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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.
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.
Correlation and simple linear regression.

PubMed

Eberly, Lynn E

2007-01-01

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

PubMed

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2014-06-01

Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.
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.
Structured functional additive regression in reproducing kernel Hilbert spaces

PubMed Central

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2013-01-01

Summary Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application. PMID:25013362
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 ...
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
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.
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
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.
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…

Genetic Programming Transforms in Linear Regression Situations

NASA Astrophysics Data System (ADS)

Castillo, Flor; Kordon, Arthur; Villa, Carlos

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

PubMed

Fenske, Nora; Fahrmeir, Ludwig; Hothorn, Torsten; Rzehak, Peter; Höhle, Michael

2013-07-25

Childhood obesity and the investigation of its risk factors has become an important public health issue. Our work is based on and motivated by a German longitudinal study including 2,226 children with up to ten measurements on their body mass index (BMI) and risk factors from birth to the age of 10 years. We introduce boosting of structured additive quantile regression as a novel distribution-free approach for longitudinal quantile regression. The quantile-specific predictors of our model include conventional linear population effects, smooth nonlinear functional effects, varying-coefficient terms, and individual-specific effects, such as intercepts and slopes. Estimation is based on boosting, a computer intensive inference method for highly complex models. We propose a component-wise functional gradient descent boosting algorithm that allows for penalized estimation of the large variety of different effects, particularly leading to individual-specific effects shrunken toward zero. This concept allows us to flexibly estimate the nonlinear age curves of upper quantiles of the BMI distribution, both on population and on individual-specific level, adjusted for further risk factors and to detect age-varying effects of categorical risk factors. Our model approach can be regarded as the quantile regression analog of Gaussian additive mixed models (or structured additive mean regression models), and we compare both model classes with respect to our obesity data.
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 Â© 2016 Elsevier Inc. All rights reserved.
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
Automating approximate Bayesian computation by local linear regression.

PubMed

Thornton, Kevin R

2009-07-07

In several biological contexts, parameter inference often relies on computationally-intensive techniques. "Approximate Bayesian Computation", or ABC, methods based on summary statistics have become increasingly popular. A particular flavor of ABC based on using a linear regression to approximate the posterior distribution of the parameters, conditional on the summary statistics, is computationally appealing, yet no standalone tool exists to automate the procedure. Here, I describe a program to implement the method. The software package ABCreg implements the local linear-regression approach to ABC. The advantages are: 1. The code is standalone, and fully-documented. 2. The program will automatically process multiple data sets, and create unique output files for each (which may be processed immediately in R), facilitating the testing of inference procedures on simulated data, or the analysis of multiple data sets. 3. The program implements two different transformation methods for the regression step. 4. Analysis options are controlled on the command line by the user, and the program is designed to output warnings for cases where the regression fails. 5. The program does not depend on any particular simulation machinery (coalescent, forward-time, etc.), and therefore is a general tool for processing the results from any simulation. 6. The code is open-source, and modular.Examples of applying the software to empirical data from Drosophila melanogaster, and testing the procedure on simulated data, are shown. In practice, the ABCreg simplifies implementing ABC based on local-linear regression.
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.…
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.
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.
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
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.
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...
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.
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...
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.
Estimating interaction on an additive scale between continuous determinants in a logistic regression model.

PubMed

Knol, Mirjam J; van der Tweel, Ingeborg; Grobbee, Diederick E; Numans, Mattijs E; Geerlings, Mirjam I

2007-10-01

To determine the presence of interaction in epidemiologic research, typically a product term is added to the regression model. In linear regression, the regression coefficient of the product term reflects interaction as departure from additivity. However, in logistic regression it refers to interaction as departure from multiplicativity. Rothman has argued that interaction estimated as departure from additivity better reflects biologic interaction. So far, literature on estimating interaction on an additive scale using logistic regression only focused on dichotomous determinants. The objective of the present study was to provide the methods to estimate interaction between continuous determinants and to illustrate these methods with a clinical example. and results From the existing literature we derived the formulas to quantify interaction as departure from additivity between one continuous and one dichotomous determinant and between two continuous determinants using logistic regression. Bootstrapping was used to calculate the corresponding confidence intervals. To illustrate the theory with an empirical example, data from the Utrecht Health Project were used, with age and body mass index as risk factors for elevated diastolic blood pressure. The methods and formulas presented in this article are intended to assist epidemiologists to calculate interaction on an additive scale between two variables on a certain outcome. The proposed methods are included in a spreadsheet which is freely available at: http://www.juliuscenter.nl/additive-interaction.xls.
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.
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…
[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.
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.

