For that, we need a robust regression method against outliers. This paper will compare the Minimum Covariance Determinant (MCD) method and the TELBS method on secondary data on the productivity of phytoplankton, which contains outliers. Based on the robust determinant coefficient value, MCD method produces a better model compared to TELBS method.

Support vector regression and artificial neural network models for stability indicating analysis of mebeverine hydrochloride and sulpiride mixtures in pharmaceutical preparation: A comparative study

NASA Astrophysics Data System (ADS)

Naguib, Ibrahim A.; Darwish, Hany W.

2012-02-01

A comparison between support vector regression (SVR) and Artificial Neural Networks (ANNs) multivariate regression methods is established showing the underlying algorithm for each and making a comparison between them to indicate the inherent advantages and limitations. In this paper we compare SVR to ANN with and without variable selection procedure (genetic algorithm (GA)). To project the comparison in a sensible way, the methods are used for the stability indicating quantitative analysis of mixtures of mebeverine hydrochloride and sulpiride in binary mixtures as a case study in presence of their reported impurities and degradation products (summing up to 6 components) in raw materials and pharmaceutical dosage form via handling the UV spectral data. For proper analysis, a 6 factor 5 level experimental design was established resulting in a training set of 25 mixtures containing different ratios of the interfering species. An independent test set consisting of 5 mixtures was used to validate the prediction ability of the suggested models. The proposed methods (linear SVR (without GA) and linear GA-ANN) were successfully applied to the analysis of pharmaceutical tablets containing mebeverine hydrochloride and sulpiride mixtures. The results manifest the problem of nonlinearity and how models like the SVR and ANN can handle it. The methods indicate the ability of the mentioned multivariate calibration models to deconvolute the highly overlapped UV spectra of the 6 components' mixtures, yet using cheap and easy to handle instruments like the UV spectrophotometer.

Secure Logistic Regression Based on Homomorphic Encryption: Design and Evaluation

PubMed Central

Song, Yongsoo; Wang, Shuang; Xia, Yuhou; Jiang, Xiaoqian

2018-01-01

Background Learning a model without accessing raw data has been an intriguing idea to security and machine learning researchers for years. In an ideal setting, we want to encrypt sensitive data to store them on a commercial cloud and run certain analyses without ever decrypting the data to preserve privacy. Homomorphic encryption technique is a promising candidate for secure data outsourcing, but it is a very challenging task to support real-world machine learning tasks. Existing frameworks can only handle simplified cases with low-degree polynomials such as linear means classifier and linear discriminative analysis. Objective The goal of this study is to provide a practical support to the mainstream learning models (eg, logistic regression). Methods We adapted a novel homomorphic encryption scheme optimized for real numbers computation. We devised (1) the least squares approximation of the logistic function for accuracy and efficiency (ie, reduce computation cost) and (2) new packing and parallelization techniques. Results Using real-world datasets, we evaluated the performance of our model and demonstrated its feasibility in speed and memory consumption. For example, it took approximately 116 minutes to obtain the training model from the homomorphically encrypted Edinburgh dataset. In addition, it gives fairly accurate predictions on the testing dataset. Conclusions We present the first homomorphically encrypted logistic regression outsourcing model based on the critical observation that the precision loss of classification models is sufficiently small so that the decision plan stays still. PMID:29666041

The effect of pore size and porosity on mechanical properties and biological response of porous titanium scaffolds.

PubMed

Torres-Sanchez, C; Al Mushref, F R A; Norrito, M; Yendall, K; Liu, Y; Conway, P P

2017-08-01

The effect of pore size and porosity on elastic modulus, strength, cell attachment and cell proliferation was studied for Ti porous scaffolds manufactured via powder metallurgy and sintering. Porous scaffolds were prepared in two ranges of porosities so that their mechanical properties could mimic those of cortical and trabecular bone respectively. Space-holder engineered pore size distributions were carefully determined to study the impact that small changes in pore size may have on mechanical and biological behaviour. The Young's moduli and compressive strengths were correlated with the relative porosity. Linear, power and exponential regressions were studied to confirm the predictability in the characterisation of the manufactured scaffolds and therefore establish them as a design tool for customisation of devices to suit patients' needs. The correlations were stronger for the linear and the power law regressions and poor for the exponential regressions. The optimal pore microarchitecture (i.e. pore size and porosity) for scaffolds to be used in bone grafting for cortical bone was set to <212μm with volumetric porosity values of 27-37%, and for trabecular tissues to 300-500μm with volumetric porosity values of 54-58%. The pore size range 212-300μm with volumetric porosity values of 38-56% was reported as the least favourable to cell proliferation in the longitudinal study of 12days of incubation. Copyright © 2017 Elsevier B.V. All rights reserved.

Orthogonal Projection in Teaching Regression and Financial Mathematics

ERIC Educational Resources Information Center

Kachapova, Farida; Kachapov, Ilias

2010-01-01

Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear…

Logistic models--an odd(s) kind of regression.

PubMed

Jupiter, Daniel C

2013-01-01

The logistic regression model bears some similarity to the multivariable linear regression with which we are familiar. However, the differences are great enough to warrant a discussion of the need for and interpretation of logistic regression. Copyright © 2013 American College of Foot and Ankle Surgeons. Published by Elsevier Inc. All rights reserved.

Study of process variables associated with manufacturing hermetically-sealed nickel-cadmium cells

NASA Technical Reports Server (NTRS)

Miller, L.; Doan, D. J.; Carr, E. S.

1971-01-01

A program to determine and study the critical process variables associated with the manufacture of aerospace, hermetically-sealed, nickel-cadmium cells is described. The determination and study of the process variables associated with the positive and negative plaque impregnation/polarization process are emphasized. The experimental data resulting from the implementation of fractional factorial design experiments are analyzed by means of a linear multiple regression analysis technique. This analysis permits the selection of preferred levels for certain process variables to achieve desirable impregnated plaque characteristics.

Net analyte signal-based simultaneous determination of ethanol and water by quartz crystal nanobalance sensor.

PubMed

Mirmohseni, A; Abdollahi, H; Rostamizadeh, K

2007-02-28

Net analyte signal (NAS)-based method called HLA/GO was applied for the selectively determination of binary mixture of ethanol and water by quartz crystal nanobalance (QCN) sensor. A full factorial design was applied for the formation of calibration and prediction sets in the concentration ranges 5.5-22.2 microg mL(-1) for ethanol and 7.01-28.07 microg mL(-1) for water. An optimal time range was selected by procedure which was based on the calculation of the net analyte signal regression plot in any considered time window for each test sample. A moving window strategy was used for searching the region with maximum linearity of NAS regression plot (minimum error indicator) and minimum of PRESS value. On the base of obtained results, the differences on the adsorption profiles in the time range between 1 and 600 s were used to determine mixtures of both compounds by HLA/GO method. The calculation of the net analytical signal using HLA/GO method allows determination of several figures of merit like selectivity, sensitivity, analytical sensitivity and limit of detection, for each component. To check the ability of the proposed method in the selection of linear regions of adsorption profile, a test for detecting non-linear regions of adsorption profile data in the presence of methanol was also described. The results showed that the method was successfully applied for the determination of ethanol and water.

Analysis of Learning Curve Fitting Techniques.

DTIC Science & Technology

1987-09-01

1986. 15. Neter, John and others. Applied Linear Regression Models. Homewood IL: Irwin, 19-33. 16. SAS User’s Guide: Basics, Version 5 Edition. SAS... Linear Regression Techniques (15:23-52). Random errors are assumed to be normally distributed when using -# ordinary least-squares, according to Johnston...lot estimated by the improvement curve formula. For a more detailed explanation of the ordinary least-squares technique, see Neter, et. al., Applied

On vertical profile of ozone at Syowa

NASA Technical Reports Server (NTRS)

Chubachi, Shigeru

1994-01-01

The difference in the vertical ozone profile at Syowa between 1966-1981 and 1982-1988 is shown. The month-height cross section of the slope of the linear regressions between ozone partial pressure and 100-mb temperature is also shown. The vertically integrated values of the slopes are in close agreement with the slopes calculated by linear regression of Dobson total ozone on 100-mb temperature in the period of 1982-1988.

Binding affinity toward human prion protein of some anti-prion compounds - Assessment based on QSAR modeling, molecular docking and non-parametric ranking.

PubMed

Kovačević, Strahinja; Karadžić, Milica; Podunavac-Kuzmanović, Sanja; Jevrić, Lidija

2018-01-01

The present study is based on the quantitative structure-activity relationship (QSAR) analysis of binding affinity toward human prion protein (huPrP C ) of quinacrine, pyridine dicarbonitrile, diphenylthiazole and diphenyloxazole analogs applying different linear and non-linear chemometric regression techniques, including univariate linear regression, multiple linear regression, partial least squares regression and artificial neural networks. The QSAR analysis distinguished molecular lipophilicity as an important factor that contributes to the binding affinity. Principal component analysis was used in order to reveal similarities or dissimilarities among the studied compounds. The analysis of in silico absorption, distribution, metabolism, excretion and toxicity (ADMET) parameters was conducted. The ranking of the studied analogs on the basis of their ADMET parameters was done applying the sum of ranking differences, as a relatively new chemometric method. The main aim of the study was to reveal the most important molecular features whose changes lead to the changes in the binding affinities of the studied compounds. Another point of view on the binding affinity of the most promising analogs was established by application of molecular docking analysis. The results of the molecular docking were proven to be in agreement with the experimental outcome. Copyright © 2017 Elsevier B.V. All rights reserved.

Classification of sodium MRI data of cartilage using machine learning.

PubMed

Madelin, Guillaume; Poidevin, Frederick; Makrymallis, Antonios; Regatte, Ravinder R

2015-11-01

To assess the possible utility of machine learning for classifying subjects with and subjects without osteoarthritis using sodium magnetic resonance imaging data. Theory: Support vector machine, k-nearest neighbors, naïve Bayes, discriminant analysis, linear regression, logistic regression, neural networks, decision tree, and tree bagging were tested. Sodium magnetic resonance imaging with and without fluid suppression by inversion recovery was acquired on the knee cartilage of 19 controls and 28 osteoarthritis patients. Sodium concentrations were measured in regions of interests in the knee for both acquisitions. Mean (MEAN) and standard deviation (STD) of these concentrations were measured in each regions of interest, and the minimum, maximum, and mean of these two measurements were calculated over all regions of interests for each subject. The resulting 12 variables per subject were used as predictors for classification. Either Min [STD] alone, or in combination with Mean [MEAN] or Min [MEAN], all from fluid suppressed data, were the best predictors with an accuracy >74%, mainly with linear logistic regression and linear support vector machine. Other good classifiers include discriminant analysis, linear regression, and naïve Bayes. Machine learning is a promising technique for classifying osteoarthritis patients and controls from sodium magnetic resonance imaging data. © 2014 Wiley Periodicals, Inc.

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

PubMed

Claessens, T E; Georgakopoulos, D; Afanasyeva, M; Vermeersch, S J; Millar, H D; Stergiopulos, N; Westerhof, N; Verdonck, P R; Segers, P

2006-04-01

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.

Does Nonlinear Modeling Play a Role in Plasmid Bioprocess Monitoring Using Fourier Transform Infrared Spectra?

PubMed

Lopes, Marta B; Calado, Cecília R C; Figueiredo, Mário A T; Bioucas-Dias, José M

2017-06-01

The monitoring of biopharmaceutical products using Fourier transform infrared (FT-IR) spectroscopy relies on calibration techniques involving the acquisition of spectra of bioprocess samples along the process. The most commonly used method for that purpose is partial least squares (PLS) regression, under the assumption that a linear model is valid. Despite being successful in the presence of small nonlinearities, linear methods may fail in the presence of strong nonlinearities. This paper studies the potential usefulness of nonlinear regression methods for predicting, from in situ near-infrared (NIR) and mid-infrared (MIR) spectra acquired in high-throughput mode, biomass and plasmid concentrations in Escherichia coli DH5-α cultures producing the plasmid model pVAX-LacZ. The linear methods PLS and ridge regression (RR) are compared with their kernel (nonlinear) versions, kPLS and kRR, as well as with the (also nonlinear) relevance vector machine (RVM) and Gaussian process regression (GPR). For the systems studied, RR provided better predictive performances compared to the remaining methods. Moreover, the results point to further investigation based on larger data sets whenever differences in predictive accuracy between a linear method and its kernelized version could not be found. The use of nonlinear methods, however, shall be judged regarding the additional computational cost required to tune their additional parameters, especially when the less computationally demanding linear methods herein studied are able to successfully monitor the variables under study.

Age-related energy values of bakery meal for broiler chickens determined using the regression method.

PubMed

Stefanello, C; Vieira, S L; Xue, P; Ajuwon, K M; Adeola, O

2016-07-01

A study was conducted to determine the ileal digestible energy (IDE), ME, and MEn contents of bakery meal using the regression method and to evaluate whether the energy values are age-dependent in broiler chickens from zero to 21 d post hatching. Seven hundred and eighty male Ross 708 chicks were fed 3 experimental diets in which bakery meal was incorporated into a corn-soybean meal-based reference diet at zero, 100, or 200 g/kg by replacing the energy-yielding ingredients. A 3 × 3 factorial arrangement of 3 ages (1, 2, or 3 wk) and 3 dietary bakery meal levels were used. Birds were fed the same experimental diets in these 3 evaluated ages. Birds were grouped by weight into 10 replicates per treatment in a randomized complete block design. Apparent ileal digestibility and total tract retention of DM, N, and energy were calculated. Expression of mucin (MUC2), sodium-dependent phosphate transporter (NaPi-IIb), solute carrier family 7 (cationic amino acid transporter, Y(+) system, SLC7A2), glucose (GLUT2), and sodium-glucose linked transporter (SGLT1) genes were measured at each age in the jejunum by real-time PCR. Addition of bakery meal to the reference diet resulted in a linear decrease in retention of DM, N, and energy, and a quadratic reduction (P < 0.05) in N retention and ME. There was a linear increase in DM, N, and energy as birds' ages increased from 1 to 3 wk. Dietary bakery meal did not affect jejunal gene expression. Expression of genes encoding MUC2, NaPi-IIb, and SLC7A2 linearly increased (P < 0.05) with age. Regression-derived MEn of bakery meal linearly increased (P < 0.05) as the age of birds increased, with values of 2,710, 2,820, and 2,923 kcal/kg DM for 1, 2, and 3 wk, respectively. Based on these results, utilization of energy and nitrogen in the basal diet decreased when bakery meal was included and increased with age of broiler chickens. © 2016 Poultry Science Association Inc.

Threshold regression to accommodate a censored covariate.

PubMed

Qian, Jing; Chiou, Sy Han; Maye, Jacqueline E; Atem, Folefac; Johnson, Keith A; Betensky, Rebecca A

2018-06-22

In several common study designs, regression modeling is complicated by the presence of censored covariates. Examples of such covariates include maternal age of onset of dementia that may be right censored in an Alzheimer's amyloid imaging study of healthy subjects, metabolite measurements that are subject to limit of detection censoring in a case-control study of cardiovascular disease, and progressive biomarkers whose baseline values are of interest, but are measured post-baseline in longitudinal neuropsychological studies of Alzheimer's disease. We propose threshold regression approaches for linear regression models with a covariate that is subject to random censoring. Threshold regression methods allow for immediate testing of the significance of the effect of a censored covariate. In addition, they provide for unbiased estimation of the regression coefficient of the censored covariate. We derive the asymptotic properties of the resulting estimators under mild regularity conditions. Simulations demonstrate that the proposed estimators have good finite-sample performance, and often offer improved efficiency over existing methods. We also derive a principled method for selection of the threshold. We illustrate the approach in application to an Alzheimer's disease study that investigated brain amyloid levels in older individuals, as measured through positron emission tomography scans, as a function of maternal age of dementia onset, with adjustment for other covariates. We have developed an R package, censCov, for implementation of our method, available at CRAN. © 2018, The International Biometric Society.

Application of General Regression Neural Network to the Prediction of LOD Change

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Hong; Wang, Qi-Jie; Zhu, Jian-Jun; Zhang, Hao

2012-01-01

Traditional methods for predicting the change in length of day (LOD change) are mainly based on some linear models, such as the least square model and autoregression model, etc. However, the LOD change comprises complicated non-linear factors and the prediction effect of the linear models is always not so ideal. Thus, a kind of non-linear neural network — general regression neural network (GRNN) model is tried to make the prediction of the LOD change and the result is compared with the predicted results obtained by taking advantage of the BP (back propagation) neural network model and other models. The comparison result shows that the application of the GRNN to the prediction of the LOD change is highly effective and feasible.

Regression-based statistical mediation and moderation analysis in clinical research: Observations, recommendations, and implementation.

PubMed

Hayes, Andrew F; Rockwood, Nicholas J

2017-11-01

There have been numerous treatments in the clinical research literature about various design, analysis, and interpretation considerations when testing hypotheses about mechanisms and contingencies of effects, popularly known as mediation and moderation analysis. In this paper we address the practice of mediation and moderation analysis using linear regression in the pages of Behaviour Research and Therapy and offer some observations and recommendations, debunk some popular myths, describe some new advances, and provide an example of mediation, moderation, and their integration as conditional process analysis using the PROCESS macro for SPSS and SAS. Our goal is to nudge clinical researchers away from historically significant but increasingly old school approaches toward modifications, revisions, and extensions that characterize more modern thinking about the analysis of the mechanisms and contingencies of effects. Copyright © 2016 Elsevier Ltd. All rights reserved.

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 third molar development and eruption models in estimating dental age in Malay sub-adults.

PubMed

Mohd Yusof, Mohd Yusmiaidil Putera; Cauwels, Rita; Deschepper, Ellen; Martens, Luc

2015-08-01

The third molar development (TMD) has been widely utilized as one of the radiographic method for dental age estimation. By using the same radiograph of the same individual, third molar eruption (TME) information can be incorporated to the TMD regression model. This study aims to evaluate the performance of dental age estimation in individual method models and the combined model (TMD and TME) based on the classic regressions of multiple linear and principal component analysis. A sample of 705 digital panoramic radiographs of Malay sub-adults aged between 14.1 and 23.8 years was collected. The techniques described by Gleiser and Hunt (modified by Kohler) and Olze were employed to stage the TMD and TME, respectively. The data was divided to develop three respective models based on the two regressions of multiple linear and principal component analysis. The trained models were then validated on the test sample and the accuracy of age prediction was compared between each model. The coefficient of determination (R²) and root mean square error (RMSE) were calculated. In both genders, adjusted R² yielded an increment in the linear regressions of combined model as compared to the individual models. The overall decrease in RMSE was detected in combined model as compared to TMD (0.03-0.06) and TME (0.2-0.8). In principal component regression, low value of adjusted R(2) and high RMSE except in male were exhibited in combined model. Dental age estimation is better predicted using combined model in multiple linear regression models. Copyright © 2015 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

40 CFR 1066.220 - Linearity verification for chassis dynamometer systems.

Code of Federal Regulations, 2014 CFR

2014-07-01

... dynamometer speed and torque at least as frequently as indicated in Table 1 of § 1066.215. The intent of... linear regression and the linearity criteria specified in Table 1 of this section. (b) Performance requirements. If a measurement system does not meet the applicable linearity criteria in Table 1 of this...

A Learning Progression Should Address Regression: Insights from Developing Non-Linear Reasoning in Ecology

ERIC Educational Resources Information Center

Hovardas, Tasos

2016-01-01

Although ecological systems at varying scales involve non-linear interactions, learners insist thinking in a linear fashion when they deal with ecological phenomena. The overall objective of the present contribution was to propose a hypothetical learning progression for developing non-linear reasoning in prey-predator systems and to provide…

Application of Hierarchical Linear Models/Linear Mixed-Effects Models in School Effectiveness Research

ERIC Educational Resources Information Center

Ker, H. W.

2014-01-01

Multilevel data are very common in educational research. Hierarchical linear models/linear mixed-effects models (HLMs/LMEs) are often utilized to analyze multilevel data nowadays. This paper discusses the problems of utilizing ordinary regressions for modeling multilevel educational data, compare the data analytic results from three regression…

Assessing the blood volume and heart rate responses during haemodialysis in fluid overloaded patients using support vector regression.