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.
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.
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.
Robust best linear estimator for Cox regression with instrumental variables in whole cohort and surrogates with additive measurement error in calibration sample.

PubMed

Wang, Ching-Yun; Song, Xiao

2016-11-01

Biomedical researchers are often interested in estimating the effect of an environmental exposure in relation to a chronic disease endpoint. However, the exposure variable of interest may be measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies an additive measurement error model, but it may not have repeated measurements. The subset in which the surrogate variables are available is called a calibration sample. In addition to the surrogate variables that are available among the subjects in the calibration sample, we consider the situation when there is an instrumental variable available for all study subjects. An instrumental variable is correlated with the unobserved true exposure variable, and hence can be useful in the estimation of the regression coefficients. In this paper, we propose a nonparametric method for Cox regression using the observed data from the whole cohort. The nonparametric estimator is the best linear combination of a nonparametric correction estimator from the calibration sample and the difference of the naive estimators from the calibration sample and the whole cohort. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via intensive simulation studies. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Robust best linear estimator for Cox regression with instrumental variables in whole cohort and surrogates with additive measurement error in calibration sample

PubMed Central

Wang, Ching-Yun; Song, Xiao

2017-01-01

SUMMARY Biomedical researchers are often interested in estimating the effect of an environmental exposure in relation to a chronic disease endpoint. However, the exposure variable of interest may be measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies an additive measurement error model, but it may not have repeated measurements. The subset in which the surrogate variables are available is called a calibration sample. In addition to the surrogate variables that are available among the subjects in the calibration sample, we consider the situation when there is an instrumental variable available for all study subjects. An instrumental variable is correlated with the unobserved true exposure variable, and hence can be useful in the estimation of the regression coefficients. In this paper, we propose a nonparametric method for Cox regression using the observed data from the whole cohort. The nonparametric estimator is the best linear combination of a nonparametric correction estimator from the calibration sample and the difference of the naive estimators from the calibration sample and the whole cohort. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via intensive simulation studies. The methods are applied to the Nutritional Biomarkers Study of the Women’s Health Initiative. PMID:27546625
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.
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
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.
Practical Session: Multiple Linear Regression

NASA Astrophysics Data System (ADS)

Clausel, M.; Grégoire, G.

2014-12-01

Three exercises are proposed to illustrate the simple linear regression. In the first one investigates the influence of several factors on atmospheric pollution. It has been proposed by D. Chessel and A.B. Dufour in Lyon 1 (see Sect. 6 of http://pbil.univ-lyon1.fr/R/pdf/tdr33.pdf) and is based on data coming from 20 cities of U.S. Exercise 2 is an introduction to model selection whereas Exercise 3 provides a first example of analysis of variance. Exercises 2 and 3 have been proposed by A. Dalalyan at ENPC (see Exercises 2 and 3 of http://certis.enpc.fr/~dalalyan/Download/TP_ENPC_5.pdf).
Modeling Fire Occurrence at the City Scale: A Comparison between Geographically Weighted Regression and Global Linear Regression.

PubMed

Song, Chao; Kwan, Mei-Po; Zhu, Jiping

2017-04-08

An increasing number of fires are occurring with the rapid development of cities, resulting in increased risk for human beings and the environment. This study compares geographically weighted regression-based models, including geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR), which integrates spatial and temporal effects and global linear regression models (LM) for modeling fire risk at the city scale. The results show that the road density and the spatial distribution of enterprises have the strongest influences on fire risk, which implies that we should focus on areas where roads and enterprises are densely clustered. In addition, locations with a large number of enterprises have fewer fire ignition records, probably because of strict management and prevention measures. A changing number of significant variables across space indicate that heterogeneity mainly exists in the northern and eastern rural and suburban areas of Hefei city, where human-related facilities or road construction are only clustered in the city sub-centers. GTWR can capture small changes in the spatiotemporal heterogeneity of the variables while GWR and LM cannot. An approach that integrates space and time enables us to better understand the dynamic changes in fire risk. Thus governments can use the results to manage fire safety at the city scale.
Modeling Fire Occurrence at the City Scale: A Comparison between Geographically Weighted Regression and Global Linear Regression

PubMed Central

Song, Chao; Kwan, Mei-Po; Zhu, Jiping

2017-01-01

An increasing number of fires are occurring with the rapid development of cities, resulting in increased risk for human beings and the environment. This study compares geographically weighted regression-based models, including geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR), which integrates spatial and temporal effects and global linear regression models (LM) for modeling fire risk at the city scale. The results show that the road density and the spatial distribution of enterprises have the strongest influences on fire risk, which implies that we should focus on areas where roads and enterprises are densely clustered. In addition, locations with a large number of enterprises have fewer fire ignition records, probably because of strict management and prevention measures. A changing number of significant variables across space indicate that heterogeneity mainly exists in the northern and eastern rural and suburban areas of Hefei city, where human-related facilities or road construction are only clustered in the city sub-centers. GTWR can capture small changes in the spatiotemporal heterogeneity of the variables while GWR and LM cannot. An approach that integrates space and time enables us to better understand the dynamic changes in fire risk. Thus governments can use the results to manage fire safety at the city scale. PMID:28397745
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.
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.
Testing a single regression coefficient in high dimensional linear models

PubMed Central

Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2017-01-01

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively. PMID:28663668
Testing a single regression coefficient in high dimensional linear models.

PubMed

Lan, Wei; Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2016-11-01

In linear regression models with high dimensional data, the classical z -test (or t -test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z -test to assess the significance of each covariate. Based on the p -value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.
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.
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…
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.

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.
Prediction of monthly rainfall in Victoria, Australia: Clusterwise linear regression approach

NASA Astrophysics Data System (ADS)

Bagirov, Adil M.; Mahmood, Arshad; Barton, Andrew

2017-05-01

This paper develops the Clusterwise Linear Regression (CLR) technique for prediction of monthly rainfall. The CLR is a combination of clustering and regression techniques. It is formulated as an optimization problem and an incremental algorithm is designed to solve it. The algorithm is applied to predict monthly rainfall in Victoria, Australia using rainfall data with five input meteorological variables over the period of 1889-2014 from eight geographically diverse weather stations. The prediction performance of the CLR method is evaluated by comparing observed and predicted rainfall values using four measures of forecast accuracy. The proposed method is also compared with the CLR using the maximum likelihood framework by the expectation-maximization algorithm, multiple linear regression, artificial neural networks and the support vector machines for regression models using computational results. The results demonstrate that the proposed algorithm outperforms other methods in most locations.
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.
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.…
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
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.
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.
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.
Predicting the occurrence of wildfires with binary structured additive regression models.

PubMed

Ríos-Pena, Laura; Kneib, Thomas; Cadarso-Suárez, Carmen; Marey-Pérez, Manuel

2017-02-01

Wildfires are one of the main environmental problems facing societies today, and in the case of Galicia (north-west Spain), they are the main cause of forest destruction. This paper used binary structured additive regression (STAR) for modelling the occurrence of wildfires in Galicia. Binary STAR models are a recent contribution to the classical logistic regression and binary generalized additive models. Their main advantage lies in their flexibility for modelling non-linear effects, while simultaneously incorporating spatial and temporal variables directly, thereby making it possible to reveal possible relationships among the variables considered. The results showed that the occurrence of wildfires depends on many covariates which display variable behaviour across space and time, and which largely determine the likelihood of ignition of a fire. The joint possibility of working on spatial scales with a resolution of 1 × 1 km cells and mapping predictions in a colour range makes STAR models a useful tool for plotting and predicting wildfire occurrence. Lastly, it will facilitate the development of fire behaviour models, which can be invaluable when it comes to drawing up fire-prevention and firefighting plans. Copyright © 2016 Elsevier Ltd. All rights reserved.
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
Prediction models for CO2 emission in Malaysia using best subsets regression and multi-linear regression

NASA Astrophysics Data System (ADS)

Tan, C. H.; Matjafri, M. Z.; Lim, H. S.

2015-10-01

This paper presents the prediction models which analyze and compute the CO2 emission in Malaysia. Each prediction model for CO2 emission will be analyzed based on three main groups which is transportation, electricity and heat production as well as residential buildings and commercial and public services. The prediction models were generated using data obtained from World Bank Open Data. Best subset method will be used to remove irrelevant data and followed by multi linear regression to produce the prediction models. From the results, high R-square (prediction) value was obtained and this implies that the models are reliable to predict the CO2 emission by using specific data. In addition, the CO2 emissions from these three groups are forecasted using trend analysis plots for observation purpose.
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.
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.
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.
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.
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).
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.
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.
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.