PubMed

Javed, Faizan; Savkin, Andrey V; Chan, Gregory S H; Middleton, Paul M; Malouf, Philip; Steel, Elizabeth; Mackie, James; Lovell, Nigel H

2009-11-01

This study aims to assess the blood volume and heart rate (HR) responses during haemodialysis in fluid overloaded patients by a nonparametric nonlinear regression approach based on a support vector machine (SVM). Relative blood volume (RBV) and electrocardiogram (ECG) was recorded from 23 haemodynamically stable renal failure patients during regular haemodialysis. Modelling was performed on 18 fluid overloaded patients (fluid removal of >2 L). SVM-based regression was used to obtain the models of RBV change with time as well as the percentage change in HR with respect to RBV. Mean squared error (MSE) and goodness of fit (R(2)) were used for comparison among different kernel functions. The design parameters were estimated using a grid search approach and the selected models were validated by a k-fold cross-validation technique. For the model of HR versus RBV change, a radial basis function (RBF) kernel (MSE = 17.37 and R(2) = 0.932) gave the least MSE compared to linear (MSE = 25.97 and R(2) = 0.898) and polynomial (MSE = 18.18 and R(2)= 0.929). The MSE was significantly lower for training data set when using RBF kernel compared to other kernels (p < 0.01). The RBF kernel also provided a slightly better fit of RBV change with time (MSE = 1.12 and R(2) = 0.91) compared to a linear kernel (MSE = 1.46 and R(2) = 0.88). The modelled HR response was characterized by an initial drop and a subsequent rise during progressive reduction in RBV, which may be interpreted as the reflex response to a transition from central hypervolaemia to hypovolaemia. These modelled curves can be used as references to a controller that can be designed to regulate the haemodynamic variables to ensure the stability of patients undergoing haemodialysis.

Estimating normative limits of Heidelberg Retina Tomograph optic disc rim area with quantile regression.

PubMed

Artes, Paul H; Crabb, David P

2010-01-01

To investigate why the specificity of the Moorfields Regression Analysis (MRA) of the Heidelberg Retina Tomograph (HRT) varies with disc size, and to derive accurate normative limits for neuroretinal rim area to address this problem. Two datasets from healthy subjects (Manchester, UK, n = 88; Halifax, Nova Scotia, Canada, n = 75) were used to investigate the physiological relationship between the optic disc and neuroretinal rim area. Normative limits for rim area were derived by quantile regression (QR) and compared with those of the MRA (derived by linear regression). Logistic regression analyses were performed to quantify the association between disc size and positive classifications with the MRA, as well as with the QR-derived normative limits. In both datasets, the specificity of the MRA depended on optic disc size. The odds of observing a borderline or outside-normal-limits classification increased by approximately 10% for each 0.1 mm(2) increase in disc area (P < 0.1). The lower specificity of the MRA with large optic discs could be explained by the failure of linear regression to model the extremes of the rim area distribution (observations far from the mean). In comparison, the normative limits predicted by QR were larger for smaller discs (less specific, more sensitive), and smaller for larger discs, such that false-positive rates became independent of optic disc size. Normative limits derived by quantile regression appear to remove the size-dependence of specificity with the MRA. Because quantile regression does not rely on the restrictive assumptions of standard linear regression, it may be a more appropriate method for establishing normative limits in other clinical applications where the underlying distributions are nonnormal or have nonconstant variance.

Drop-Weight Impact Test on U-Shape Concrete Specimens with Statistical and Regression Analyses

PubMed Central

Zhu, Xue-Chao; Zhu, Han; Li, Hao-Ran

2015-01-01

According to the principle and method of drop-weight impact test, the impact resistance of concrete was measured using self-designed U-shape specimens and a newly designed drop-weight impact test apparatus. A series of drop-weight impact tests were carried out with four different masses of drop hammers (0.875, 0.8, 0.675 and 0.5 kg). The test results show that the impact resistance results fail to follow a normal distribution. As expected, U-shaped specimens can predetermine the location of the cracks very well. It is also easy to record the cracks propagation during the test. The maximum of coefficient of variation in this study is 31.2%; it is lower than the values obtained from the American Concrete Institute (ACI) impact tests in the literature. By regression analysis, the linear relationship between the first-crack and ultimate failure impact resistance is good. It can suggested that a minimum number of specimens is required to reliably measure the properties of the material based on the observed levels of variation. PMID:28793540

Stochastic search, optimization and regression with energy applications

NASA Astrophysics Data System (ADS)

Hannah, Lauren A.

Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings. Finally, we study convex stochastic search problems where a noisy objective function value is observed after a decision is made. There are many stochastic search problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation to take observations from the joint state-outcome distribution and use them to infer the optimal decision for a given query state. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We examine two weighting schemes, kernel-based weights and Dirichlet process-based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour-ahead wind commitment problem. Our results show that in some cases Dirichlet process weights offer substantial benefits over kernel based weights and more generally that nonparametric estimation methods provide good solutions to otherwise intractable problems.

[Optimal extraction of effective constituents from Aralia elata by central composite design and response surface methodology].

PubMed

Lv, Shao-Wa; Liu, Dong; Hu, Pan-Pan; Ye, Xu-Yan; Xiao, Hong-Bin; Kuang, Hai-Xue

2010-03-01

To optimize the process of extracting effective constituents from Aralia elata by response surface methodology. The independent variables were ethanol concentration, reflux time and solvent fold, the dependent variable was extraction rate of total saponins in Aralia elata. Linear or no-linear mathematic models were used to estimate the relationship between independent and dependent variables. Response surface methodology was used to optimize the process of extraction. The prediction was carried out through comparing the observed and predicted values. Regression coefficient of binomial fitting complex model was as high as 0.9617, the optimum conditions of extraction process were 70% ethanol, 2.5 hours for reflux, 20-fold solvent and 3 times for extraction. The bias between observed and predicted values was -2.41%. It shows the optimum model is highly predictive.

Linear Multivariable Regression Models for Prediction of Eddy Dissipation Rate from Available Meteorological Data

NASA Technical Reports Server (NTRS)

MCKissick, Burnell T. (Technical Monitor); Plassman, Gerald E.; Mall, Gerald H.; Quagliano, John R.

2005-01-01

Linear multivariable regression models for predicting day and night Eddy Dissipation Rate (EDR) from available meteorological data sources are defined and validated. Model definition is based on a combination of 1997-2000 Dallas/Fort Worth (DFW) data sources, EDR from Aircraft Vortex Spacing System (AVOSS) deployment data, and regression variables primarily from corresponding Automated Surface Observation System (ASOS) data. Model validation is accomplished through EDR predictions on a similar combination of 1994-1995 Memphis (MEM) AVOSS and ASOS data. Model forms include an intercept plus a single term of fixed optimal power for each of these regression variables; 30-minute forward averaged mean and variance of near-surface wind speed and temperature, variance of wind direction, and a discrete cloud cover metric. Distinct day and night models, regressing on EDR and the natural log of EDR respectively, yield best performance and avoid model discontinuity over day/night data boundaries.

Spatio-temporal water quality mapping from satellite images using geographically and temporally weighted regression

NASA Astrophysics Data System (ADS)

Chu, Hone-Jay; Kong, Shish-Jeng; Chang, Chih-Hua

2018-03-01

The turbidity (TB) of a water body varies with time and space. Water quality is traditionally estimated via linear regression based on satellite images. However, estimating and mapping water quality require a spatio-temporal nonstationary model, while TB mapping necessitates the use of geographically and temporally weighted regression (GTWR) and geographically weighted regression (GWR) models, both of which are more precise than linear regression. Given the temporal nonstationary models for mapping water quality, GTWR offers the best option for estimating regional water quality. Compared with GWR, GTWR provides highly reliable information for water quality mapping, boasts a relatively high goodness of fit, improves the explanation of variance from 44% to 87%, and shows a sufficient space-time explanatory power. The seasonal patterns of TB and the main spatial patterns of TB variability can be identified using the estimated TB maps from GTWR and by conducting an empirical orthogonal function (EOF) analysis.

Mental chronometry with simple linear regression.

PubMed

Chen, J Y

1997-10-01

Typically, mental chronometry is performed by means of introducing an independent variable postulated to affect selectively some stage of a presumed multistage process. However, the effect could be a global one that spreads proportionally over all stages of the process. Currently, there is no method to test this possibility although simple linear regression might serve the purpose. In the present study, the regression approach was tested with tasks (memory scanning and mental rotation) that involved a selective effect and with a task (word superiority effect) that involved a global effect, by the dominant theories. The results indicate (1) the manipulation of the size of a memory set or of angular disparity affects the intercept of the regression function that relates the times for memory scanning with different set sizes or for mental rotation with different angular disparities and (2) the manipulation of context affects the slope of the regression function that relates the times for detecting a target character under word and nonword conditions. These ratify the regression approach as a useful method for doing mental chronometry.

RRegrs: an R package for computer-aided model selection with multiple regression models.

PubMed

Tsiliki, Georgia; Munteanu, Cristian R; Seoane, Jose A; Fernandez-Lozano, Carlos; Sarimveis, Haralambos; Willighagen, Egon L

2015-01-01

Predictive regression models can be created with many different modelling approaches. Choices need to be made for data set splitting, cross-validation methods, specific regression parameters and best model criteria, as they all affect the accuracy and efficiency of the produced predictive models, and therefore, raising model reproducibility and comparison issues. Cheminformatics and bioinformatics are extensively using predictive modelling and exhibit a need for standardization of these methodologies in order to assist model selection and speed up the process of predictive model development. A tool accessible to all users, irrespectively of their statistical knowledge, would be valuable if it tests several simple and complex regression models and validation schemes, produce unified reports, and offer the option to be integrated into more extensive studies. Additionally, such methodology should be implemented as a free programming package, in order to be continuously adapted and redistributed by others. We propose an integrated framework for creating multiple regression models, called RRegrs. The tool offers the option of ten simple and complex regression methods combined with repeated 10-fold and leave-one-out cross-validation. Methods include Multiple Linear regression, Generalized Linear Model with Stepwise Feature Selection, Partial Least Squares regression, Lasso regression, and Support Vector Machines Recursive Feature Elimination. The new framework is an automated fully validated procedure which produces standardized reports to quickly oversee the impact of choices in modelling algorithms and assess the model and cross-validation results. The methodology was implemented as an open source R package, available at https://www.github.com/enanomapper/RRegrs, by reusing and extending on the caret package. The universality of the new methodology is demonstrated using five standard data sets from different scientific fields. Its efficiency in cheminformatics and QSAR modelling is shown with three use cases: proteomics data for surface-modified gold nanoparticles, nano-metal oxides descriptor data, and molecular descriptors for acute aquatic toxicity data. The results show that for all data sets RRegrs reports models with equal or better performance for both training and test sets than those reported in the original publications. Its good performance as well as its adaptability in terms of parameter optimization could make RRegrs a popular framework to assist the initial exploration of predictive models, and with that, the design of more comprehensive in silico screening applications.Graphical abstractRRegrs is a computer-aided model selection framework for R multiple regression models; this is a fully validated procedure with application to QSAR modelling.

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

Distance correction system for localization based on linear regression and smoothing in ambient intelligence display.

PubMed

Kim, Dae-Hee; Choi, Jae-Hun; Lim, Myung-Eun; Park, Soo-Jun

2008-01-01

This paper suggests the method of correcting distance between an ambient intelligence display and a user based on linear regression and smoothing method, by which distance information of a user who approaches to the display can he accurately output even in an unanticipated condition using a passive infrared VIR) sensor and an ultrasonic device. The developed system consists of an ambient intelligence display and an ultrasonic transmitter, and a sensor gateway. Each module communicates with each other through RF (Radio frequency) communication. The ambient intelligence display includes an ultrasonic receiver and a PIR sensor for motion detection. In particular, this system selects and processes algorithms such as smoothing or linear regression for current input data processing dynamically through judgment process that is determined using the previous reliable data stored in a queue. In addition, we implemented GUI software with JAVA for real time location tracking and an ambient intelligence display.

How is the weather? Forecasting inpatient glycemic control

PubMed Central

Saulnier, George E; Castro, Janna C; Cook, Curtiss B; Thompson, Bithika M

2017-01-01

Aim: Apply methods of damped trend analysis to forecast inpatient glycemic control. Method: Observed and calculated point-of-care blood glucose data trends were determined over 62 weeks. Mean absolute percent error was used to calculate differences between observed and forecasted values. Comparisons were drawn between model results and linear regression forecasting. Results: The forecasted mean glucose trends observed during the first 24 and 48 weeks of projections compared favorably to the results provided by linear regression forecasting. However, in some scenarios, the damped trend method changed inferences compared with linear regression. In all scenarios, mean absolute percent error values remained below the 10% accepted by demand industries. Conclusion: Results indicate that forecasting methods historically applied within demand industries can project future inpatient glycemic control. Additional study is needed to determine if forecasting is useful in the analyses of other glucometric parameters and, if so, how to apply the techniques to quality improvement. PMID:29134125

BFLCRM: A BAYESIAN FUNCTIONAL LINEAR COX REGRESSION MODEL FOR PREDICTING TIME TO CONVERSION TO ALZHEIMER’S DISEASE*

PubMed Central

Lee, Eunjee; Zhu, Hongtu; Kong, Dehan; Wang, Yalin; Giovanello, Kelly Sullivan; Ibrahim, Joseph G

2015-01-01

The aim of this paper is to develop a Bayesian functional linear Cox regression model (BFLCRM) with both functional and scalar covariates. This new development is motivated by establishing the likelihood of conversion to Alzheimer’s disease (AD) in 346 patients with mild cognitive impairment (MCI) enrolled in the Alzheimer’s Disease Neuroimaging Initiative 1 (ADNI-1) and the early markers of conversion. These 346 MCI patients were followed over 48 months, with 161 MCI participants progressing to AD at 48 months. The functional linear Cox regression model was used to establish that functional covariates including hippocampus surface morphology and scalar covariates including brain MRI volumes, cognitive performance (ADAS-Cog), and APOE status can accurately predict time to onset of AD. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BFLCRM. PMID:26900412

Liquid electrolyte informatics using an exhaustive search with linear regression.

PubMed

Sodeyama, Keitaro; Igarashi, Yasuhiko; Nakayama, Tomofumi; Tateyama, Yoshitaka; Okada, Masato

2018-06-14

Exploring new liquid electrolyte materials is a fundamental target for developing new high-performance lithium-ion batteries. In contrast to solid materials, disordered liquid solution properties have been less studied by data-driven information techniques. Here, we examined the estimation accuracy and efficiency of three information techniques, multiple linear regression (MLR), least absolute shrinkage and selection operator (LASSO), and exhaustive search with linear regression (ES-LiR), by using coordination energy and melting point as test liquid properties. We then confirmed that ES-LiR gives the most accurate estimation among the techniques. We also found that ES-LiR can provide the relationship between the "prediction accuracy" and "calculation cost" of the properties via a weight diagram of descriptors. This technique makes it possible to choose the balance of the "accuracy" and "cost" when the search of a huge amount of new materials was carried out.

Estimation and Selection via Absolute Penalized Convex Minimization And Its Multistage Adaptive Applications

PubMed Central

Huang, Jian; Zhang, Cun-Hui

2013-01-01

The ℓ1-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of high-dimensional statistical problems. In this article, we consider a class of weighted ℓ1-penalized estimators for convex loss functions of a general form, including the generalized linear models. We study the estimation, prediction, selection and sparsity properties of the weighted ℓ1-penalized estimator in sparse, high-dimensional settings where the number of predictors p can be much larger than the sample size n. Adaptive Lasso is considered as a special case. A multistage method is developed to approximate concave regularized estimation by applying an adaptive Lasso recursively. We provide prediction and estimation oracle inequalities for single- and multi-stage estimators, a general selection consistency theorem, and an upper bound for the dimension of the Lasso estimator. Important models including the linear regression, logistic regression and log-linear models are used throughout to illustrate the applications of the general results. PMID:24348100

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

PubMed

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-06-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-01-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

Delineating chalk sand distribution of Ekofisk formation using probabilistic neural network (PNN) and stepwise regression (SWR): Case study Danish North Sea field

NASA Astrophysics Data System (ADS)

Haris, A.; Nafian, M.; Riyanto, A.

2017-07-01

Danish North Sea Fields consist of several formations (Ekofisk, Tor, and Cromer Knoll) that was started from the age of Paleocene to Miocene. In this study, the integration of seismic and well log data set is carried out to determine the chalk sand distribution in the Danish North Sea field. The integration of seismic and well log data set is performed by using the seismic inversion analysis and seismic multi-attribute. The seismic inversion algorithm, which is used to derive acoustic impedance (AI), is model-based technique. The derived AI is then used as external attributes for the input of multi-attribute analysis. Moreover, the multi-attribute analysis is used to generate the linear and non-linear transformation of among well log properties. In the case of the linear model, selected transformation is conducted by weighting step-wise linear regression (SWR), while for the non-linear model is performed by using probabilistic neural networks (PNN). The estimated porosity, which is resulted by PNN shows better suited to the well log data compared with the results of SWR. This result can be understood since PNN perform non-linear regression so that the relationship between the attribute data and predicted log data can be optimized. The distribution of chalk sand has been successfully identified and characterized by porosity value ranging from 23% up to 30%.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.

PubMed

Kong, Shengchun; Nan, Bin

2014-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

PubMed Central

Kong, Shengchun; Nan, Bin

2013-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses. PMID:24516328

The Influence of Assay Design, Blinding, and Gymnema sylvestre on Sucrose Detection by Humans.

PubMed

Aleman, Max G; Marconi, Lauren J; Nguyen, Nam H; Park, Jae M; Patino, Maria M; Wang, Yuchi; Watkins, Celeste S; Shelley, Chris

2016-01-01

The detection and grading of tastes corresponding to different taste modalities can be tested in engaging laboratory sessions using students themselves as test subjects. This article describes a series of experiments in which data pertaining to the detection of salty and sweet tastes are obtained, and the ability of the herb Gymnema sylvestre to disrupt the detection of sucrose is quantified. The effects of blinding and different assay designs on EC50 estimation are also investigated. The data obtained allow for substantial data analysis, including non-linear regression using fixed and free parameters to quantify dose-response relationships, and the use of often under-utilized permutation tests to determine significant differences when the underlying data display heteroscedasticity.

The Influence of Assay Design, Blinding, and Gymnema sylvestre on Sucrose Detection by Humans

PubMed Central

Aleman, Max G.; Marconi, Lauren J.; Nguyen, Nam H.; Park, Jae M.; Patino, Maria M.; Wang, Yuchi; Watkins, Celeste S.; Shelley, Chris

2016-01-01

The detection and grading of tastes corresponding to different taste modalities can be tested in engaging laboratory sessions using students themselves as test subjects. This article describes a series of experiments in which data pertaining to the detection of salty and sweet tastes are obtained, and the ability of the herb Gymnema sylvestre to disrupt the detection of sucrose is quantified. The effects of blinding and different assay designs on EC50 estimation are also investigated. The data obtained allow for substantial data analysis, including non-linear regression using fixed and free parameters to quantify dose-response relationships, and the use of often under-utilized permutation tests to determine significant differences when the underlying data display heteroscedasticity. PMID:27980466

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

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,…

Isolating and Examining Sources of Suppression and Multicollinearity in Multiple Linear Regression

ERIC Educational Resources Information Center

Beckstead, Jason W.

2012-01-01

The presence of suppression (and multicollinearity) in multiple regression analysis complicates interpretation of predictor-criterion relationships. The mathematical conditions that produce suppression in regression analysis have received considerable attention in the methodological literature but until now nothing in the way of an analytic…

Suppression Situations in Multiple Linear Regression

ERIC Educational Resources Information Center

Shieh, Gwowen

2006-01-01

This article proposes alternative expressions for the two most prevailing definitions of suppression without resorting to the standardized regression modeling. The formulation provides a simple basis for the examination of their relationship. For the two-predictor regression, the author demonstrates that the previous results in the literature are…

Predictors of caregiver burden in Iranian family caregivers of cancer patients.

PubMed

Mirsoleymani, Seyed Reza; Rohani, Camelia; Matbouei, Mahsa; Nasiri, Malihe; Vasli, Parvaneh

2017-01-01

Caregiver burden threatens the psychological, emotional, functional and even physical health of caregivers. The aims of this study were to determine caregiver burden and family distress and the relationship between them, also to explore predictors of caregiver burden in a sample of Iranian family caregivers of cancer patients. This is a cross-sectional study with correlational design. A total of 104 family caregivers of cancer patients were asked to respond to the Caregiver Burden Inventory (CBI) and the Family Distress Index (FDI) together with a sociodemographic questionnaire. For evaluating the relationship between CBI and FDI scores, the Pearson's product-moment correlation was used. In addition, multiple linear regression analysis was applied to explore the predictive factors of caregiver burden. A high burden was experienced by almost half of the caregivers (48.1%). The FDI mean score was 9.76 ± 5.40 ranged from 0 to 24. A strong positive correlation was found between the caregiver burden and family distress ( r = 0.76). Multiple linear regression results showed the predictive role of FDI score (β = 0.71, P = 0.001), patient's gender (β = -0.25, P = 0.001), and early cancer diagnosis (β =0.13, P = 0.027) in caregiver burden. They could explain 65% of variance in the level of burden in family caregivers. Family nurses should consider the caregivers burden and vulnerability of families with cancer patient, especially if the patient is a male or has a new diagnosis. They should also design special programs for the whole family as a system that family can adapt to the new situation.

Emotional expression in music: contribution, linearity, and additivity of primary musical cues

PubMed Central

Eerola, Tuomas; Friberg, Anders; Bresin, Roberto

2013-01-01

The aim of this study is to manipulate musical cues systematically to determine the aspects of music that contribute to emotional expression, and whether these cues operate in additive or interactive fashion, and whether the cue levels can be characterized as linear or non-linear. An optimized factorial design was used with six primary musical cues (mode, tempo, dynamics, articulation, timbre, and register) across four different music examples. Listeners rated 200 musical examples according to four perceived emotional characters (happy, sad, peaceful, and scary). The results exhibited robust effects for all cues and the ranked importance of these was established by multiple regression. The most important cue was mode followed by tempo, register, dynamics, articulation, and timbre, although the ranking varied across the emotions. The second main result suggested that most cue levels contributed to the emotions in a linear fashion, explaining 77–89% of variance in ratings. Quadratic encoding of cues did lead to minor but significant increases of the models (0–8%). Finally, the interactions between the cues were non-existent suggesting that the cues operate mostly in an additive fashion, corroborating recent findings on emotional expression in music (Juslin and Lindström, 2010). PMID:23908642

Emotional expression in music: contribution, linearity, and additivity of primary musical cues.

PubMed

Eerola, Tuomas; Friberg, Anders; Bresin, Roberto

2013-01-01

The aim of this study is to manipulate musical cues systematically to determine the aspects of music that contribute to emotional expression, and whether these cues operate in additive or interactive fashion, and whether the cue levels can be characterized as linear or non-linear. An optimized factorial design was used with six primary musical cues (mode, tempo, dynamics, articulation, timbre, and register) across four different music examples. Listeners rated 200 musical examples according to four perceived emotional characters (happy, sad, peaceful, and scary). The results exhibited robust effects for all cues and the ranked importance of these was established by multiple regression. The most important cue was mode followed by tempo, register, dynamics, articulation, and timbre, although the ranking varied across the emotions. The second main result suggested that most cue levels contributed to the emotions in a linear fashion, explaining 77-89% of variance in ratings. Quadratic encoding of cues did lead to minor but significant increases of the models (0-8%). Finally, the interactions between the cues were non-existent suggesting that the cues operate mostly in an additive fashion, corroborating recent findings on emotional expression in music (Juslin and Lindström, 2010).

Society of Thoracic Surgeons Risk Score Predicts Hospital Charges and Resource Utilization After Aortic Valve Replacement

PubMed Central

Arnaoutakis, George J.; George, Timothy J.; Alejo, Diane E.; Merlo, Christian A.; Baumgartner, William A.; Cameron, Duke E.; Shah, Ashish S.

2011-01-01

Context The impact of Society of Thoracic Surgeons (STS) predicted mortality risk score on resource utilization after aortic valve replacement (AVR) has not been previously studied. Objective We hypothesize that increasing STS risk scores in patients having AVR are associated with greater hospital charges. Design, Setting, and Patients Clinical and financial data for patients undergoing AVR at a tertiary care, university hospital over a ten-year period (1/2000–12/2009) were retrospectively reviewed. The current STS formula (v2.61) for in-hospital mortality was used for all patients. After stratification into risk quartiles (Q), index admission hospital charges were compared across risk strata with Rank-Sum tests. Linear regression and Spearman’s coefficient assessed correlation and goodness of fit. Multivariable analysis assessed relative contributions of individual variables on overall charges. Main Outcome Measures Inflation-adjusted index hospitalization total charges Results 553 patients had AVR during the study period. Average predicted mortality was 2.9% (±3.4) and actual mortality was 3.4% for AVR. Median charges were greater in the upper Q of AVR patients [Q1–3,$39,949 (IQR32,708–51,323) vs Q4,$62,301 (IQR45,952–97,103), p=<0.01]. On univariate linear regression, there was a positive correlation between STS risk score and log-transformed charges (coefficient: 0.06, 95%CI 0.05–0.07, p<0.01). Spearman’s correlation R-value was 0.51. This positive correlation persisted in risk-adjusted multivariable linear regression. Each 1% increase in STS risk score was associated with an added $3,000 in hospital charges. Conclusions This study showed increasing STS risk score predicts greater charges after AVR. As competing therapies such as percutaneous valve replacement emerge to treat high risk patients, these results serve as a benchmark to compare resource utilization. PMID:21497834

Regression equations for estimation of annual peak-streamflow frequency for undeveloped watersheds in Texas using an L-moment-based, PRESS-minimized, residual-adjusted approach

USGS Publications Warehouse

Asquith, William H.; Roussel, Meghan C.

2009-01-01

Annual peak-streamflow frequency estimates are needed for flood-plain management; for objective assessment of flood risk; for cost-effective design of dams, levees, and other flood-control structures; and for design of roads, bridges, and culverts. Annual peak-streamflow frequency represents the peak streamflow for nine recurrence intervals of 2, 5, 10, 25, 50, 100, 200, 250, and 500 years. Common methods for estimation of peak-streamflow frequency for ungaged or unmonitored watersheds are regression equations for each recurrence interval developed for one or more regions; such regional equations are the subject of this report. The method is based on analysis of annual peak-streamflow data from U.S. Geological Survey streamflow-gaging stations (stations). Beginning in 2007, the U.S. Geological Survey, in cooperation with the Texas Department of Transportation and in partnership with Texas Tech University, began a 3-year investigation concerning the development of regional equations to estimate annual peak-streamflow frequency for undeveloped watersheds in Texas. The investigation focuses primarily on 638 stations with 8 or more years of data from undeveloped watersheds and other criteria. The general approach is explicitly limited to the use of L-moment statistics, which are used in conjunction with a technique of multi-linear regression referred to as PRESS minimization. The approach used to develop the regional equations, which was refined during the investigation, is referred to as the 'L-moment-based, PRESS-minimized, residual-adjusted approach'. For the approach, seven unique distributions are fit to the sample L-moments of the data for each of 638 stations and trimmed means of the seven results of the distributions for each recurrence interval are used to define the station specific, peak-streamflow frequency. As a first iteration of regression, nine weighted-least-squares, PRESS-minimized, multi-linear regression equations are computed using the watershed characteristics of drainage area, dimensionless main-channel slope, and mean annual precipitation. The residuals of the nine equations are spatially mapped, and residuals for the 10-year recurrence interval are selected for generalization to 1-degree latitude and longitude quadrangles. The generalized residual is referred to as the OmegaEM parameter and represents a generalized terrain and climate index that expresses peak-streamflow potential not otherwise represented in the three watershed characteristics. The OmegaEM parameter was assigned to each station, and using OmegaEM, nine additional regression equations are computed. Because of favorable diagnostics, the OmegaEM equations are expected to be generally reliable estimators of peak-streamflow frequency for undeveloped and ungaged stream locations in Texas. The mean residual standard error, adjusted R-squared, and percentage reduction of PRESS by use of OmegaEM are 0.30log10, 0.86, and -21 percent, respectively. Inclusion of the OmegaEM parameter provides a substantial reduction in the PRESS statistic of the regression equations and removes considerable spatial dependency in regression residuals. Although the OmegaEM parameter requires interpretation on the part of analysts and the potential exists that different analysts could estimate different values for a given watershed, the authors suggest that typical uncertainty in the OmegaEM estimate might be about +or-0.1010. Finally, given the two ensembles of equations reported herein and those in previous reports, hydrologic design engineers and other analysts have several different methods, which represent different analytical tracks, to make comparisons of peak-streamflow frequency estimates for ungaged watersheds in the study area.

Predicting U.S. Army Reserve Unit Manning Using Market Demographics

DTIC Science & Technology

2015-06-01

develops linear regression , classification tree, and logistic regression models to determine the ability of the location to support manning requirements... logistic regression model delivers predictive results that allow decision-makers to identify locations with a high probability of meeting unit...manning requirements. The recommendation of this thesis is that the USAR implement the logistic regression model. 14. SUBJECT TERMS U.S

[Use of multiple regression models in observational studies (1970-2013) and requirements of the STROBE guidelines in Spanish scientific journals].

PubMed

Real, J; Cleries, R; Forné, C; Roso-Llorach, A; Martínez-Sánchez, J M

In medicine and biomedical research, statistical techniques like logistic, linear, Cox and Poisson regression are widely known. The main objective is to describe the evolution of multivariate techniques used in observational studies indexed in PubMed (1970-2013), and to check the requirements of the STROBE guidelines in the author guidelines in Spanish journals indexed in PubMed. A targeted PubMed search was performed to identify papers that used logistic linear Cox and Poisson models. Furthermore, a review was also made of the author guidelines of journals published in Spain and indexed in PubMed and Web of Science. Only 6.1% of the indexed manuscripts included a term related to multivariate analysis, increasing from 0.14% in 1980 to 12.3% in 2013. In 2013, 6.7, 2.5, 3.5, and 0.31% of the manuscripts contained terms related to logistic, linear, Cox and Poisson regression, respectively. On the other hand, 12.8% of journals author guidelines explicitly recommend to follow the STROBE guidelines, and 35.9% recommend the CONSORT guideline. A low percentage of Spanish scientific journals indexed in PubMed include the STROBE statement requirement in the author guidelines. Multivariate regression models in published observational studies such as logistic regression, linear, Cox and Poisson are increasingly used both at international level, as well as in journals published in Spanish. Copyright © 2015 Sociedad Española de Médicos de Atención Primaria (SEMERGEN). Publicado por Elsevier España, S.L.U. All rights reserved.

Examining the influence of link function misspecification in conventional regression models for developing crash modification factors.

PubMed

Wu, Lingtao; Lord, Dominique

2017-05-01

This study further examined the use of regression models for developing crash modification factors (CMFs), specifically focusing on the misspecification in the link function. The primary objectives were to validate the accuracy of CMFs derived from the commonly used regression models (i.e., generalized linear models or GLMs with additive linear link functions) when some of the variables have nonlinear relationships and quantify the amount of bias as a function of the nonlinearity. Using the concept of artificial realistic data, various linear and nonlinear crash modification functions (CM-Functions) were assumed for three variables. Crash counts were randomly generated based on these CM-Functions. CMFs were then derived from regression models for three different scenarios. The results were compared with the assumed true values. The main findings are summarized as follows: (1) when some variables have nonlinear relationships with crash risk, the CMFs for these variables derived from the commonly used GLMs are all biased, especially around areas away from the baseline conditions (e.g., boundary areas); (2) with the increase in nonlinearity (i.e., nonlinear relationship becomes stronger), the bias becomes more significant; (3) the quality of CMFs for other variables having linear relationships can be influenced when mixed with those having nonlinear relationships, but the accuracy may still be acceptable; and (4) the misuse of the link function for one or more variables can also lead to biased estimates for other parameters. This study raised the importance of the link function when using regression models for developing CMFs. Copyright © 2017 Elsevier Ltd. All rights reserved.

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…

Precision Efficacy Analysis for Regression.

ERIC Educational Resources Information Center

Brooks, Gordon P.

When multiple linear regression is used to develop a prediction model, sample size must be large enough to ensure stable coefficients. If the derivation sample size is inadequate, the model may not predict well for future subjects. The precision efficacy analysis for regression (PEAR) method uses a cross- validity approach to select sample sizes…

Using Linear Regression To Determine the Number of Factors To Retain in Factor Analysis and the Number of Issues To Retain in Delphi Studies and Other Surveys.

ERIC Educational Resources Information Center

Jurs, Stephen; And Others

The scree test and its linear regression technique are reviewed, and results of its use in factor analysis and Delphi data sets are described. The scree test was originally a visual approach for making judgments about eigenvalues, which considered the relationships of the eigenvalues to one another as well as their actual values. The graph that is…

Evaluation of accuracy of linear regression models in predicting urban stormwater discharge characteristics.

PubMed

Madarang, Krish J; Kang, Joo-Hyon

2014-06-01

Stormwater runoff has been identified as a source of pollution for the environment, especially for receiving waters. In order to quantify and manage the impacts of stormwater runoff on the environment, predictive models and mathematical models have been developed. Predictive tools such as regression models have been widely used to predict stormwater discharge characteristics. Storm event characteristics, such as antecedent dry days (ADD), have been related to response variables, such as pollutant loads and concentrations. However it has been a controversial issue among many studies to consider ADD as an important variable in predicting stormwater discharge characteristics. In this study, we examined the accuracy of general linear regression models in predicting discharge characteristics of roadway runoff. A total of 17 storm events were monitored in two highway segments, located in Gwangju, Korea. Data from the monitoring were used to calibrate United States Environmental Protection Agency's Storm Water Management Model (SWMM). The calibrated SWMM was simulated for 55 storm events, and the results of total suspended solid (TSS) discharge loads and event mean concentrations (EMC) were extracted. From these data, linear regression models were developed. R(2) and p-values of the regression of ADD for both TSS loads and EMCs were investigated. Results showed that pollutant loads were better predicted than pollutant EMC in the multiple regression models. Regression may not provide the true effect of site-specific characteristics, due to uncertainty in the data. Copyright © 2014 The Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Birthweight Related Factors in Northwestern Iran: Using Quantile Regression Method.

PubMed

Fallah, Ramazan; Kazemnejad, Anoshirvan; Zayeri, Farid; Shoghli, Alireza

2015-11-18

Birthweight is one of the most important predicting indicators of the health status in adulthood. Having a balanced birthweight is one of the priorities of the health system in most of the industrial and developed countries. This indicator is used to assess the growth and health status of the infants. The aim of this study was to assess the birthweight of the neonates by using quantile regression in Zanjan province. This analytical descriptive study was carried out using pre-registered (March 2010 - March 2012) data of neonates in urban/rural health centers of Zanjan province using multiple-stage cluster sampling. Data were analyzed using multiple linear regressions andquantile regression method and SAS 9.2 statistical software. From 8456 newborn baby, 4146 (49%) were female. The mean age of the mothers was 27.1±5.4 years. The mean birthweight of the neonates was 3104 ± 431 grams. Five hundred and seventy-three patients (6.8%) of the neonates were less than 2500 grams. In all quantiles, gestational age of neonates (p<0.05), weight and educational level of the mothers (p<0.05) showed a linear significant relationship with the i of the neonates. However, sex and birth rank of the neonates, mothers age, place of residence (urban/rural) and career were not significant in all quantiles (p>0.05). This study revealed the results of multiple linear regression and quantile regression were not identical. We strictly recommend the use of quantile regression when an asymmetric response variable or data with outliers is available.

Classification and regression tree analysis vs. multivariable linear and logistic regression methods as statistical tools for studying haemophilia.

PubMed

Henrard, S; Speybroeck, N; Hermans, C

2015-11-01

Haemophilia is a rare genetic haemorrhagic disease characterized by partial or complete deficiency of coagulation factor VIII, for haemophilia A, or IX, for haemophilia B. As in any other medical research domain, the field of haemophilia research is increasingly concerned with finding factors associated with binary or continuous outcomes through multivariable models. Traditional models include multiple logistic regressions, for binary outcomes, and multiple linear regressions for continuous outcomes. Yet these regression models are at times difficult to implement, especially for non-statisticians, and can be difficult to interpret. The present paper sought to didactically explain how, why, and when to use classification and regression tree (CART) analysis for haemophilia research. The CART method is non-parametric and non-linear, based on the repeated partitioning of a sample into subgroups based on a certain criterion. Breiman developed this method in 1984. Classification trees (CTs) are used to analyse categorical outcomes and regression trees (RTs) to analyse continuous ones. The CART methodology has become increasingly popular in the medical field, yet only a few examples of studies using this methodology specifically in haemophilia have to date been published. Two examples using CART analysis and previously published in this field are didactically explained in details. There is increasing interest in using CART analysis in the health domain, primarily due to its ease of implementation, use, and interpretation, thus facilitating medical decision-making. This method should be promoted for analysing continuous or categorical outcomes in haemophilia, when applicable. © 2015 John Wiley & Sons Ltd.

Birthweight Related Factors in Northwestern Iran: Using Quantile Regression Method

PubMed Central

Fallah, Ramazan; Kazemnejad, Anoshirvan; Zayeri, Farid; Shoghli, Alireza

2016-01-01

Introduction: Birthweight is one of the most important predicting indicators of the health status in adulthood. Having a balanced birthweight is one of the priorities of the health system in most of the industrial and developed countries. This indicator is used to assess the growth and health status of the infants. The aim of this study was to assess the birthweight of the neonates by using quantile regression in Zanjan province. Methods: This analytical descriptive study was carried out using pre-registered (March 2010 - March 2012) data of neonates in urban/rural health centers of Zanjan province using multiple-stage cluster sampling. Data were analyzed using multiple linear regressions andquantile regression method and SAS 9.2 statistical software. Results: From 8456 newborn baby, 4146 (49%) were female. The mean age of the mothers was 27.1±5.4 years. The mean birthweight of the neonates was 3104 ± 431 grams. Five hundred and seventy-three patients (6.8%) of the neonates were less than 2500 grams. In all quantiles, gestational age of neonates (p<0.05), weight and educational level of the mothers (p<0.05) showed a linear significant relationship with the i of the neonates. However, sex and birth rank of the neonates, mothers age, place of residence (urban/rural) and career were not significant in all quantiles (p>0.05). Conclusion: This study revealed the results of multiple linear regression and quantile regression were not identical. We strictly recommend the use of quantile regression when an asymmetric response variable or data with outliers is available. PMID:26925889

Application of face centred central composite design to optimise compression force and tablet diameter for the formulation of mechanically strong and fast disintegrating orodispersible tablets.

PubMed

Pabari, Ritesh M; Ramtoola, Zebunnissa

2012-07-01

A two factor, three level (3(2)) face centred, central composite design (CCD) was applied to investigate the main and interaction effects of tablet diameter and compression force (CF) on hardness, disintegration time (DT) and porosity of mannitol based orodispersible tablets (ODTs). Tablet diameters of 10, 13 and 15 mm, and CF of 10, 15 and 20 kN were studied. Results of multiple linear regression analysis show that both the tablet diameter and CF influence tablet characteristics. A negative value of regression coefficient for tablet diameter showed an inverse relationship with hardness and DT. A positive value of regression coefficient for CF indicated an increase in hardness and DT with increasing CF as a result of the decrease in tablet porosity. Interestingly, at the larger tablet diameter of 15 mm, while hardness increased and porosity decreased with an increase in CF, the DT was resistant to change. The optimised combination was a tablet of 15 mm diameter compressed at 15 kN showing a rapid DT of 37.7s and high hardness of 71.4N. Using these parameters, ODTs containing ibuprofen showed no significant change in DT (ANOVA; p>0.05) irrespective of the hydrophobicity of the ibuprofen. Copyright © 2012 Elsevier B.V. All rights reserved.

Relationship between Gender Roles and Sexual Assertiveness in Married Women.