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
Regression of non-linear coupling of noise in LIGO detectors

NASA Astrophysics Data System (ADS)

Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.

2018-03-01

In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.
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
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…
Does the high–tech industry consistently reduce CO{sub 2} emissions? Results from nonparametric additive regression model

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

Xu, Bin; Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013; Lin, Boqiang, E-mail: bqlin@xmu.edu.cn

China is currently the world's largest carbon dioxide (CO{sub 2}) emitter. Moreover, total energy consumption and CO{sub 2} emissions in China will continue to increase due to the rapid growth of industrialization and urbanization. Therefore, vigorously developing the high–tech industry becomes an inevitable choice to reduce CO{sub 2} emissions at the moment or in the future. However, ignoring the existing nonlinear links between economic variables, most scholars use traditional linear models to explore the impact of the high–tech industry on CO{sub 2} emissions from an aggregate perspective. Few studies have focused on nonlinear relationships and regional differences in China. Basedmore » on panel data of 1998–2014, this study uses the nonparametric additive regression model to explore the nonlinear effect of the high–tech industry from a regional perspective. The estimated results show that the residual sum of squares (SSR) of the nonparametric additive regression model in the eastern, central and western regions are 0.693, 0.054 and 0.085 respectively, which are much less those that of the traditional linear regression model (3.158, 4.227 and 7.196). This verifies that the nonparametric additive regression model has a better fitting effect. Specifically, the high–tech industry produces an inverted “U–shaped” nonlinear impact on CO{sub 2} emissions in the eastern region, but a positive “U–shaped” nonlinear effect in the central and western regions. Therefore, the nonlinear impact of the high–tech industry on CO{sub 2} emissions in the three regions should be given adequate attention in developing effective abatement policies. - Highlights: • The nonlinear effect of the high–tech industry on CO{sub 2} emissions was investigated. • The high–tech industry yields an inverted “U–shaped” effect in the eastern region. • The high–tech industry has a positive “U–shaped” nonlinear effect in other regions. • The linear
Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.

PubMed

Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo

2015-08-01

Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.
Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape

PubMed Central

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS
Modeling Linguistic Variables With Regression Models: Addressing Non-Gaussian Distributions, Non-independent Observations, and Non-linear Predictors With Random Effects and Generalized Additive Models for Location, Scale, and Shape.

PubMed

Coupé, Christophe

2018-01-01

As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for 'difficult' variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we
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…
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.
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
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.
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…
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.
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.
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.
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…
Aspects of porosity prediction using multivariate linear regression

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

Byrnes, A.P.; Wilson, M.D.

1991-03-01

Highly accurate multiple linear regression models have been developed for sandstones of diverse compositions. Porosity reduction or enhancement processes are controlled by the fundamental variables, Pressure (P), Temperature (T), Time (t), and Composition (X), where composition includes mineralogy, size, sorting, fluid composition, etc. The multiple linear regression equation, of which all linear porosity prediction models are subsets, takes the generalized form: Porosity = C{sub 0} + C{sub 1}(P) + C{sub 2}(T) + C{sub 3}(X) + C{sub 4}(t) + C{sub 5}(PT) + C{sub 6}(PX) + C{sub 7}(Pt) + C{sub 8}(TX) + C{sub 9}(Tt) + C{sub 10}(Xt) + C{sub 11}(PTX) + C{submore » 12}(PXt) + C{sub 13}(PTt) + C{sub 14}(TXt) + C{sub 15}(PTXt). The first four primary variables are often interactive, thus requiring terms involving two or more primary variables (the form shown implies interaction and not necessarily multiplication). The final terms used may also involve simple mathematic transforms such as log X, e{sup T}, X{sup 2}, or more complex transformations such as the Time-Temperature Index (TTI). The X term in the equation above represents a suite of compositional variable and, therefore, a fully expanded equation may include a series of terms incorporating these variables. Numerous published bivariate porosity prediction models involving P (or depth) or Tt (TTI) are effective to a degree, largely because of the high degree of colinearity between p and TTI. However, all such bivariate models ignore the unique contributions of P and Tt, as well as various X terms. These simpler models become poor predictors in regions where colinear relations change, were important variables have been ignored, or where the database does not include a sufficient range or weight distribution for the critical variables.« less
Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

NASA Astrophysics Data System (ADS)

Caimmi, R.