PubMed

Azmoude, Elham; Firoozi, Mahbobe; Sadeghi Sahebzad, Elahe; Asgharipour, Neghar

2016-10-01

Evidence indicates that sexual assertiveness is one of the important factors affecting sexual satisfaction. According to some studies, traditional gender norms conflict with women's capability in expressing sexual desires. This study examined the relationship between gender roles and sexual assertiveness in married women in Mashhad, Iran. This cross-sectional study was conducted on 120 women who referred to Mashhad health centers through convenient sampling in 2014-15. Data were collected using Bem Sex Role Inventory (BSRI) and Hulbert index of sexual assertiveness. Data were analyzed using SPSS 16 by Pearson and Spearman's correlation tests and linear Regression Analysis. The mean scores of sexual assertiveness was 54.93±13.20. According to the findings, there was non-significant correlation between Femininity and masculinity score with sexual assertiveness (P=0.069 and P=0.080 respectively). Linear regression analysis indicated that among the predictor variables, only Sexual function satisfaction was identified as the sexual assertiveness summary predictor variables (P=0.001). Based on the results, sexual assertiveness in married women does not comply with gender role, but it is related to Sexual function satisfaction. So, counseling psychologists need to consider this variable when designing intervention programs for modifying sexual assertiveness and find other variables that affect sexual assertiveness.

Impact of Trichiasis Surgery on Physical Functioning in Ethiopian Patients: STAR Trial

PubMed Central

Wolle, Meraf A.; Cassard, Sandra D.; Gower, Emily W.; Munoz, Beatriz E.; Wang, Jiangxia; Alemayehu, Wondu; West, Sheila K.

2010-01-01

Purpose To evaluate the physical functioning of Ethiopian trichiasis surgery patients before and six months after surgery. Design Nested Cohort Study Methods This study was nested within the Surgery for Trichiasis, Antibiotics to Prevent Recurrence (STAR) clinical trial conducted in Ethiopia. Demographic information, ocular examinations, and physical functioning assessments were collected before and 6 months after surgery. A single score for patients’ physical functioning was constructed using Rasch analysis. A multivariate linear regression model was used to determine if change in physical functioning was associated with change in visual acuity. Results Of the 438 participants, 411 (93.8%) had both baseline and follow-up questionnaires. Physical functioning scores at baseline ranged from −6.32 (great difficulty) to +6.01 (no difficulty). The percent of participants reporting no difficulty in physical functioning increased by 32.6%; the proportion of participants in the mild/no visual impairment category increased by 8.6%. A multivariate linear regression model showed that for every line of vision gained, physical functioning improves significantly (0.09 units; 95% CI: 0.02–0.16). Conclusions Surgery to correct trichiasis appears to improve patients’ physical functioning as measured at 6 months. More effort in promoting trichiasis surgery is essential, not only to prevent corneal blindness, but also to enable improved functioning in daily life. PMID:21333268

Decisional balance and self-efficacy of physical activity among the elderly in Rasht in 2013 based on the transtheoretical model

PubMed Central

Abbaspour, Seddigheh; Farmanbar, Rabiollah; Njafi, Fateme; Ghiasvand, Arezoo Mohamadkhani; Dehghankar, Leila

2017-01-01

Background Regular physical activity has been considered as health promotion, and identifying different effective psycho-social variables on physical has proven to be essential. Objective To identify the relationship between decisional balance and self-efficacy in physical activities using the transtheoretical model in the members of a retirement center in Rasht, Guillen. Methods A descriptive cross-sectional study was conducted in 2013 by using convenient sampling on 262 elderly people who are the members of retirement centers in Rasht. Data were collected using Stages of change, Decisional balance, Self-efficacy and Physical Activity Scale for the Elderly (PASE). Data was analyzed using SPSS-16 software, descriptive and analytic statistic (Pearson correlation, Spearman, ANOVA, HSD Tukey, linear and ordinal regression). Results The majority of participants were in maintenance stage. Mean and standard deviation physical activity for the elderly was 119.35±51.50. Stages of change and physical activities were significantly associated with decisional balance and self-efficacy (p<0.0001); however, cons had a significant and reverse association. According to linear and ordinal regression the only predicator variable of physical activity behavior was self-efficacy. Conclusion By increase in pros and self-efficacy on doing physical activity, it can be benefited in designing appropriate intervention programs. PMID:28713520

Relationship between Gender Roles and Sexual Assertiveness in Married Women

PubMed Central

Azmoude, Elham; Firoozi, Mahbobe; Sadeghi Sahebzad, Elahe; Asgharipour, Neghar

2016-01-01

ABSTRACT Background: Evidence indicates that sexual assertiveness is one of the important factors affecting sexual satisfaction. According to some studies, traditional gender norms conflict with women’s capability in expressing sexual desires. This study examined the relationship between gender roles and sexual assertiveness in married women in Mashhad, Iran. Methods: This cross-sectional study was conducted on 120 women who referred to Mashhad health centers through convenient sampling in 2014-15. Data were collected using Bem Sex Role Inventory (BSRI) and Hulbert index of sexual assertiveness. Data were analyzed using SPSS 16 by Pearson and Spearman’s correlation tests and linear Regression Analysis. Results: The mean scores of sexual assertiveness was 54.93±13.20. According to the findings, there was non-significant correlation between Femininity and masculinity score with sexual assertiveness (P=0.069 and P=0.080 respectively). Linear regression analysis indicated that among the predictor variables, only Sexual function satisfaction was identified as the sexual assertiveness summary predictor variables (P=0.001). Conclusion: Based on the results, sexual assertiveness in married women does not comply with gender role, but it is related to Sexual function satisfaction. So, counseling psychologists need to consider this variable when designing intervention programs for modifying sexual assertiveness and find other variables that affect sexual assertiveness. PMID:27713899

Factors affecting metacognition of undergraduate nursing students in a blended learning environment.

PubMed

Hsu, Li-Ling; Hsieh, Suh-Ing

2014-06-01

This paper is a report of a study to examine the influence of demographic, learning involvement and learning performance variables on metacognition of undergraduate nursing students in a blended learning environment. A cross-sectional, correlational survey design was adopted. Ninety-nine students invited to participate in the study were enrolled in a professional nursing ethics course at a public nursing college. The blended learning intervention is basically an assimilation of classroom learning and online learning. Simple linear regression showed significant associations between frequency of online dialogues, the Case Analysis Attitude Scale scores, the Case Analysis Self Evaluation Scale scores, the Blended Learning Satisfaction Scale scores, and Metacognition Scale scores. Multiple linear regression indicated that frequency of online dialogues, the Case Analysis Self Evaluation Scale and the Blended Learning Satisfaction Scale were significant independent predictors of metacognition. Overall, the model accounted for almost half of the variance in metacognition. The blended learning module developed in this study proved successful in the end as a catalyst for the exercising of metacognitive abilities by the sample of nursing students. Learners are able to develop metacognitive ability in comprehension, argumentation, reasoning and various forms of higher order thinking through the blended learning process. © 2013 Wiley Publishing Asia Pty Ltd.

Efficient robust doubly adaptive regularized regression with applications.

PubMed

Karunamuni, Rohana J; Kong, Linglong; Tu, Wei

2018-01-01

We consider the problem of estimation and variable selection for general linear regression models. Regularized regression procedures have been widely used for variable selection, but most existing methods perform poorly in the presence of outliers. We construct a new penalized procedure that simultaneously attains full efficiency and maximum robustness. Furthermore, the proposed procedure satisfies the oracle properties. The new procedure is designed to achieve sparse and robust solutions by imposing adaptive weights on both the decision loss and the penalty function. The proposed method of estimation and variable selection attains full efficiency when the model is correct and, at the same time, achieves maximum robustness when outliers are present. We examine the robustness properties using the finite-sample breakdown point and an influence function. We show that the proposed estimator attains the maximum breakdown point. Furthermore, there is no loss in efficiency when there are no outliers or the error distribution is normal. For practical implementation of the proposed method, we present a computational algorithm. We examine the finite-sample and robustness properties using Monte Carlo studies. Two datasets are also analyzed.

A piecewise regression approach for determining biologically relevant hydraulic thresholds for the protection of fishes at river infrastructure.

PubMed

Boys, C A; Robinson, W; Miller, B; Pflugrath, B; Baumgartner, L J; Navarro, A; Brown, R; Deng, Z

2016-05-01

A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species, Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus, following simulated infrastructure passage in a barometric chamber. The probability of injuries such as swimbladder rupture, exophthalmia and haemorrhage, and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change, R(NE:A) ) reduced. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in R(NE:A) that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multispecies precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (R(NE:A) of 0·7) should protect downstream migrating juveniles of these two physoclistous species sufficiently. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones. © 2016 The Fisheries Society of the British Isles.

The application of SVR model in the improvement of QbD: a case study of the extraction of podophyllotoxin.

PubMed

Zhai, Chun-Hui; Xuan, Jian-Bang; Fan, Hai-Liu; Zhao, Teng-Fei; Jiang, Jian-Lan

2018-05-03

In order to make a further optimization of process design via increasing the stability of design space, we brought in the model of Support Vector Regression (SVR). In this work, the extraction of podophyllotoxin was researched as a case study based on Quality by Design (QbD). We compared the fitting effect of SVR and the most used quadratic polynomial model (QPM) in QbD, and an analysis was made between the two design spaces obtained by SVR and QPM. As a result, the SVR stayed ahead of QPM in prediction accuracy, the stability of model and the generalization ability. The introduction of SVR into QbD made the extraction process of podophyllotoxin well designed and easier to control. The better fitting effect of SVR improved the application effect of QbD and the universal applicability of SVR, especially for non-linear, complicated and weak-regularity problems, widened the application field of QbD.

Medical image enhancement using resolution synthesis

NASA Astrophysics Data System (ADS)

Wong, Tak-Shing; Bouman, Charles A.; Thibault, Jean-Baptiste; Sauer, Ken D.

2011-03-01

We introduce a post-processing approach to improve the quality of CT reconstructed images. The scheme is adapted from the resolution-synthesis (RS)1 interpolation algorithm. In this approach, we consider the input image, scanned at a particular dose level, as a degraded version of a high quality image scanned at a high dose level. Image enhancement is achieved by predicting the high quality image by classification based linear regression. To improve the robustness of our scheme, we also apply the minimum description length principle to determine the optimal number of predictors to use in the scheme, and the ridge regression to regularize the design of the predictors. Experimental results show that our scheme is effective in reducing the noise in images reconstructed from filtered back projection without significant loss of image details. Alternatively, our scheme can also be applied to reduce dose while maintaining image quality at an acceptable level.

Some comparisons of complexity in dictionary-based and linear computational models.

PubMed

Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

2011-03-01

Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator. Copyright © 2010 Elsevier Ltd. All rights reserved.

Comparison of linear and non-linear models for predicting energy expenditure from raw accelerometer data.

PubMed

Montoye, Alexander H K; Begum, Munni; Henning, Zachary; Pfeiffer, Karin A

2017-02-01

This study had three purposes, all related to evaluating energy expenditure (EE) prediction accuracy from body-worn accelerometers: (1) compare linear regression to linear mixed models, (2) compare linear models to artificial neural network models, and (3) compare accuracy of accelerometers placed on the hip, thigh, and wrists. Forty individuals performed 13 activities in a 90 min semi-structured, laboratory-based protocol. Participants wore accelerometers on the right hip, right thigh, and both wrists and a portable metabolic analyzer (EE criterion). Four EE prediction models were developed for each accelerometer: linear regression, linear mixed, and two ANN models. EE prediction accuracy was assessed using correlations, root mean square error (RMSE), and bias and was compared across models and accelerometers using repeated-measures analysis of variance. For all accelerometer placements, there were no significant differences for correlations or RMSE between linear regression and linear mixed models (correlations: r  =  0.71-0.88, RMSE: 1.11-1.61 METs; p  >  0.05). For the thigh-worn accelerometer, there were no differences in correlations or RMSE between linear and ANN models (ANN-correlations: r  =  0.89, RMSE: 1.07-1.08 METs. Linear models-correlations: r  =  0.88, RMSE: 1.10-1.11 METs; p  >  0.05). Conversely, one ANN had higher correlations and lower RMSE than both linear models for the hip (ANN-correlation: r  =  0.88, RMSE: 1.12 METs. Linear models-correlations: r  =  0.86, RMSE: 1.18-1.19 METs; p  <  0.05), and both ANNs had higher correlations and lower RMSE than both linear models for the wrist-worn accelerometers (ANN-correlations: r  =  0.82-0.84, RMSE: 1.26-1.32 METs. Linear models-correlations: r  =  0.71-0.73, RMSE: 1.55-1.61 METs; p  <  0.01). For studies using wrist-worn accelerometers, machine learning models offer a significant improvement in EE prediction accuracy over linear models. Conversely, linear models showed similar EE prediction accuracy to machine learning models for hip- and thigh-worn accelerometers and may be viable alternative modeling techniques for EE prediction for hip- or thigh-worn accelerometers.

Diagnosis of Enzyme Inhibition Using Excel Solver: A Combined Dry and Wet Laboratory Exercise

ERIC Educational Resources Information Center

Dias, Albino A.; Pinto, Paula A.; Fraga, Irene; Bezerra, Rui M. F.

2014-01-01

In enzyme kinetic studies, linear transformations of the Michaelis-Menten equation, such as the Lineweaver-Burk double-reciprocal transformation, present some constraints. The linear transformation distorts the experimental error and the relationship between "x" and "y" axes; consequently, linear regression of transformed data…

4D-LQTA-QSAR and docking study on potent Gram-negative specific LpxC inhibitors: a comparison to CoMFA modeling.

PubMed

Ghasemi, Jahan B; Safavi-Sohi, Reihaneh; Barbosa, Euzébio G

2012-02-01

A quasi 4D-QSAR has been carried out on a series of potent Gram-negative LpxC inhibitors. This approach makes use of the molecular dynamics (MD) trajectories and topology information retrieved from the GROMACS package. This new methodology is based on the generation of a conformational ensemble profile, CEP, for each compound instead of only one conformation, followed by the calculation intermolecular interaction energies at each grid point considering probes and all aligned conformations resulting from MD simulations. These interaction energies are independent variables employed in a QSAR analysis. The comparison of the proposed methodology to comparative molecular field analysis (CoMFA) formalism was performed. This methodology explores jointly the main features of CoMFA and 4D-QSAR models. Step-wise multiple linear regression was used for the selection of the most informative variables. After variable selection, multiple linear regression (MLR) and partial least squares (PLS) methods used for building the regression models. Leave-N-out cross-validation (LNO), and Y-randomization were performed in order to confirm the robustness of the model in addition to analysis of the independent test set. Best models provided the following statistics: [Formula in text] (PLS) and [Formula in text] (MLR). Docking study was applied to investigate the major interactions in protein-ligand complex with CDOCKER algorithm. Visualization of the descriptors of the best model helps us to interpret the model from the chemical point of view, supporting the applicability of this new approach in rational drug design.

A decline in the prevalence of injecting drug users in Estonia, 2005–2009

PubMed Central

Uusküla, A; Rajaleid, K; Talu, A; Abel-Ollo, K; Des Jarlais, DC

2013-01-01

Aims and setting Descriptions of behavioural epidemics have received little attention compared with infectious disease epidemics in Eastern Europe. Here we report a study aimed at estimating trends in the prevalence of injection drug use between 2005 and 2009 in Estonia. Design and methods The number of injection drug users (IDUs) aged 15–44 each year between 2005 and 2009 was estimated using capture-recapture methodology based on 4 data sources (2 treatment data bases: drug abuse and non-fatal overdose treatment; criminal justice (drug related offences) and mortality (injection drug use related deaths) data). Poisson log-linear regression models were applied to the matched data, with interactions between data sources fitted to replicate the dependencies between the data sources. Linear regression was used to estimate average change over time. Findings there were 24305, 12292, 238, 545 records and 8100, 1655, 155, 545 individual IDUs identified in the four capture sources (Police, drug treatment, overdose, and death registry, accordingly) over the period 2005 – 2009. The estimated prevalence of IDUs among the population aged 15–44 declined from 2.7% (1.8–7.9%) in 2005 to 2.0% (1.4–5.0%) in 2008, and 0.9% (0.7–1.7%) in 2009. Regression analysis indicated an average reduction of over 1700 injectors per year. Conclusion While the capture-recapture method has known limitations, the results are consistent with other data from Estonia. Identifying the drivers of change in the prevalence of injection drug use warrants further research. PMID:23290632

Secure Logistic Regression Based on Homomorphic Encryption: Design and Evaluation.

PubMed

Kim, Miran; Song, Yongsoo; Wang, Shuang; Xia, Yuhou; Jiang, Xiaoqian

2018-04-17

Learning a model without accessing raw data has been an intriguing idea to security and machine learning researchers for years. In an ideal setting, we want to encrypt sensitive data to store them on a commercial cloud and run certain analyses without ever decrypting the data to preserve privacy. Homomorphic encryption technique is a promising candidate for secure data outsourcing, but it is a very challenging task to support real-world machine learning tasks. Existing frameworks can only handle simplified cases with low-degree polynomials such as linear means classifier and linear discriminative analysis. The goal of this study is to provide a practical support to the mainstream learning models (eg, logistic regression). We adapted a novel homomorphic encryption scheme optimized for real numbers computation. We devised (1) the least squares approximation of the logistic function for accuracy and efficiency (ie, reduce computation cost) and (2) new packing and parallelization techniques. Using real-world datasets, we evaluated the performance of our model and demonstrated its feasibility in speed and memory consumption. For example, it took approximately 116 minutes to obtain the training model from the homomorphically encrypted Edinburgh dataset. In addition, it gives fairly accurate predictions on the testing dataset. We present the first homomorphically encrypted logistic regression outsourcing model based on the critical observation that the precision loss of classification models is sufficiently small so that the decision plan stays still. ©Miran Kim, Yongsoo Song, Shuang Wang, Yuhou Xia, Xiaoqian Jiang. Originally published in JMIR Medical Informatics (http://medinform.jmir.org), 17.04.2018.

Correlation of Vitamin D status and orthodontic-induced external apical root resorption.

PubMed

Tehranchi, Azita; Sadighnia, Azin; Younessian, Farnaz; Abdi, Amir H; Shirvani, Armin

2017-01-01

Adequate Vitamin D is essential for dental and skeletal health in children and adult. The purpose of this study was to assess the correlation of serum Vitamin D level with external-induced apical root resorption (EARR) following fixed orthodontic treatment. In this cross-sectional study, the prevalence of Vitamin D deficiency (defined by25-hydroxyvitamin-D) was determined in 34 patients (23.5% male; age range 12-23 years; mean age 16.63 ± 2.84) treated with fixed orthodontic treatment. Root resorption of four maxillary incisors was measured using before and after periapical radiographs (136 measured teeth) by means of a design-to-purpose software to optimize data collection. Teeth with a maximum percentage of root resorption (%EARR) were indicated as representative root resorption for each patient. A multiple linear regression model and Pearson correlation coefficient were used to assess the association of Vitamin D status and observed EARR. P < 0.05 was considered statistically significant. The Pearson coefficient between these two variables was determined about 0.15 ( P = 0.38). Regression analysis revealed that Vitamin D status of the patients demonstrated no significant statistical correlation with EARR, after adjustment of confounding variables using linear regression model ( P > 0.05). This study suggests that Vitamin D level is not among the clinical variables that are potential contributors for EARR. The prevalence of Vitamin D deficiency does not differ in patients with higher EARR. These data suggest the possibility that Vitamin D insufficiency may not contribute to the development of more apical root resorption although this remains to be confirmed by further longitudinal cohort studies.

Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

PubMed

Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan

2012-01-01

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

Clustering performance comparison using K-means and expectation maximization algorithms.

PubMed

Jung, Yong Gyu; Kang, Min Soo; Heo, Jun

2014-11-14

Clustering is an important means of data mining based on separating data categories by similar features. Unlike the classification algorithm, clustering belongs to the unsupervised type of algorithms. Two representatives of the clustering algorithms are the K -means and the expectation maximization (EM) algorithm. Linear regression analysis was extended to the category-type dependent variable, while logistic regression was achieved using a linear combination of independent variables. To predict the possibility of occurrence of an event, a statistical approach is used. However, the classification of all data by means of logistic regression analysis cannot guarantee the accuracy of the results. In this paper, the logistic regression analysis is applied to EM clusters and the K -means clustering method for quality assessment of red wine, and a method is proposed for ensuring the accuracy of the classification results.

Improvement of Storm Forecasts Using Gridded Bayesian Linear Regression for Northeast United States

NASA Astrophysics Data System (ADS)

Yang, J.; Astitha, M.; Schwartz, C. S.

2017-12-01

Bayesian linear regression (BLR) is a post-processing technique in which regression coefficients are derived and used to correct raw forecasts based on pairs of observation-model values. This study presents the development and application of a gridded Bayesian linear regression (GBLR) as a new post-processing technique to improve numerical weather prediction (NWP) of rain and wind storm forecasts over northeast United States. Ten controlled variables produced from ten ensemble members of the National Center for Atmospheric Research (NCAR) real-time prediction system are used for a GBLR model. In the GBLR framework, leave-one-storm-out cross-validation is utilized to study the performances of the post-processing technique in a database composed of 92 storms. To estimate the regression coefficients of the GBLR, optimization procedures that minimize the systematic and random error of predicted atmospheric variables (wind speed, precipitation, etc.) are implemented for the modeled-observed pairs of training storms. The regression coefficients calculated for meteorological stations of the National Weather Service are interpolated back to the model domain. An analysis of forecast improvements based on error reductions during the storms will demonstrate the value of GBLR approach. This presentation will also illustrate how the variances are optimized for the training partition in GBLR and discuss the verification strategy for grid points where no observations are available. The new post-processing technique is successful in improving wind speed and precipitation storm forecasts using past event-based data and has the potential to be implemented in real-time.

Kinetic microplate bioassays for relative potency of antibiotics improved by partial Least Square (PLS) regression.

PubMed

Francisco, Fabiane Lacerda; Saviano, Alessandro Morais; Almeida, Túlia de Souza Botelho; Lourenço, Felipe Rebello

2016-05-01

Microbiological assays are widely used to estimate the relative potencies of antibiotics in order to guarantee the efficacy, safety, and quality of drug products. Despite of the advantages of turbidimetric bioassays when compared to other methods, it has limitations concerning the linearity and range of the dose-response curve determination. Here, we proposed to use partial least squares (PLS) regression to solve these limitations and to improve the prediction of relative potencies of antibiotics. Kinetic-reading microplate turbidimetric bioassays for apramacyin and vancomycin were performed using Escherichia coli (ATCC 8739) and Bacillus subtilis (ATCC 6633), respectively. Microbial growths were measured as absorbance up to 180 and 300min for apramycin and vancomycin turbidimetric bioassays, respectively. Conventional dose-response curves (absorbances or area under the microbial growth curve vs. log of antibiotic concentration) showed significant regression, however there were significant deviation of linearity. Thus, they could not be used for relative potency estimations. PLS regression allowed us to construct a predictive model for estimating the relative potencies of apramycin and vancomycin without over-fitting and it improved the linear range of turbidimetric bioassay. In addition, PLS regression provided predictions of relative potencies equivalent to those obtained from agar diffusion official methods. Therefore, we conclude that PLS regression may be used to estimate the relative potencies of antibiotics with significant advantages when compared to conventional dose-response curve determination. Copyright © 2016 Elsevier B.V. All rights reserved.

A Note on the Relationship between the Number of Indicators and Their Reliability in Detecting Regression Coefficients in Latent Regression Analysis

ERIC Educational Resources Information Center

Dolan, Conor V.; Wicherts, Jelte M.; Molenaar, Peter C. M.

2004-01-01

We consider the question of how variation in the number and reliability of indicators affects the power to reject the hypothesis that the regression coefficients are zero in latent linear regression analysis. We show that power remains constant as long as the coefficient of determination remains unchanged. Any increase in the number of indicators…

Experimental design and data analysis of Ago-RIP-Seq experiments for the identification of microRNA targets.

PubMed

Tichy, Diana; Pickl, Julia Maria Anna; Benner, Axel; Sültmann, Holger

2017-03-31

The identification of microRNA (miRNA) target genes is crucial for understanding miRNA function. Many methods for the genome-wide miRNA target identification have been developed in recent years; however, they have several limitations including the dependence on low-confident prediction programs and artificial miRNA manipulations. Ago-RNA immunoprecipitation combined with high-throughput sequencing (Ago-RIP-Seq) is a promising alternative. However, appropriate statistical data analysis algorithms taking into account the experimental design and the inherent noise of such experiments are largely lacking.Here, we investigate the experimental design for Ago-RIP-Seq and examine biostatistical methods to identify de novo miRNA target genes. Statistical approaches considered are either based on a negative binomial model fit to the read count data or applied to transformed data using a normal distribution-based generalized linear model. We compare them by a real data simulation study using plasmode data sets and evaluate the suitability of the approaches to detect true miRNA targets by sensitivity and false discovery rates. Our results suggest that simple approaches like linear regression models on (appropriately) transformed read count data are preferable. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

A regression technique for evaluation and quantification for water quality parameters from remote sensing data

NASA Technical Reports Server (NTRS)

Whitlock, C. H.; Kuo, C. Y.

1979-01-01

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

Breakfast intake among adults with type 2 diabetes: is bigger better?

PubMed Central

Jarvandi, Soghra; Schootman, Mario; Racette, Susan B.

2015-01-01

Objective To assess the association between breakfast energy and total daily energy intake among individuals with type 2 diabetes. Design Cross-sectional study. Daily energy intake was computed from a 24-h dietary recall. Multiple regression models were used to estimate the association between daily energy intake (dependent variable) and quartiles of energy intake at breakfast (independent variable) expressed as either absolute or relative (% of total daily energy intake) terms. Orthogonal polynomial contrasts were used to test for linear and quadratic trends. Models were controlled for sex, age, race/ethnicity, body mass index, physical activity and smoking. In addition, we used separate multiple regression models to test the effect of quartiles of absolute and relative breakfast energy on intake at lunch, dinner, and snacks. Setting The 1999–2004 National Health and Nutrition Examination Survey (NHANES). Subjects Participants aged ≥ 30 years with self-reported history of diabetes (N = 1,146). Results Daily energy intake increased as absolute breakfast energy intake increased (linear trend, P < 0.0001; quadratic trend, P = 0.02), but decreased as relative breakfast energy intake increased (linear trend, P < 0.0001). In addition, while higher quartiles of absolute breakfast intake had no associations with energy intake at subsequent meals, higher quartiles of relative breakfast intake were associated with lower energy intake during all subsequent meals and snacks (P < 0.05). Conclusions Consuming a breakfast that provided less energy or comprised a greater proportion of daily energy intake was associated with lower total daily energy intake in adults with type 2 diabetes. PMID:25529061

Prostate specific antigen velocity as a measure of the natural history of prostate cancer: defining a 'rapid riser' subset.

PubMed

Nam, R K; Klotz, L H; Jewett, M A; Danjoux, C; Trachtenberg, J

1998-01-01

To study the rate of change in prostate specific antigen (PSA velocity) in patients with prostate cancer initially managed by 'watchful waiting'. Serial PSA levels were determined in 141 patients with prostate cancer confirmed by biopsy, who were initially managed expectantly and enrolled between May 1990 and December 1995. Sixty-seven patients eventually underwent surgery (mean age 59 years) because they chose it (the decision for surgery was not based on PSA velocity). A cohort of 74 patients remained on 'watchful waiting' (mean age 69 years). Linear regression and logarithmic transformations were used to segregate those patients who showed a rapid rise, defined as a > 50% rise in PSA per year (or a doubling time of < 2 years) and designated 'rapid risers'. An initial analysis based on a minimum of two PSA values showed that 31% were rapid risers. Only 15% of patients with more than three serial PSA determinations over > or = 6 months showed a rapid rise in PSA level. There was no advantage of log-linear analysis over linear regression models. Three serial PSA determinations over > or = 6 months in patients with clinically localized prostate cancer identifies a subset (15%) of patients with a rapidly rising PSA level. Shorter PSA surveillance with fewer PSA values may falsely identify patients with rapid rises in PSA level. However, further follow-up is required to determine if a rapid rise in PSA level identifies a subset of patients with an aggressive biological phenotype who are either still curable or who have already progressed to incurability through metastatic disease.

Physical activity volume in relation to risk of atrial fibrillation. A non-linear meta-regression analysis.

PubMed

Ricci, Cristian; Gervasi, Federico; Gaeta, Maddalena; Smuts, Cornelius M; Schutte, Aletta E; Leitzmann, Michael F

2018-05-01

Background Light physical activity is known to reduce atrial fibrillation risk, whereas moderate to vigorous physical activity may result in an increased risk. However, the question of what volume of physical activity can be considered beneficial remains poorly understood. The scope of the present work was to examine the relation between physical activity volume and atrial fibrillation risk. Design A comprehensive systematic review was performed following the PRISMA guidelines. Methods A non-linear meta-regression considering the amount of energy spent in physical activity was carried out. The first derivative of the non-linear relation between physical activity and atrial fibrillation risk was evaluated to determine the volume of physical activity that carried the minimum atrial fibrillation risk. Results The dose-response analysis of the relation between physical activity and atrial fibrillation risk showed that physical activity at volumes of 5-20 metabolic equivalents per week (MET-h/week) was associated with significant reduction in atrial fibrillation risk (relative risk for 19 MET-h/week = 0.92 (0.87, 0.98). By comparison, physical activity volumes exceeding 20 MET-h/week were unrelated to atrial fibrillation risk (relative risk for 21 MET-h/week = 0.95 (0.88, 1.02). Conclusion These data show a J-shaped relation between physical activity volume and atrial fibrillation risk. Physical activity at volumes of up to 20 MET-h/week is associated with reduced atrial fibrillation risk, whereas volumes exceeding 20 MET-h/week show no relation with risk.

Quantifying Main Trends in Lysozyme Nucleation: The Effects of Precipitant Concentration, Supersaturation and Impurities

NASA Technical Reports Server (NTRS)

Burke, Michael W.; Leardi, Riccardo; Judge, Russell A.; Pusey, Marc L.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Full factorial experimental design incorporating multi-linear regression analysis of the experimental data allows quick identification of main trends and effects using a limited number of experiments. In this study these techniques were employed to identify the effect of precipitant concentration, supersaturation, and the presence of an impurity, the physiological lysozyme dimer, on the nucleation rate and crystal dimensions of the tetragonal forin of chicken egg white lysozyme. Decreasing precipitant concentration, increasing supers aturation, and increasing impurity, were found to increase crystal numbers. The crystal axial ratio decreased with increasing precipitant concentration, independent of impurity.

Designing pinhole vacancies in graphene towards functionalization: Effects on critical buckling load

NASA Astrophysics Data System (ADS)

Georgantzinos, S. K.; Markolefas, S.; Giannopoulos, G. I.; Katsareas, D. E.; Anifantis, N. K.

2017-03-01

The effect of size and placement of pinhole-type atom vacancies on Euler's critical load on free-standing, monolayer graphene, is investigated. The graphene is modeled by a structural spring-based finite element approach, in which every interatomic interaction is approached as a linear spring. The geometry of graphene and the pinhole size lead to the assembly of the stiffness matrix of the nanostructure. Definition of the boundary conditions of the problem leads to the solution of the eigenvalue problem and consequently to the critical buckling load. Comparison to results found in the literature illustrates the validity and accuracy of the proposed method. Parametric analysis regarding the placement and size of the pinhole-type vacancy, as well as the graphene geometry, depicts the effects on critical buckling load. Non-linear regression analysis leads to empirical-analytical equations for predicting the buckling behavior of graphene, with engineered pinhole-type atom vacancies.

Analysis of relativistic nucleus-nucleus interactions in emulsion chambers

NASA Technical Reports Server (NTRS)

Mcguire, Stephen C.

1987-01-01

The development of a computer-assisted method is reported for the determination of the angular distribution data for secondary particles produced in relativistic nucleus-nucleus collisions in emulsions. The method is applied to emulsion detectors that were placed in a constant, uniform magnetic field and exposed to beams of 60 and 200 GeV/nucleon O-16 ions at the Super Proton Synchrotron (SPS) of the European Center for Nuclear Research (CERN). Linear regression analysis is used to determine the azimuthal and polar emission angles from measured track coordinate data. The software, written in BASIC, is designed to be machine independent, and adaptable to an automated system for acquiring the track coordinates. The fitting algorithm is deterministic, and takes into account the experimental uncertainty in the measured points. Further, a procedure for using the track data to estimate the linear momenta of the charged particles observed in the detectors is included.

Development of a Multiple Linear Regression Model to Forecast Facility Electrical Consumption at an Air Force Base.

DTIC Science & Technology

1981-09-01

corresponds to the same square footage that consumed the electrical energy. 3. The basic assumptions of multiple linear regres- sion, as enumerated in...7. Data related to the sample of bases is assumed to be representative of bases in the population. Limitations Basic limitations on this research were... Ratemaking --Overview. Rand Report R-5894, Santa Monica CA, May 1977. Chatterjee, Samprit, and Bertram Price. Regression Analysis by Example. New York: John

Cumulative childhood risk and adult functioning in abused and neglected children grown up

PubMed Central

HORAN, JACQUELINE M.; WIDOM, CATHY SPATZ

2017-01-01

This paper examines the relationship between childhood exposure to cumulative risk and three indicators of psychosocial adjustment in adulthood (educational attainment, mental health, and criminal behavior) and tests three different models (linear, quadratic, and interaction). Data were collected over several time points from individuals who were part of a prospective cohort design study that matched children with documented cases of abuse and/or neglect with children without such histories and followed them into adulthood. Hierarchical multiple regressions compared linear and quadratic models and then examined potential moderating effects of child abuse/neglect and gender. Exposure to a greater number of childhood risk factors was significantly related to fewer years of education, more anxiety and depression symptomatology, and more criminal arrests in adulthood. The relationship between cumulative risk and years of education demonstrated a curvilinear pattern, whereas the relationship between cumulative risk and both mental health and criminal arrests was linear. Child abuse/neglect did not moderate these relationships, although there were direct effects for both child abuse/neglect and gender on criminal arrests, with more arrests for abused/neglected individuals than controls and more for males than females. Gender interacted with cumulative risk to impact educational attainment and criminal behavior, suggesting that interventions may be more effective if tailored differently for males and females. Interventions may need to be multifaceted and designed to address these different domains of functioning. PMID:25196178

Cumulative childhood risk and adult functioning in abused and neglected children grown up.

PubMed

Horan, Jacqueline M; Widom, Cathy Spatz

2015-08-01

This paper examines the relationship between childhood exposure to cumulative risk and three indicators of psychosocial adjustment in adulthood (educational attainment, mental health, and criminal behavior) and tests three different models (linear, quadratic, and interaction). Data were collected over several time points from individuals who were part of a prospective cohort design study that matched children with documented cases of abuse and/or neglect with children without such histories and followed them into adulthood. Hierarchical multiple regressions compared linear and quadratic models and then examined potential moderating effects of child abuse/neglect and gender. Exposure to a greater number of childhood risk factors was significantly related to fewer years of education, more anxiety and depression symptomatology, and more criminal arrests in adulthood. The relationship between cumulative risk and years of education demonstrated a curvilinear pattern, whereas the relationship between cumulative risk and both mental health and criminal arrests was linear. Child abuse/neglect did not moderate these relationships, although there were direct effects for both child abuse/neglect and gender on criminal arrests, with more arrests for abused/neglected individuals than controls and more for males than females. Gender interacted with cumulative risk to impact educational attainment and criminal behavior, suggesting that interventions may be more effective if tailored differently for males and females. Interventions may need to be multifaceted and designed to address these different domains of functioning.

Study on power grid characteristics in summer based on Linear regression analysis

NASA Astrophysics Data System (ADS)

Tang, Jin-hui; Liu, You-fei; Liu, Juan; Liu, Qiang; Liu, Zhuan; Xu, Xi

2018-05-01

The correlation analysis of power load and temperature is the precondition and foundation for accurate load prediction, and a great deal of research has been made. This paper constructed the linear correlation model between temperature and power load, then the correlation of fault maintenance work orders with the power load is researched. Data details of Jiangxi province in 2017 summer such as temperature, power load, fault maintenance work orders were adopted in this paper to develop data analysis and mining. Linear regression models established in this paper will promote electricity load growth forecast, fault repair work order review, distribution network operation weakness analysis and other work to further deepen the refinement.

Linear models for assessing mechanisms of sperm competition: the trouble with transformations.

PubMed

Eggert, Anne-Katrin; Reinhardt, Klaus; Sakaluk, Scott K

2003-01-01

Although sperm competition is a pervasive selective force shaping the reproductive tactics of males, the mechanisms underlying different patterns of sperm precedence remain obscure. Parker et al. (1990) developed a series of linear models designed to identify two of the more basic mechanisms: sperm lotteries and sperm displacement; the models can be tested experimentally by manipulating the relative numbers of sperm transferred by rival males and determining the paternity of offspring. Here we show that tests of the model derived for sperm lotteries can result in misleading inferences about the underlying mechanism of sperm precedence because the required inverse transformations may lead to a violation of fundamental assumptions of linear regression. We show that this problem can be remedied by reformulating the model using the actual numbers of offspring sired by each male, and log-transforming both sides of the resultant equation. Reassessment of data from a previous study (Sakaluk and Eggert 1996) using the corrected version of the model revealed that we should not have excluded a simple sperm lottery as a possible mechanism of sperm competition in decorated crickets, Gryllodes sigillatus.

Interpreting Regression Results: beta Weights and Structure Coefficients are Both Important.

ERIC Educational Resources Information Center

Thompson, Bruce

Various realizations have led to less frequent use of the "OVA" methods (analysis of variance--ANOVA--among others) and to more frequent use of general linear model approaches such as regression. However, too few researchers understand all the various coefficients produced in regression. This paper explains these coefficients and their…

Spatial Assessment of Model Errors from Four Regression Techniques

Treesearch

Lianjun Zhang; Jeffrey H. Gove; Jeffrey H. Gove

2005-01-01

Fomst modelers have attempted to account for the spatial autocorrelations among trees in growth and yield models by applying alternative regression techniques such as linear mixed models (LMM), generalized additive models (GAM), and geographicalIy weighted regression (GWR). However, the model errors are commonly assessed using average errors across the entire study...

Quantile Regression in the Study of Developmental Sciences

ERIC Educational Resources Information Center

Petscher, Yaacov; Logan, Jessica A. R.

2014-01-01

Linear regression analysis is one of the most common techniques applied in developmental research, but only allows for an estimate of the average relations between the predictor(s) and the outcome. This study describes quantile regression, which provides estimates of the relations between the predictor(s) and outcome, but across multiple points of…

Maintenance Operations in Mission Oriented Protective Posture Level IV (MOPPIV)

DTIC Science & Technology

1987-10-01

Repair FADAC Printed Circuit Board ............. 6 3. Data Analysis Techniques ............................. 6 a. Multiple Linear Regression... ANALYSIS /DISCUSSION ............................... 12 1. Exa-ple of Regression Analysis ..................... 12 S2. Regression results for all tasks...6 * TABLE 9. Task Grouping for Analysis ........................ 7 "TABXLE 10. Remove/Replace H60A3 Power Pack................. 8 TABLE

Experimental and computational prediction of glass transition temperature of drugs.

PubMed

Alzghoul, Ahmad; Alhalaweh, Amjad; Mahlin, Denny; Bergström, Christel A S

2014-12-22

Glass transition temperature (Tg) is an important inherent property of an amorphous solid material which is usually determined experimentally. In this study, the relation between Tg and melting temperature (Tm) was evaluated using a data set of 71 structurally diverse druglike compounds. Further, in silico models for prediction of Tg were developed based on calculated molecular descriptors and linear (multilinear regression, partial least-squares, principal component regression) and nonlinear (neural network, support vector regression) modeling techniques. The models based on Tm predicted Tg with an RMSE of 19.5 K for the test set. Among the five computational models developed herein the support vector regression gave the best result with RMSE of 18.7 K for the test set using only four chemical descriptors. Hence, two different models that predict Tg of drug-like molecules with high accuracy were developed. If Tm is available, a simple linear regression can be used to predict Tg. However, the results also suggest that support vector regression and calculated molecular descriptors can predict Tg with equal accuracy, already before compound synthesis.