2011-08-01

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts ( York, 1966, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter ( Isobe et al., 1990; Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]-[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (∓ σ) for both

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…
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).
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...
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.
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.
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
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.
The extinction law from photometric data: linear regression methods

NASA Astrophysics Data System (ADS)

Ascenso, J.; Lombardi, M.; Lada, C. J.; Alves, J.

2012-04-01

Context. The properties of dust grains, in particular their size distribution, are expected to differ from the interstellar medium to the high-density regions within molecular clouds. Since the extinction at near-infrared wavelengths is caused by dust, the extinction law in cores should depart from that found in low-density environments if the dust grains have different properties. Aims: We explore methods to measure the near-infrared extinction law produced by dense material in molecular cloud cores from photometric data. Methods: Using controlled sets of synthetic and semi-synthetic data, we test several methods for linear regression applied to the specific problem of deriving the extinction law from photometric data. We cover the parameter space appropriate to this type of observations. Results: We find that many of the common linear-regression methods produce biased results when applied to the extinction law from photometric colors. We propose and validate a new method, LinES, as the most reliable for this effect. We explore the use of this method to detect whether or not the extinction law of a given reddened population has a break at some value of extinction. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile (ESO programmes 069.C-0426 and 074.C-0728).
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.
Linear regression metamodeling as a tool to summarize and present simulation model results.

PubMed

Jalal, Hawre; Dowd, Bryan; Sainfort, François; Kuntz, Karen M

2013-10-01

Modelers lack a tool to systematically and clearly present complex model results, including those from sensitivity analyses. The objective was to propose linear regression metamodeling as a tool to increase transparency of decision analytic models and better communicate their results. We used a simplified cancer cure model to demonstrate our approach. The model computed the lifetime cost and benefit of 3 treatment options for cancer patients. We simulated 10,000 cohorts in a probabilistic sensitivity analysis (PSA) and regressed the model outcomes on the standardized input parameter values in a set of regression analyses. We used the regression coefficients to describe measures of sensitivity analyses, including threshold and parameter sensitivity analyses. We also compared the results of the PSA to deterministic full-factorial and one-factor-at-a-time designs. The regression intercept represented the estimated base-case outcome, and the other coefficients described the relative parameter uncertainty in the model. We defined simple relationships that compute the average and incremental net benefit of each intervention. Metamodeling produced outputs similar to traditional deterministic 1-way or 2-way sensitivity analyses but was more reliable since it used all parameter values. Linear regression metamodeling is a simple, yet powerful, tool that can assist modelers in communicating model characteristics and sensitivity analyses.
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.
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.
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
Sparse brain network using penalized linear regression

NASA Astrophysics Data System (ADS)

Lee, Hyekyoung; Lee, Dong Soo; Kang, Hyejin; Kim, Boong-Nyun; Chung, Moo K.

2011-03-01

Sparse partial correlation is a useful connectivity measure for brain networks when it is difficult to compute the exact partial correlation in the small-n large-p setting. In this paper, we formulate the problem of estimating partial correlation as a sparse linear regression with a l1-norm penalty. The method is applied to brain network consisting of parcellated regions of interest (ROIs), which are obtained from FDG-PET images of the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. To validate the results, we check their reproducibilities of the obtained brain networks by the leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.
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
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.
Distributed Monitoring of the R(sup 2) Statistic for Linear Regression

NASA Technical Reports Server (NTRS)

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

2011-01-01

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

PubMed

Agier, Lydiane; Portengen, Lützen; Chadeau-Hyam, Marc; Basagaña, Xavier; Giorgis-Allemand, Lise; Siroux, Valérie; Robinson, Oliver; Vlaanderen, Jelle; González, Juan R; Nieuwenhuijsen, Mark J; Vineis, Paolo; Vrijheid, Martine; Slama, Rémy; Vermeulen, Roel