Multiresponse semiparametric regression for modelling the effect of regional socio-economic variables on the use of information technology

NASA Astrophysics Data System (ADS)

Wibowo, Wahyu; Wene, Chatrien; Budiantara, I. Nyoman; Permatasari, Erma Oktania

2017-03-01

Multiresponse semiparametric regression is simultaneous equation regression model and fusion of parametric and nonparametric model. The regression model comprise several models and each model has two components, parametric and nonparametric. The used model has linear function as parametric and polynomial truncated spline as nonparametric component. The model can handle both linearity and nonlinearity relationship between response and the sets of predictor variables. The aim of this paper is to demonstrate the application of the regression model for modeling of effect of regional socio-economic on use of information technology. More specific, the response variables are percentage of households has access to internet and percentage of households has personal computer. Then, predictor variables are percentage of literacy people, percentage of electrification and percentage of economic growth. Based on identification of the relationship between response and predictor variable, economic growth is treated as nonparametric predictor and the others are parametric predictors. The result shows that the multiresponse semiparametric regression can be applied well as indicate by the high coefficient determination, 90 percent.

Regression analysis using dependent Polya trees.

PubMed

Schörgendorfer, Angela; Branscum, Adam J

2013-11-30

Many commonly used models for linear regression analysis force overly simplistic shape and scale constraints on the residual structure of data. We propose a semiparametric Bayesian model for regression analysis that produces data-driven inference by using a new type of dependent Polya tree prior to model arbitrary residual distributions that are allowed to evolve across increasing levels of an ordinal covariate (e.g., time, in repeated measurement studies). By modeling residual distributions at consecutive covariate levels or time points using separate, but dependent Polya tree priors, distributional information is pooled while allowing for broad pliability to accommodate many types of changing residual distributions. We can use the proposed dependent residual structure in a wide range of regression settings, including fixed-effects and mixed-effects linear and nonlinear models for cross-sectional, prospective, and repeated measurement data. A simulation study illustrates the flexibility of our novel semiparametric regression model to accurately capture evolving residual distributions. In an application to immune development data on immunoglobulin G antibodies in children, our new model outperforms several contemporary semiparametric regression models based on a predictive model selection criterion. Copyright © 2013 John Wiley & Sons, Ltd.

Analytical framework for reconstructing heterogeneous environmental variables from mammal community structure.

PubMed

Louys, Julien; Meloro, Carlo; Elton, Sarah; Ditchfield, Peter; Bishop, Laura C

2015-01-01

We test the performance of two models that use mammalian communities to reconstruct multivariate palaeoenvironments. While both models exploit the correlation between mammal communities (defined in terms of functional groups) and arboreal heterogeneity, the first uses a multiple multivariate regression of community structure and arboreal heterogeneity, while the second uses a linear regression of the principal components of each ecospace. The success of these methods means the palaeoenvironment of a particular locality can be reconstructed in terms of the proportions of heavy, moderate, light, and absent tree canopy cover. The linear regression is less biased, and more precisely and accurately reconstructs heavy tree canopy cover than the multiple multivariate model. However, the multiple multivariate model performs better than the linear regression for all other canopy cover categories. Both models consistently perform better than randomly generated reconstructions. We apply both models to the palaeocommunity of the Upper Laetolil Beds, Tanzania. Our reconstructions indicate that there was very little heavy tree cover at this site (likely less than 10%), with the palaeo-landscape instead comprising a mixture of light and absent tree cover. These reconstructions help resolve the previous conflicting palaeoecological reconstructions made for this site. Copyright © 2014 Elsevier Ltd. All rights reserved.

Building a new predictor for multiple linear regression technique-based corrective maintenance turnaround time.

PubMed

Cruz, Antonio M; Barr, Cameron; Puñales-Pozo, Elsa

2008-01-01

This research's main goals were to build a predictor for a turnaround time (TAT) indicator for estimating its values and use a numerical clustering technique for finding possible causes of undesirable TAT values. The following stages were used: domain understanding, data characterisation and sample reduction and insight characterisation. Building the TAT indicator multiple linear regression predictor and clustering techniques were used for improving corrective maintenance task efficiency in a clinical engineering department (CED). The indicator being studied was turnaround time (TAT). Multiple linear regression was used for building a predictive TAT value model. The variables contributing to such model were clinical engineering department response time (CE(rt), 0.415 positive coefficient), stock service response time (Stock(rt), 0.734 positive coefficient), priority level (0.21 positive coefficient) and service time (0.06 positive coefficient). The regression process showed heavy reliance on Stock(rt), CE(rt) and priority, in that order. Clustering techniques revealed the main causes of high TAT values. This examination has provided a means for analysing current technical service quality and effectiveness. In doing so, it has demonstrated a process for identifying areas and methods of improvement and a model against which to analyse these methods' effectiveness.

A New SEYHAN's Approach in Case of Heterogeneity of Regression Slopes in ANCOVA.

PubMed

Ankarali, Handan; Cangur, Sengul; Ankarali, Seyit

2018-06-01

In this study, when the assumptions of linearity and homogeneity of regression slopes of conventional ANCOVA are not met, a new approach named as SEYHAN has been suggested to use conventional ANCOVA instead of robust or nonlinear ANCOVA. The proposed SEYHAN's approach involves transformation of continuous covariate into categorical structure when the relationship between covariate and dependent variable is nonlinear and the regression slopes are not homogenous. A simulated data set was used to explain SEYHAN's approach. In this approach, we performed conventional ANCOVA in each subgroup which is constituted according to knot values and analysis of variance with two-factor model after MARS method was used for categorization of covariate. The first model is a simpler model than the second model that includes interaction term. Since the model with interaction effect has more subjects, the power of test also increases and the existing significant difference is revealed better. We can say that linearity and homogeneity of regression slopes are not problem for data analysis by conventional linear ANCOVA model by helping this approach. It can be used fast and efficiently for the presence of one or more covariates.

The Influential Effect of Blending, Bump, Changing Period, and Eclipsing Cepheids on the Leavitt Law

NASA Astrophysics Data System (ADS)

García-Varela, A.; Muñoz, J. R.; Sabogal, B. E.; Vargas Domínguez, S.; Martínez, J.

2016-06-01

The investigation of the nonlinearity of the Leavitt law (LL) is a topic that began more than seven decades ago, when some of the studies in this field found that the LL has a break at about 10 days. The goal of this work is to investigate a possible statistical cause of this nonlinearity. By applying linear regressions to OGLE-II and OGLE-IV data, we find that to obtain the LL by using linear regression, robust techniques to deal with influential points and/or outliers are needed instead of the ordinary least-squares regression traditionally used. In particular, by using M- and MM-regressions we establish firmly and without doubt the linearity of the LL in the Large Magellanic Cloud, without rejecting or excluding Cepheid data from the analysis. This implies that light curves of Cepheids suggesting blending, bumps, eclipses, or period changes do not affect the LL for this galaxy. For the Small Magellanic Cloud, when including Cepheids of this kind, it is not possible to find an adequate model, probably because of the geometry of the galaxy. In that case, a possible influence of these stars could exist.

Multiple regression technique for Pth degree polynominals with and without linear cross products

NASA Technical Reports Server (NTRS)

Davis, J. W.

1973-01-01

A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent analysis. To implement this technique, separate computer programs were developed for the case without linear cross products and for the case incorporating such cross products which evaluate the various constants in the model regression equation. In addition, the significance of the estimated regression equation is considered and the standard deviation, the F statistic, the maximum absolute percent error, and the average of the absolute values of the percent of error evaluated. The computer programs and their manner of utilization are described. Sample problems are included to illustrate the use and capability of the technique which show the output formats and typical plots comparing computer results to each set of input data.

Bayesian quantile regression-based partially linear mixed-effects joint models for longitudinal data with multiple features.

PubMed

Zhang, Hanze; Huang, Yangxin; Wang, Wei; Chen, Henian; Langland-Orban, Barbara

2017-01-01

In longitudinal AIDS studies, it is of interest to investigate the relationship between HIV viral load and CD4 cell counts, as well as the complicated time effect. Most of common models to analyze such complex longitudinal data are based on mean-regression, which fails to provide efficient estimates due to outliers and/or heavy tails. Quantile regression-based partially linear mixed-effects models, a special case of semiparametric models enjoying benefits of both parametric and nonparametric models, have the flexibility to monitor the viral dynamics nonparametrically and detect the varying CD4 effects parametrically at different quantiles of viral load. Meanwhile, it is critical to consider various data features of repeated measurements, including left-censoring due to a limit of detection, covariate measurement error, and asymmetric distribution. In this research, we first establish a Bayesian joint models that accounts for all these data features simultaneously in the framework of quantile regression-based partially linear mixed-effects models. The proposed models are applied to analyze the Multicenter AIDS Cohort Study (MACS) data. Simulation studies are also conducted to assess the performance of the proposed methods under different scenarios.

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

PubMed

Kumar, K Vasanth

2006-10-11

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

Adjusted variable plots for Cox's proportional hazards regression model.

PubMed

Hall, C B; Zeger, S L; Bandeen-Roche, K J

1996-01-01

Adjusted variable plots are useful in linear regression for outlier detection and for qualitative evaluation of the fit of a model. In this paper, we extend adjusted variable plots to Cox's proportional hazards model for possibly censored survival data. We propose three different plots: a risk level adjusted variable (RLAV) plot in which each observation in each risk set appears, a subject level adjusted variable (SLAV) plot in which each subject is represented by one point, and an event level adjusted variable (ELAV) plot in which the entire risk set at each failure event is represented by a single point. The latter two plots are derived from the RLAV by combining multiple points. In each point, the regression coefficient and standard error from a Cox proportional hazards regression is obtained by a simple linear regression through the origin fit to the coordinates of the pictured points. The plots are illustrated with a reanalysis of a dataset of 65 patients with multiple myeloma.

Selection of a Geostatistical Method to Interpolate Soil Properties of the State Crop Testing Fields using Attributes of a Digital Terrain Model

NASA Astrophysics Data System (ADS)

Sahabiev, I. A.; Ryazanov, S. S.; Kolcova, T. G.; Grigoryan, B. R.

2018-03-01

The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.

Why are we regressing?

PubMed

Jupiter, Daniel C

2012-01-01

In this first of a series of statistical methodology commentaries for the clinician, we discuss the use of multivariate linear regression. Copyright © 2012 American College of Foot and Ankle Surgeons. Published by Elsevier Inc. All rights reserved.

An evaluation of bias in propensity score-adjusted non-linear regression models.

PubMed

Wan, Fei; Mitra, Nandita

2018-03-01

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

Comparison of sampling designs for estimating deforestation from landsat TM and MODIS imagery: a case study in Mato Grosso, Brazil.

PubMed

Zhu, Shanyou; Zhang, Hailong; Liu, Ronggao; Cao, Yun; Zhang, Guixin

2014-01-01

Sampling designs are commonly used to estimate deforestation over large areas, but comparisons between different sampling strategies are required. Using PRODES deforestation data as a reference, deforestation in the state of Mato Grosso in Brazil from 2005 to 2006 is evaluated using Landsat imagery and a nearly synchronous MODIS dataset. The MODIS-derived deforestation is used to assist in sampling and extrapolation. Three sampling designs are compared according to the estimated deforestation of the entire study area based on simple extrapolation and linear regression models. The results show that stratified sampling for strata construction and sample allocation using the MODIS-derived deforestation hotspots provided more precise estimations than simple random and systematic sampling. Moreover, the relationship between the MODIS-derived and TM-derived deforestation provides a precise estimate of the total deforestation area as well as the distribution of deforestation in each block.

Comparison of Sampling Designs for Estimating Deforestation from Landsat TM and MODIS Imagery: A Case Study in Mato Grosso, Brazil

PubMed Central

Zhu, Shanyou; Zhang, Hailong; Liu, Ronggao; Cao, Yun; Zhang, Guixin

2014-01-01

Sampling designs are commonly used to estimate deforestation over large areas, but comparisons between different sampling strategies are required. Using PRODES deforestation data as a reference, deforestation in the state of Mato Grosso in Brazil from 2005 to 2006 is evaluated using Landsat imagery and a nearly synchronous MODIS dataset. The MODIS-derived deforestation is used to assist in sampling and extrapolation. Three sampling designs are compared according to the estimated deforestation of the entire study area based on simple extrapolation and linear regression models. The results show that stratified sampling for strata construction and sample allocation using the MODIS-derived deforestation hotspots provided more precise estimations than simple random and systematic sampling. Moreover, the relationship between the MODIS-derived and TM-derived deforestation provides a precise estimate of the total deforestation area as well as the distribution of deforestation in each block. PMID:25258742

Modification of the USLE K factor for soil erodibility assessment on calcareous soils in Iran

NASA Astrophysics Data System (ADS)

Ostovari, Yaser; Ghorbani-Dashtaki, Shoja; Bahrami, Hossein-Ali; Naderi, Mehdi; Dematte, Jose Alexandre M.; Kerry, Ruth

2016-11-01

The measurement of soil erodibility (K) in the field is tedious, time-consuming and expensive; therefore, its prediction through pedotransfer functions (PTFs) could be far less costly and time-consuming. The aim of this study was to develop new PTFs to estimate the K factor using multiple linear regression, Mamdani fuzzy inference systems, and artificial neural networks. For this purpose, K was measured in 40 erosion plots with natural rainfall. Various soil properties including the soil particle size distribution, calcium carbonate equivalent, organic matter, permeability, and wet-aggregate stability were measured. The results showed that the mean measured K was 0.014 t h MJ- 1 mm- 1 and 2.08 times less than the estimated mean K (0.030 t h MJ- 1 mm- 1) using the USLE model. Permeability, wet-aggregate stability, very fine sand, and calcium carbonate were selected as independent variables by forward stepwise regression in order to assess the ability of multiple linear regression, Mamdani fuzzy inference systems and artificial neural networks to predict K. The calcium carbonate equivalent, which is not accounted for in the USLE model, had a significant impact on K in multiple linear regression due to its strong influence on the stability of aggregates and soil permeability. Statistical indices in validation and calibration datasets determined that the artificial neural networks method with the highest R2, lowest RMSE, and lowest ME was the best model for estimating the K factor. A strong correlation (R2 = 0.81, n = 40, p < 0.05) between the estimated K from multiple linear regression and measured K indicates that the use of calcium carbonate equivalent as a predictor variable gives a better estimation of K in areas with calcareous soils.

Postmolar gestational trophoblastic neoplasia: beyond the traditional risk factors.

PubMed

Bakhtiyari, Mahmood; Mirzamoradi, Masoumeh; Kimyaiee, Parichehr; Aghaie, Abbas; Mansournia, Mohammd Ali; Ashrafi-Vand, Sepideh; Sarfjoo, Fatemeh Sadat

2015-09-01

To investigate the slope of linear regression of postevacuation serum hCG as an independent risk factor for postmolar gestational trophoblastic neoplasia (GTN). Multicenter retrospective cohort study. Academic referral health care centers. All subjects with confirmed hydatidiform mole and at least four measurements of β-hCG titer. None. Type and magnitude of the relationship between the slope of linear regression of β-hCG as a new risk factor and GTN using Bayesian logistic regression with penalized log-likelihood estimation. Among the high-risk and low-risk molar pregnancy cases, 11 (18.6%) and 19 cases (13.3%) had GTN, respectively. No significant relationship was found between the components of a high-risk pregnancy and GTN. The β-hCG return slope was higher in the spontaneous cure group. However, the initial level of this hormone in the first measurement was higher in the GTN group compared with in the spontaneous recovery group. The average time for diagnosing GTN in the high-risk molar pregnancy group was 2 weeks less than that of the low-risk molar pregnancy group. In addition to slope of linear regression of β-hCG (odds ratio [OR], 12.74, confidence interval [CI], 5.42-29.2), abortion history (OR, 2.53; 95% CI, 1.27-5.04) and large uterine height for gestational age (OR, 1.26; CI, 1.04-1.54) had the maximum effects on GTN outcome, respectively. The slope of linear regression of β-hCG was introduced as an independent risk factor, which could be used for clinical decision making based on records of β-hCG titer and subsequent prevention program. Copyright © 2015 American Society for Reproductive Medicine. Published by Elsevier Inc. All rights reserved.

Tolerance of ciliated protozoan Paramecium bursaria (Protozoa, Ciliophora) to ammonia and nitrites

NASA Astrophysics Data System (ADS)

Xu, Henglong; Song, Weibo; Lu, Lu; Alan, Warren

2005-09-01

The tolerance to ammonia and nitrites in freshwater ciliate Paramecium bursaria was measured in a conventional open system. The ciliate was exposed to different concentrations of ammonia and nitrites for 2h and 12h in order to determine the lethal concentrations. Linear regression analysis revealed that the 2h-LC50 value for ammonia was 95.94 mg/L and for nitrite 27.35 mg/L using probit scale method (with 95% confidence intervals). There was a linear correlation between the mortality probit scale and logarithmic concentration of ammonia which fit by a regression equation y=7.32 x 9.51 ( R 2=0.98; y, mortality probit scale; x, logarithmic concentration of ammonia), by which 2 h-LC50 value for ammonia was found to be 95.50 mg/L. A linear correlation between mortality probit scales and logarithmic concentration of nitrite is also followed the regression equation y=2.86 x+0.89 ( R 2=0.95; y, mortality probit scale; x, logarithmic concentration of nitrite). The regression analysis of toxicity curves showed that the linear correlation between exposed time of ammonia-N LC50 value and ammonia-N LC50 value followed the regression equation y=2 862.85 e -0.08 x ( R 2=0.95; y, duration of exposure to LC50 value; x, LC50 value), and that between exposed time of nitrite-N LC50 value and nitrite-N LC50 value followed the regression equation y=127.15 e -0.13 x ( R 2=0.91; y, exposed time of LC50 value; x, LC50 value). The results demonstrate that the tolerance to ammonia in P. bursaria is considerably higher than that of the larvae or juveniles of some metozoa, e.g. cultured prawns and oysters. In addition, ciliates, as bacterial predators, are likely to play a positive role in maintaining and improving water quality in aquatic environments with high-level ammonium, such as sewage treatment systems.

GWAS with longitudinal phenotypes: performance of approximate procedures

PubMed Central

Sikorska, Karolina; Montazeri, Nahid Mostafavi; Uitterlinden, André; Rivadeneira, Fernando; Eilers, Paul HC; Lesaffre, Emmanuel

2015-01-01

Analysis of genome-wide association studies with longitudinal data using standard procedures, such as linear mixed model (LMM) fitting, leads to discouragingly long computation times. There is a need to speed up the computations significantly. In our previous work (Sikorska et al: Fast linear mixed model computations for genome-wide association studies with longitudinal data. Stat Med 2012; 32.1: 165–180), we proposed the conditional two-step (CTS) approach as a fast method providing an approximation to the P-value for the longitudinal single-nucleotide polymorphism (SNP) effect. In the first step a reduced conditional LMM is fit, omitting all the SNP terms. In the second step, the estimated random slopes are regressed on SNPs. The CTS has been applied to the bone mineral density data from the Rotterdam Study and proved to work very well even in unbalanced situations. In another article (Sikorska et al: GWAS on your notebook: fast semi-parallel linear and logistic regression for genome-wide association studies. BMC Bioinformatics 2013; 14: 166), we suggested semi-parallel computations, greatly speeding up fitting many linear regressions. Combining CTS with fast linear regression reduces the computation time from several weeks to a few minutes on a single computer. Here, we explore further the properties of the CTS both analytically and by simulations. We investigate the performance of our proposal in comparison with a related but different approach, the two-step procedure. It is analytically shown that for the balanced case, under mild assumptions, the P-value provided by the CTS is the same as from the LMM. For unbalanced data and in realistic situations, simulations show that the CTS method does not inflate the type I error rate and implies only a minimal loss of power. PMID:25712081

Local linear regression for function learning: an analysis based on sample discrepancy.

PubMed

Cervellera, Cristiano; Macciò, Danilo

2014-11-01

Local linear regression models, a kind of nonparametric structures that locally perform a linear estimation of the target function, are analyzed in the context of empirical risk minimization (ERM) for function learning. The analysis is carried out with emphasis on geometric properties of the available data. In particular, the discrepancy of the observation points used both to build the local regression models and compute the empirical risk is considered. This allows to treat indifferently the case in which the samples come from a random external source and the one in which the input space can be freely explored. Both consistency of the ERM procedure and approximating capabilities of the estimator are analyzed, proving conditions to ensure convergence. Since the theoretical analysis shows that the estimation improves as the discrepancy of the observation points becomes smaller, low-discrepancy sequences, a family of sampling methods commonly employed for efficient numerical integration, are also analyzed. Simulation results involving two different examples of function learning are provided.

Adaptive local linear regression with application to printer color management.

PubMed

Gupta, Maya R; Garcia, Eric K; Chin, Erika

2008-06-01

Local learning methods, such as local linear regression and nearest neighbor classifiers, base estimates on nearby training samples, neighbors. Usually, the number of neighbors used in estimation is fixed to be a global "optimal" value, chosen by cross validation. This paper proposes adapting the number of neighbors used for estimation to the local geometry of the data, without need for cross validation. The term enclosing neighborhood is introduced to describe a set of neighbors whose convex hull contains the test point when possible. It is proven that enclosing neighborhoods yield bounded estimation variance under some assumptions. Three such enclosing neighborhood definitions are presented: natural neighbors, natural neighbors inclusive, and enclosing k-NN. The effectiveness of these neighborhood definitions with local linear regression is tested for estimating lookup tables for color management. Significant improvements in error metrics are shown, indicating that enclosing neighborhoods may be a promising adaptive neighborhood definition for other local learning tasks as well, depending on the density of training samples.

Energy expenditure estimation during daily military routine with body-fixed sensors.

PubMed

Wyss, Thomas; Mäder, Urs

2011-05-01

The purpose of this study was to develop and validate an algorithm for estimating energy expenditure during the daily military routine on the basis of data collected using body-fixed sensors. First, 8 volunteers completed isolated physical activities according to an established protocol, and the resulting data were used to develop activity-class-specific multiple linear regressions for physical activity energy expenditure on the basis of hip acceleration, heart rate, and body mass as independent variables. Second, the validity of these linear regressions was tested during the daily military routine using indirect calorimetry (n = 12). Volunteers' mean estimated energy expenditure did not significantly differ from the energy expenditure measured with indirect calorimetry (p = 0.898, 95% confidence interval = -1.97 to 1.75 kJ/min). We conclude that the developed activity-class-specific multiple linear regressions applied to the acceleration and heart rate data allow estimation of energy expenditure in 1-minute intervals during daily military routine, with accuracy equal to indirect calorimetry.

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian; Punjabi, Naresh M.

2013-01-01

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis. PMID:22241689

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.

TG study of the Li0.4Fe2.4Zn0.2O4 ferrite synthesis

NASA Astrophysics Data System (ADS)

Lysenko, E. N.; Nikolaev, E. V.; Surzhikov, A. P.

2016-02-01

In this paper, the kinetic analysis of Li-Zn ferrite synthesis was studied using thermogravimetry (TG) method through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression). Using TG-curves obtained for the four heating rates and Netzsch Thermokinetics software package, the kinetic models with minimal adjustable parameters were selected to quantitatively describe the reaction of Li-Zn ferrite synthesis. It was shown that the experimental TG-curves clearly suggest a two-step process for the ferrite synthesis and therefore a model-fitting kinetic analysis based on multivariate non-linear regressions was conducted. The complex reaction was described by a two-step reaction scheme consisting of sequential reaction steps. It is established that the best results were obtained using the Yander three-dimensional diffusion model at the first stage and Ginstling-Bronstein model at the second step. The kinetic parameters for lithium-zinc ferrite synthesis reaction were found and discussed.

A Feature-Free 30-Disease Pathological Brain Detection System by Linear Regression Classifier.

PubMed

Chen, Yi; Shao, Ying; Yan, Jie; Yuan, Ti-Fei; Qu, Yanwen; Lee, Elizabeth; Wang, Shuihua

2017-01-01

Alzheimer's disease patients are increasing rapidly every year. Scholars tend to use computer vision methods to develop automatic diagnosis system. (Background) In 2015, Gorji et al. proposed a novel method using pseudo Zernike moment. They tested four classifiers: learning vector quantization neural network, pattern recognition neural network trained by Levenberg-Marquardt, by resilient backpropagation, and by scaled conjugate gradient. This study presents an improved method by introducing a relatively new classifier-linear regression classification. Our method selects one axial slice from 3D brain image, and employed pseudo Zernike moment with maximum order of 15 to extract 256 features from each image. Finally, linear regression classification was harnessed as the classifier. The proposed approach obtains an accuracy of 97.51%, a sensitivity of 96.71%, and a specificity of 97.73%. Our method performs better than Gorji's approach and five other state-of-the-art approaches. Therefore, it can be used to detect Alzheimer's disease. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Reasons for Hierarchical Linear Modeling: A Reminder.

ERIC Educational Resources Information Center

Wang, Jianjun

1999-01-01

Uses examples of hierarchical linear modeling (HLM) at local and national levels to illustrate proper applications of HLM and dummy variable regression. Raises cautions about the circumstances under which hierarchical data do not need HLM. (SLD)

BIODEGRADATION PROBABILITY PROGRAM (BIODEG)

EPA Science Inventory

The Biodegradation Probability Program (BIODEG) calculates the probability that a chemical under aerobic conditions with mixed cultures of microorganisms will biodegrade rapidly or slowly. It uses fragment constants developed using multiple linear and non-linear regressions and d...

The Use of Linear Programming for Prediction.

ERIC Educational Resources Information Center

Schnittjer, Carl J.

The purpose of the study was to develop a linear programming model to be used for prediction, test the accuracy of the predictions, and compare the accuracy with that produced by curvilinear multiple regression analysis. (Author)

Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis

ERIC Educational Resources Information Center

Luo, Wen; Azen, Razia

2013-01-01

Dominance analysis (DA) is a method used to evaluate the relative importance of predictors that was originally proposed for linear regression models. This article proposes an extension of DA that allows researchers to determine the relative importance of predictors in hierarchical linear models (HLM). Commonly used measures of model adequacy in…

Independent contrasts and PGLS regression estimators are equivalent.

PubMed

Blomberg, Simon P; Lefevre, James G; Wells, Jessie A; Waterhouse, Mary

2012-05-01

We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.

Dimensional analysis of detrimental ozone generation by positive wire-to-plate corona discharge in air

NASA Astrophysics Data System (ADS)

Bo, Z.; Chen, J. H.

2010-02-01

The dimensional analysis technique is used to formulate a correlation between ozone generation rate and various parameters that are important in the design and operation of positive wire-to-plate corona discharges in indoor air. The dimensionless relation is determined by linear regression analysis based on the results from 36 laboratory-scale experiments. The derived equation is validated by experimental data and a numerical model published in the literature. Applications of such derived equation are illustrated through an example selection of the appropriate set of operating conditions in the design/operation of a photocopier to follow the federal regulations of ozone emission. Finally, a new current-voltage characteristic equation is proposed for positive wire-to-plate corona discharges based on the derived dimensionless equation.

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.

Seasonal forecasting of high wind speeds over Western Europe

NASA Astrophysics Data System (ADS)

Palutikof, J. P.; Holt, T.

2003-04-01

As financial losses associated with extreme weather events escalate, there is interest from end users in the forestry and insurance industries, for example, in the development of seasonal forecasting models with a long lead time. This study uses exceedences of the 90th, 95th, and 99th percentiles of daily maximum wind speed over the period 1958 to present to derive predictands of winter wind extremes. The source data is the 6-hourly NCEP Reanalysis gridded surface wind field. Predictor variables include principal components of Atlantic sea surface temperature and several indices of climate variability, including the NAO and SOI. Lead times of up to a year are considered, in monthly increments. Three regression techniques are evaluated; multiple linear regression (MLR), principal component regression (PCR), and partial least squares regression (PLS). PCR and PLS proved considerably superior to MLR with much lower standard errors. PLS was chosen to formulate the predictive model since it offers more flexibility in experimental design and gave slightly better results than PCR. The results indicate that winter windiness can be predicted with considerable skill one year ahead for much of coastal Europe, but that this deteriorates rapidly in the hinterland. The experiment succeeded in highlighting PLS as a very useful method for developing more precise forecasting models, and in identifying areas of high predictability.

Continuing Medical Education Speakers with High Evaluation Scores Use more Image-based Slides.

PubMed

Ferguson, Ian; Phillips, Andrew W; Lin, Michelle

2017-01-01

Although continuing medical education (CME) presentations are common across health professions, it is unknown whether slide design is independently associated with audience evaluations of the speaker. Based on the conceptual framework of Mayer's theory of multimedia learning, this study aimed to determine whether image use and text density in presentation slides are associated with overall speaker evaluations. This retrospective analysis of six sequential CME conferences (two annual emergency medicine conferences over a three-year period) used a mixed linear regression model to assess whether post-conference speaker evaluations were associated with image fraction (percentage of image-based slides per presentation) and text density (number of words per slide). A total of 105 unique lectures were given by 49 faculty members, and 1,222 evaluations (70.1% response rate) were available for analysis. On average, 47.4% (SD=25.36) of slides had at least one educationally-relevant image (image fraction). Image fraction significantly predicted overall higher evaluation scores [F(1, 100.676)=6.158, p=0.015] in the mixed linear regression model. The mean (SD) text density was 25.61 (8.14) words/slide but was not a significant predictor [F(1, 86.293)=0.55, p=0.815]. Of note, the individual speaker [χ 2 (1)=2.952, p=0.003] and speaker seniority [F(3, 59.713)=4.083, p=0.011] significantly predicted higher scores. This is the first published study to date assessing the linkage between slide design and CME speaker evaluations by an audience of practicing clinicians. The incorporation of images was associated with higher evaluation scores, in alignment with Mayer's theory of multimedia learning. Contrary to this theory, however, text density showed no significant association, suggesting that these scores may be multifactorial. Professional development efforts should focus on teaching best practices in both slide design and presentation skills.

Combination of partial least squares regression and design of experiments to model the retention of pharmaceutical compounds in supercritical fluid chromatography.

PubMed

Andri, Bertyl; Dispas, Amandine; Marini, Roland Djang'Eing'a; Hubert, Philippe; Sassiat, Patrick; Al Bakain, Ramia; Thiébaut, Didier; Vial, Jérôme

2017-03-31

This work presents a first attempt to establish a model of the retention behaviour for pharmaceutical compounds in gradient mode SFC. For this purpose, multivariate statistics were applied on the basis of data gathered with the Design of Experiment (DoE) methodology. It permitted to build optimally the experiments needed, and served as a basis for providing relevant physicochemical interpretation of the effects observed. Data gathered over a broad experimental domain enabled the establishment of well-fit linear models of the retention of the individual compounds in presence of methanol as co-solvent. These models also allowed the appreciation of the impact of each experimental parameter and their factorial combinations. This approach was carried out with two organic modifiers (i.e. methanol and ethanol) and provided comparable results. Therefore, it demonstrates the feasibility to model retention in gradient mode SFC for individual compounds as a function of the experimental conditions. This approach also permitted to highlight the predominant effect of some parameters (e.g. gradient slope and pressure) on the retention of compounds. Because building of individual models of retention was possible, the next step considered the establishment of a global model of the retention to predict the behaviour of given compounds on the basis of, on the one side, the physicochemical descriptors of the compounds (e.g. Linear Solvation Energy Relationship (LSER) descriptors) and, on the other side, of the experimental conditions. This global model was established by means of partial least squares regression for the selected compounds, in an experimental domain defined by the Design of Experiment (DoE) methodology. Assessment of the model's predictive capabilities revealed satisfactory agreement between predicted and actual retention (i.e. R 2 =0.942, slope=1.004) of the assessed compounds, which is unprecedented in the field. Copyright © 2017 Elsevier B.V. All rights reserved.

Reliability of the Load-Velocity Relationship Obtained Through Linear and Polynomial Regression Models to Predict the One-Repetition Maximum Load.

PubMed

Pestaña-Melero, Francisco Luis; Haff, G Gregory; Rojas, Francisco Javier; Pérez-Castilla, Alejandro; García-Ramos, Amador

2017-12-18

This study aimed to compare the between-session reliability of the load-velocity relationship between (1) linear vs. polynomial regression models, (2) concentric-only vs. eccentric-concentric bench press variants, as well as (3) the within-participants vs. the between-participants variability of the velocity attained at each percentage of the one-repetition maximum (%1RM). The load-velocity relationship of 30 men (age: 21.2±3.8 y; height: 1.78±0.07 m, body mass: 72.3±7.3 kg; bench press 1RM: 78.8±13.2 kg) were evaluated by means of linear and polynomial regression models in the concentric-only and eccentric-concentric bench press variants in a Smith Machine. Two sessions were performed with each bench press variant. The main findings were: (1) first-order-polynomials (CV: 4.39%-4.70%) provided the load-velocity relationship with higher reliability than second-order-polynomials (CV: 4.68%-5.04%); (2) the reliability of the load-velocity relationship did not differ between the concentric-only and eccentric-concentric bench press variants; (3) the within-participants variability of the velocity attained at each %1RM was markedly lower than the between-participants variability. Taken together, these results highlight that, regardless of the bench press variant considered, the individual determination of the load-velocity relationship by a linear regression model could be recommended to monitor and prescribe the relative load in the Smith machine bench press exercise.

Effect of removing the common mode errors on linear regression analysis of noise amplitudes in position time series of a regional GPS network & a case study of GPS stations in Southern California

NASA Astrophysics Data System (ADS)

Jiang, Weiping; Ma, Jun; Li, Zhao; Zhou, Xiaohui; Zhou, Boye

2018-05-01

The analysis of the correlations between the noise in different components of GPS stations has positive significance to those trying to obtain more accurate uncertainty of velocity with respect to station motion. Previous research into noise in GPS position time series focused mainly on single component evaluation, which affects the acquisition of precise station positions, the velocity field, and its uncertainty. In this study, before and after removing the common-mode error (CME), we performed one-dimensional linear regression analysis of the noise amplitude vectors in different components of 126 GPS stations with a combination of white noise, flicker noise, and random walking noise in Southern California. The results show that, on the one hand, there are above-moderate degrees of correlation between the white noise amplitude vectors in all components of the stations before and after removal of the CME, while the correlations between flicker noise amplitude vectors in horizontal and vertical components are enhanced from un-correlated to moderately correlated by removing the CME. On the other hand, the significance tests show that, all of the obtained linear regression equations, which represent a unique function of the noise amplitude in any two components, are of practical value after removing the CME. According to the noise amplitude estimates in two components and the linear regression equations, more accurate noise amplitudes can be acquired in the two components.

The 11-year solar cycle in current reanalyses: a (non)linear attribution study of the middle atmosphere

NASA Astrophysics Data System (ADS)

Kuchar, A.; Sacha, P.; Miksovsky, J.; Pisoft, P.

2015-06-01

This study focusses on the variability of temperature, ozone and circulation characteristics in the stratosphere and lower mesosphere with regard to the influence of the 11-year solar cycle. It is based on attribution analysis using multiple nonlinear techniques (support vector regression, neural networks) besides the multiple linear regression approach. The analysis was applied to several current reanalysis data sets for the 1979-2013 period, including MERRA, ERA-Interim and JRA-55, with the aim to compare how these types of data resolve especially the double-peaked solar response in temperature and ozone variables and the consequent changes induced by these anomalies. Equatorial temperature signals in the tropical stratosphere were found to be in qualitative agreement with previous attribution studies, although the agreement with observational results was incomplete, especially for JRA-55. The analysis also pointed to the solar signal in the ozone data sets (i.e. MERRA and ERA-Interim) not being consistent with the observed double-peaked ozone anomaly extracted from satellite measurements. The results obtained by linear regression were confirmed by the nonlinear approach through all data sets, suggesting that linear regression is a relevant tool to sufficiently resolve the solar signal in the middle atmosphere. The seasonal evolution of the solar response was also discussed in terms of dynamical causalities in the winter hemispheres. The hypothetical mechanism of a weaker Brewer-Dobson circulation at solar maxima was reviewed together with a discussion of polar vortex behaviour.

Predicting birth weight with conditionally linear transformation models.

PubMed

Möst, Lisa; Schmid, Matthias; Faschingbauer, Florian; Hothorn, Torsten

2016-12-01

Low and high birth weight (BW) are important risk factors for neonatal morbidity and mortality. Gynecologists must therefore accurately predict BW before delivery. Most prediction formulas for BW are based on prenatal ultrasound measurements carried out within one week prior to birth. Although successfully used in clinical practice, these formulas focus on point predictions of BW but do not systematically quantify uncertainty of the predictions, i.e. they result in estimates of the conditional mean of BW but do not deliver prediction intervals. To overcome this problem, we introduce conditionally linear transformation models (CLTMs) to predict BW. Instead of focusing only on the conditional mean, CLTMs model the whole conditional distribution function of BW given prenatal ultrasound parameters. Consequently, the CLTM approach delivers both point predictions of BW and fetus-specific prediction intervals. Prediction intervals constitute an easy-to-interpret measure of prediction accuracy and allow identification of fetuses subject to high prediction uncertainty. Using a data set of 8712 deliveries at the Perinatal Centre at the University Clinic Erlangen (Germany), we analyzed variants of CLTMs and compared them to standard linear regression estimation techniques used in the past and to quantile regression approaches. The best-performing CLTM variant was competitive with quantile regression and linear regression approaches in terms of conditional coverage and average length of the prediction intervals. We propose that CLTMs be used because they are able to account for possible heteroscedasticity, kurtosis, and skewness of the distribution of BWs. © The Author(s) 2014.

Toward customer-centric organizational science: A common language effect size indicator for multiple linear regressions and regressions with higher-order terms.

PubMed

Krasikova, Dina V; Le, Huy; Bachura, Eric

2018-06-01

To address a long-standing concern regarding a gap between organizational science and practice, scholars called for more intuitive and meaningful ways of communicating research results to users of academic research. In this article, we develop a common language effect size index (CLβ) that can help translate research results to practice. We demonstrate how CLβ can be computed and used to interpret the effects of continuous and categorical predictors in multiple linear regression models. We also elaborate on how the proposed CLβ index is computed and used to interpret interactions and nonlinear effects in regression models. In addition, we test the robustness of the proposed index to violations of normality and provide means for computing standard errors and constructing confidence intervals around its estimates. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

[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.

Schistosomiasis Breeding Environment Situation Analysis in Dongting Lake Area

NASA Astrophysics Data System (ADS)

Li, Chuanrong; Jia, Yuanyuan; Ma, Lingling; Liu, Zhaoyan; Qian, Yonggang

2013-01-01

Monitoring environmental characteristics, such as vegetation, soil moisture et al., of Oncomelania hupensis (O. hupensis)’ spatial/temporal distribution is of vital importance to the schistosomiasis prevention and control. In this study, the relationship between environmental factors derived from remotely sensed data and the density of O. hupensis was analyzed by a multiple linear regression model. Secondly, spatial analysis of the regression residual was investigated by the semi-variogram method. Thirdly, spatial analysis of the regression residual and the multiple linear regression model were both employed to estimate the spatial variation of O. hupensis density. Finally, the approach was used to monitor and predict the spatial and temporal variations of oncomelania of Dongting Lake region, China. And the areas of potential O. hupensis habitats were predicted and the influence of Three Gorges Dam (TGB)project on the density of O. hupensis was analyzed.

Isotherm investigation for the sorption of fluoride onto Bio-F: comparison of linear and non-linear regression method

NASA Astrophysics Data System (ADS)

Yadav, Manish; Singh, Nitin Kumar

2017-12-01

A comparison of the linear and non-linear regression method in selecting the optimum isotherm among three most commonly used adsorption isotherms (Langmuir, Freundlich, and Redlich-Peterson) was made to the experimental data of fluoride (F) sorption onto Bio-F at a solution temperature of 30 ± 1 °C. The coefficient of correlation (r2) was used to select the best theoretical isotherm among the investigated ones. A total of four Langmuir linear equations were discussed and out of which linear form of most popular Langmuir-1 and Langmuir-2 showed the higher coefficient of determination (0.976 and 0.989) as compared to other Langmuir linear equations. Freundlich and Redlich-Peterson isotherms showed a better fit to the experimental data in linear least-square method, while in non-linear method Redlich-Peterson isotherm equations showed the best fit to the tested data set. The present study showed that the non-linear method could be a better way to obtain the isotherm parameters and represent the most suitable isotherm. Redlich-Peterson isotherm was found to be the best representative (r2 = 0.999) for this sorption system. It is also observed that the values of β are not close to unity, which means the isotherms are approaching the Freundlich but not the Langmuir isotherm.

Principal component regression analysis with SPSS.

PubMed

Liu, R X; Kuang, J; Gong, Q; Hou, X L

2003-06-01

The paper introduces all indices of multicollinearity diagnoses, the basic principle of principal component regression and determination of 'best' equation method. The paper uses an example to describe how to do principal component regression analysis with SPSS 10.0: including all calculating processes of the principal component regression and all operations of linear regression, factor analysis, descriptives, compute variable and bivariate correlations procedures in SPSS 10.0. The principal component regression analysis can be used to overcome disturbance of the multicollinearity. The simplified, speeded up and accurate statistical effect is reached through the principal component regression analysis with SPSS.

Linear and nonlinear methods in modeling the aqueous solubility of organic compounds.

PubMed

Catana, Cornel; Gao, Hua; Orrenius, Christian; Stouten, Pieter F W

2005-01-01

Solubility data for 930 diverse compounds have been analyzed using linear Partial Least Square (PLS) and nonlinear PLS methods, Continuum Regression (CR), and Neural Networks (NN). 1D and 2D descriptors from MOE package in combination with E-state or ISIS keys have been used. The best model was obtained using linear PLS for a combination between 22 MOE descriptors and 65 ISIS keys. It has a correlation coefficient (r2) of 0.935 and a root-mean-square error (RMSE) of 0.468 log molar solubility (log S(w)). The model validated on a test set of 177 compounds not included in the training set has r2 0.911 and RMSE 0.475 log S(w). The descriptors were ranked according to their importance, and at the top of the list have been found the 22 MOE descriptors. The CR model produced results as good as PLS, and because of the way in which cross-validation has been done it is expected to be a valuable tool in prediction besides PLS model. The statistics obtained using nonlinear methods did not surpass those got with linear ones. The good statistic obtained for linear PLS and CR recommends these models to be used in prediction when it is difficult or impossible to make experimental measurements, for virtual screening, combinatorial library design, and efficient leads optimization.

A New Test of Linear Hypotheses in OLS Regression under Heteroscedasticity of Unknown Form

ERIC Educational Resources Information Center

Cai, Li; Hayes, Andrew F.

2008-01-01

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM)…

Deriving the Regression Equation without Using Calculus

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

Relationships of Measurement Error and Prediction Error in Observed-Score Regression

ERIC Educational Resources Information Center

Moses, Tim

2012-01-01

The focus of this paper is assessing the impact of measurement errors on the prediction error of an observed-score regression. Measures are presented and described for decomposing the linear regression's prediction error variance into parts attributable to the true score variance and the error variances of the dependent variable and the predictor…

Nutritional characteristics of camelina meal for 3-week-old broiler chickens.

PubMed

Pekel, A Y; Kim, J I; Chapple, C; Adeola, O

2015-03-01

Limited information on nutritional characteristics on camelina meal for broiler chickens limits its use in diets of broiler chickens. The objectives of this study were to determine the ileal digestible energy (IDE), ME, and MEn contents of 2 different camelina meal (CM1 and CM2) samples for 3-wk-old broiler chickens using the regression method and to determine glucosinolate compounds in the camelina meal samples. The CM1 and CM2 were incorporated into a corn-soybean meal-based reference diet at 3 levels (0, 100, or 200 g/kg) by replacing the energy-yielding ingredients. These 5 diets (reference diet, and 100 and 200 g/kg camelina meal from each of CM1 and CM2) were fed to 320 male Ross 708 broilers from d 21 to 28 post hatching with 8 birds per cage and 8 replicates per treatment in a randomized complete block design. Excreta were collected twice daily from d 25 to 28, and jejunal digesta and ileal digesta from the Meckel's diverticulum to approximately 2 cm proximal to the ileocecal junction were collected on d 28. The total glucosinolate content for CM1 and CM2 were 24.2 and 22.7 nmol/mg, respectively. Jejunal digesta viscosity was linearly increased (P<0.001) from 2.2 to 4.1 cP with increasing dietary camelina meal levels. There were linear effects (P<0.001) of CM1 and CM2 substitution on final weight, weight gain, feed intake, and G:F. The inclusion of CM1 and CM2 linearly decreased (P<0.001) ileal digestibility of DM, energy, and IDE. The supplementation of CM1 and CM2 linearly decreased (P<0.001) the retention of DM, nitrogen, and energy; ME, and MEn. By regressing the CM1 and CM2-associated IDE intake in kilocalories against kilograms of CM1 and CM2 intake, the IDE regression equation was Y=-10+1,429×CM1+2,125×CM2, r2=0.55, which indicates that IDE values were 1,429 kcal/kg of DM for CM1 and 2,125 kcal/kg of DM for CM2. The ME regression was Y=5+882×CM1+925×CM2, r2=0.54, which implies ME values of 882 kcal/kg of DM for CM1 and 925 kcal/kg of DM for CM2. MEn regression was Y=2+795×CM1+844×CM2, r2=0.52, which implies MEn values of 795 kcal/kg of DM for CM1 and 844 kcal/kg of DM for CM2. Based on these results, utilization of energy and nitrogen in camelina meal by broiler chickens is low and the high viscosity observed in jejunal digesta as well as the total glucosinolate in camelina meal may have contributed to the poor energy and nitrogen utilization. © 2015 Poultry Science Association Inc.

Burden Experience of Caregivers of Acute Lymphoblastic Leukemia: Impact of Coping and Spirituality

PubMed Central

Chivukula, Usha; Kota, Sirisha; Nandinee, Durgesh

2018-01-01

Background: When a child is diagnosed with cancer the parents as caregivers experience severe anxiety, trauma, ambiguity, and grief. Caregivers of cancer patients thus deal with the management of their own psychological distress along with the child's illness. Aim: Coping plays a crucial role in improving the caregivers' physical and emotional well-being. Spirituality is an important means of consolation, strength, and emotional support during this phase. The present study aims to investigate the impact of coping and spirituality on caregiver burden. Methods: A total of 100 caregivers of children between the age group of 3–11 years, diagnosed with acute lymphoblastic leukemia were the participants of the study. The participants were recruited from cancer hospitals in Hyderabad. The study adopted a between-group design to find out if mothers and fathers differed in their coping strategies, spirituality, and caregiver burden. The study also adopted a correlation design to find the relationship between coping, spirituality, and caregiver burden. Descriptive statistics and multiple linear regression analysis were conducted to identify if coping and spirituality predict caregiver burden. Results: The results showed no significant difference in the burden experienced by both mothers and fathers; however, mothers and fathers used different coping strategies and differed on the dimensions of spirituality. The results of multiple linear regression indicated that dimensions of coping and spirituality were significant predictors of caregiver burden. Conclusion: Cancer in the child impacts the parent's burden but providing sufficient support and implementing effective coping strategies, will help in mitigating the intensity of caregiver burden. It is essential that the hospital authorities and policymakers understand that a professional health psychologist could be a liaison between the doctor, patient, and the caregiver in bringing down the levels of burden and psychological distress in caregivers as well as patients. PMID:29736124

The relationship between psychological distress and baseline sports-related concussion testing.

PubMed

Bailey, Christopher M; Samples, Hillary L; Broshek, Donna K; Freeman, Jason R; Barth, Jeffrey T

2010-07-01

This study examined the effect of psychological distress on neurocognitive performance measured during baseline concussion testing. Archival data were utilized to examine correlations between personality testing and computerized baseline concussion testing. Significantly correlated personality measures were entered into linear regression analyses, predicting baseline concussion testing performance. Suicidal ideation was examined categorically. Athletes underwent testing and screening at a university athletic training facility. Participants included 47 collegiate football players 17 to 19 years old, the majority of whom were in their first year of college. Participants were administered the Concussion Resolution Index (CRI), an internet-based neurocognitive test designed to monitor and manage both at-risk and concussed athletes. Participants took the Personality Assessment Inventory (PAI), a self-administered inventory designed to measure clinical syndromes, treatment considerations, and interpersonal style. Scales and subscales from the PAI were utilized to determine the influence psychological distress had on the CRI indices: simple reaction time, complex reaction time, and processing speed. Analyses revealed several significant correlations among aspects of somatic concern, depression, anxiety, substance abuse, and suicidal ideation and CRI performance, each with at least a moderate effect. When entered into a linear regression, the block of combined psychological symptoms accounted for a significant amount of baseline CRI performance, with moderate to large effects (r = 0.23-0.30). When examined categorically, participants with suicidal ideation showed significantly slower simple reaction time and complex reaction time, with a similar trend on processing speed. Given the possibility of obscured concussion deficits after injury, implications for premature return to play, and the need to target psychological distress outright, these findings heighten the clinical importance of screening for psychological distress during baseline and post-injury concussion evaluations.

Optimized multiple linear mappings for single image super-resolution

NASA Astrophysics Data System (ADS)

Zhang, Kaibing; Li, Jie; Xiong, Zenggang; Liu, Xiuping; Gao, Xinbo

2017-12-01

Learning piecewise linear regression has been recognized as an effective way for example learning-based single image super-resolution (SR) in literature. In this paper, we employ an expectation-maximization (EM) algorithm to further improve the SR performance of our previous multiple linear mappings (MLM) based SR method. In the training stage, the proposed method starts with a set of linear regressors obtained by the MLM-based method, and then jointly optimizes the clustering results and the low- and high-resolution subdictionary pairs for regression functions by using the metric of the reconstruction errors. In the test stage, we select the optimal regressor for SR reconstruction by accumulating the reconstruction errors of m-nearest neighbors in the training set. Thorough experimental results carried on six publicly available datasets demonstrate that the proposed SR method can yield high-quality images with finer details and sharper edges in terms of both quantitative and perceptual image quality assessments.

AHP based Anthropometric Analysis of University Hall Bed Design in Bangladesh

NASA Astrophysics Data System (ADS)

Halder, Pobitra; Sarker, Eity; Karmaker, Chitralekha

2018-05-01

In university hall, different types of bed are used for providing sleeping environment to the students. Although there are wide variations in the design of students' bed in Bangladeshi university hall, none of them are designed properly considering the anthropometric data. In this study, four anthropometric measurements related to normal students' bed dimensions were measured from 300 students from a public university hall in Bangladesh. The feedbacks regarding different health problems and their reasons were collected from considering practical situations of the students and gathering experts' opinions. Chi-square test showed that back pain, blood circulation problem, fatigue, comfort, and sleeping problem are related to students' anthropometric measurements. The analytic hierarchy process (AHP) analysis identified students' bed length as the most responsible attribute for ergonomic problems of the students. Finally, the linear regression and correlation analysis suggested the bed dimensions based on stature of the students. This study can be a helpful guideline for industrial engineers and manufacturers in designing more comfortable students' bed.

Application of neural networks with orthogonal activation functions in control of dynamical systems

NASA Astrophysics Data System (ADS)

Nikolić, Saša S.; Antić, Dragan S.; Milojković, Marko T.; Milovanović, Miroslav B.; Perić, Staniša Lj.; Mitić, Darko B.

2016-04-01

In this article, we present a new method for the synthesis of almost and quasi-orthogonal polynomials of arbitrary order. Filters designed on the bases of these functions are generators of generalised quasi-orthogonal signals for which we derived and presented necessary mathematical background. Based on theoretical results, we designed and practically implemented generalised first-order (k = 1) quasi-orthogonal filter and proved its quasi-orthogonality via performed experiments. Designed filters can be applied in many scientific areas. In this article, generated functions were successfully implemented in Nonlinear Auto Regressive eXogenous (NARX) neural network as activation functions. One practical application of the designed orthogonal neural network is demonstrated through the example of control of the complex technical non-linear system - laboratory magnetic levitation system. Obtained results were compared with neural networks with standard activation functions and orthogonal functions of trigonometric shape. The proposed network demonstrated superiority over existing solutions in the sense of system performances.

Optimizing the physical ergonomics indices for the use of partial pressure suits.

PubMed

Ding, Li; Li, Xianxue; Hedge, Alan; Hu, Huimin; Feathers, David; Qin, Zhifeng; Xiao, Huajun; Xue, Lihao; Zhou, Qianxiang

2015-03-01

This study developed an ergonomic evaluation system for the design of high-altitude partial pressure suits (PPSs). A total of twenty-one Chinese males participated in the experiment which tested three types of ergonomics indices (manipulative mission, operational reach and operational strength) were studied using a three-dimensional video-based motion capture system, a target-pointing board, a hand dynamometer, and a step-tread apparatus. In total, 36 ergonomics indices were evaluated and optimized using regression and fitting analysis. Some indices that were found to be linearly related and redundant were removed from the study. An optimal ergonomics index system was established that can be used to conveniently and quickly evaluate the performance of different pressurized/non-pressurized suit designs. The resulting ergonomics index system will provide a theoretical basis and practical guidance for mission planners, suit designers and engineers to design equipment for human use, and to aid in assessing partial pressure suits. Copyright © 2014 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Biomass Stoves and Lens Opacity and Cataract in Nepalese Women

PubMed Central

Pokhrel, Amod K.; Bates, Michael N.; Shrestha, Sachet P.; Bailey, Ian L.; DiMartino, Robert B.; Smith, Kirk R.; Joshi, N. D.

2014-01-01

Purpose Cataract is the most prevalent cause of blindness in Nepal. Several epidemiologic studies have associated cataracts with use of biomass cookstoves. These studies, however, have had limitations, including potential control selection bias and limited adjustment for possible confounding. This study, in Pokhara city, in an area of Nepal where biomass cookstoves are widely used without direct venting of the smoke to the outdoors, focuses on pre-clinical measures of opacity, while avoiding selection bias and taking into account comprehensive data on potential confounding factors Methods Using a cross-sectional study design, severity of lenticular damage, judged on the LOCS III scales, was investigated in females (n=143), aged 20-65 years, without previously diagnosed cataract. Linear and logistic regression analyses were used to examine the relationships with stove type and length of use. Clinically significant cataract, used in the logistic regression models, was defined as a LOCS III score > 2. Results Using gas cookstoves as the reference group, logistic regression analysis for nuclear cataract showed the evidence of relationships with stove type: for biomass stoves, the odds ratio (OR) was 2.58 (95% confidence interval [CI]: 1.22-5.46) and, for kerosene stoves, the OR was 5.18 (95% CI: 0.88-30.38). Similar results were found for nuclear color (LOCS III score > 2), but no association was found with cortical cataracts. Supporting a relationship between biomass stoves and nuclear cataract was a trend with years of exposure to biomass cookstoves (p=0.01). Linear regression analyses did not show clear evidence of an association between lenticular damage and stove types. Biomass fuel used for heating was not associated with any form of opacity. Conclusions This study provides support for associations of biomass and kerosene cookstoves with nuclear opacity and change in nuclear color. The novel associations with kerosene cookstove use deserve further investigation. PMID:23400024

Impact of the Japanese 5S management method on patients' and caretakers' satisfaction: a quasi-experimental study in Senegal.

PubMed

Kanamori, Shogo; Castro, Marcia C; Sow, Seydou; Matsuno, Rui; Cissokho, Alioune; Jimba, Masamine

2016-01-01

The 5S method is a lean management tool for workplace organization, with 5S being an abbreviation for five Japanese words that translate to English as Sort, Set in Order, Shine, Standardize, and Sustain. In Senegal, the 5S intervention program was implemented in 10 health centers in two regions between 2011 and 2014. To identify the impact of the 5S intervention program on the satisfaction of clients (patients and caretakers) who visited the health centers. A standardized 5S intervention protocol was implemented in the health centers using a quasi-experimental separate pre-post samples design (four intervention and three control health facilities). A questionnaire with 10 five-point Likert items was used to measure client satisfaction. Linear regression analysis was conducted to identify the intervention's effect on the client satisfaction scores, represented by an equally weighted average of the 10 Likert items (Cronbach's alpha=0.83). Additional regression analyses were conducted to identify the intervention's effect on the scores of each Likert item. Backward stepwise linear regression ( n= 1,928) indicated a statistically significant effect of the 5S intervention, represented by an increase of 0.19 points in the client satisfaction scores in the intervention group, 6 to 8 months after the intervention ( p= 0.014). Additional regression analyses showed significant score increases of 0.44 ( p= 0.002), 0.14 ( p= 0.002), 0.06 ( p= 0.019), and 0.17 ( p= 0.044) points on four items, which, respectively were healthcare staff members' communication, explanations about illnesses or cases, and consultation duration, and clients' overall satisfaction. The 5S has the potential to improve client satisfaction at resource-poor health facilities and could therefore be recommended as a strategic option for improving the quality of healthcare service in low- and middle-income countries. To explore more effective intervention modalities, further studies need to address the mechanisms by which 5S leads to attitude changes in healthcare staff.

Carbon dioxide stripping in aquaculture -- part III: model verification

USGS Publications Warehouse

Colt, John; Watten, Barnaby; Pfeiffer, Tim

2012-01-01

Based on conventional mass transfer models developed for oxygen, the use of the non-linear ASCE method, 2-point method, and one parameter linear-regression method were evaluated for carbon dioxide stripping data. For values of KLaCO2 < approximately 1.5/h, the 2-point or ASCE method are a good fit to experimental data, but the fit breaks down at higher values of KLaCO2. How to correct KLaCO2 for gas phase enrichment remains to be determined. The one-parameter linear regression model was used to vary the C*CO2 over the test, but it did not result in a better fit to the experimental data when compared to the ASCE or fixed C*CO2 assumptions.

Pyrogenic carbon distribution in mineral topsoils of the northeastern United States

USGS Publications Warehouse

Jauss, Verena; Sullivan, Patrick J.; Sanderman, Jonathan; Smith, David; Lehmann, Johannes

2017-01-01

Due to its slow turnover rates in soil, pyrogenic carbon (PyC) is considered an important C pool and relevant to climate change processes. Therefore, the amounts of soil PyC were compared to environmental covariates over an area of 327,757 km2 in the northeastern United States in order to understand the controls on PyC distribution over large areas. Topsoil (defined as the soil A horizon, after removal of any organic horizons) samples were collected at 165 field sites in a generalised random tessellation stratified design that corresponded to approximately 1 site per 1600 km2 and PyC was estimated from diffuse reflectance mid-infrared spectroscopy measurements using a partial least-squares regression analysis in conjunction with a large database of PyC measurements based on a solid-state 13C nuclear magnetic resonance spectroscopy technique. Three spatial models were applied to the data in order to relate critical environmental covariates to the changes in spatial density of PyC over the landscape. Regional mean density estimates of PyC were 11.0 g kg− 1 (0.84 Gg km− 2) for Ordinary Kriging, 25.8 g kg− 1(12.2 Gg km− 2) for Multivariate Linear Regression, and 26.1 g kg− 1 (12.4 Gg km− 2) for Bayesian Regression Kriging. Akaike Information Criterion (AIC) indicated that the Multivariate Linear Regression model performed best (AIC = 842.6; n = 165) compared to Ordinary Kriging (AIC = 982.4) and Bayesian Regression Kriging (AIC = 979.2). Soil PyC concentrations correlated well with total soil sulphur (P < 0.001; n = 165), plant tissue lignin (P = 0.003), and drainage class (P = 0.008). This suggests the opportunity of including related environmental parameters in the spatial assessment of PyC in soils. Better estimates of the contribution of PyC to the global carbon cycle will thus also require more accurate assessments of these covariates.

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.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Relationships between otolith size and fish length in some mesopelagic teleosts (Myctophidae, Paralepididae, Phosichthyidae and Stomiidae).

PubMed

Battaglia, P; Malara, D; Ammendolia, G; Romeo, T; Andaloro, F

2015-09-01

Length-mass relationships and linear regressions are given for otolith size (length and height) and standard length (LS ) of certain mesopelagic fishes (Myctophidae, Paralepididae, Phosichthyidae and Stomiidae) living in the central Mediterranean Sea. The length-mass relationship showed isometric growth in six species, whereas linear regressions of LS and otolith size fit the data well for all species. These equations represent a useful tool for dietary studies on Mediterranean marine predators. © 2015 The Fisheries Society of the British Isles.