2016-12-01

The exposome constitutes a promising framework to improve understanding of the effects of environmental exposures on health by explicitly considering multiple testing and avoiding selective reporting. However, exposome studies are challenged by the simultaneous consideration of many correlated exposures. We compared the performances of linear regression-based statistical methods in assessing exposome-health associations. In a simulation study, we generated 237 exposure covariates with a realistic correlation structure and with a health outcome linearly related to 0 to 25 of these covariates. Statistical methods were compared primarily in terms of false discovery proportion (FDP) and sensitivity. On average over all simulation settings, the elastic net and sparse partial least-squares regression showed a sensitivity of 76% and an FDP of 44%; Graphical Unit Evolutionary Stochastic Search (GUESS) and the deletion/substitution/addition (DSA) algorithm revealed a sensitivity of 81% and an FDP of 34%. The environment-wide association study (EWAS) underperformed these methods in terms of FDP (average FDP, 86%) despite a higher sensitivity. Performances decreased considerably when assuming an exposome exposure matrix with high levels of correlation between covariates. Correlation between exposures is a challenge for exposome research, and the statistical methods investigated in this study were limited in their ability to efficiently differentiate true predictors from correlated covariates in a realistic exposome context. Although GUESS and DSA provided a marginally better balance between sensitivity and FDP, they did not outperform the other multivariate methods across all scenarios and properties examined, and computational complexity and flexibility should also be considered when choosing between these methods. Citation: Agier L, Portengen L, Chadeau-Hyam M, Basagaña X, Giorgis-Allemand L, Siroux V, Robinson O, Vlaanderen J, González JR, Nieuwenhuijsen MJ, Vineis P
Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data.

PubMed

Ying, Gui-Shuang; Maguire, Maureen G; Glynn, Robert; Rosner, Bernard

2017-04-01

To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data. We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field in the elderly. When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI -0.03 to 0.32D, p = 0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, p = 0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller p-values, while analysis of the worse eye provided larger p-values than mixed effects models and marginal models. In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision.
Weighted functional linear regression models for gene-based association analysis.

PubMed

Belonogova, Nadezhda M; Svishcheva, Gulnara R; Wilson, James F; Campbell, Harry; Axenovich, Tatiana I

2018-01-01

Functional linear regression models are effectively used in gene-based association analysis of complex traits. These models combine information about individual genetic variants, taking into account their positions and reducing the influence of noise and/or observation errors. To increase the power of methods, where several differently informative components are combined, weights are introduced to give the advantage to more informative components. Allele-specific weights have been introduced to collapsing and kernel-based approaches to gene-based association analysis. Here we have for the first time introduced weights to functional linear regression models adapted for both independent and family samples. Using data simulated on the basis of GAW17 genotypes and weights defined by allele frequencies via the beta distribution, we demonstrated that type I errors correspond to declared values and that increasing the weights of causal variants allows the power of functional linear models to be increased. We applied the new method to real data on blood pressure from the ORCADES sample. Five of the six known genes with P < 0.1 in at least one analysis had lower P values with weighted models. Moreover, we found an association between diastolic blood pressure and the VMP1 gene (P = 8.18×10-6), when we used a weighted functional model. For this gene, the unweighted functional and weighted kernel-based models had P = 0.004 and 0.006, respectively. The new method has been implemented in the program package FREGAT, which is freely available at https://cran.r-project.org/web/packages/FREGAT/index.html.

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…
Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data

PubMed Central

Ying, Gui-shuang; Maguire, Maureen G; Glynn, Robert; Rosner, Bernard

2017-01-01

Purpose To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data. Methods We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field data in the elderly. Results When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI −0.03 to 0.32D, P=0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, P=0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller P-values, while analysis of the worse eye provided larger P-values than mixed effects models and marginal models. Conclusion In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision. PMID:28102741
[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.
Detection of epistatic effects with logic regression and a classical linear regression model.

PubMed

Malina, Magdalena; Ickstadt, Katja; Schwender, Holger; Posch, Martin; Bogdan, Małgorzata

2014-02-01

To locate multiple interacting quantitative trait loci (QTL) influencing a trait of interest within experimental populations, usually methods as the Cockerham's model are applied. Within this framework, interactions are understood as the part of the joined effect of several genes which cannot be explained as the sum of their additive effects. However, if a change in the phenotype (as disease) is caused by Boolean combinations of genotypes of several QTLs, this Cockerham's approach is often not capable to identify them properly. To detect such interactions more efficiently, we propose a logic regression framework. Even though with the logic regression approach a larger number of models has to be considered (requiring more stringent multiple testing correction) the efficient representation of higher order logic interactions in logic regression models leads to a significant increase of power to detect such interactions as compared to a Cockerham's approach. The increase in power is demonstrated analytically for a simple two-way interaction model and illustrated in more complex settings with simulation study and real data analysis.
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.
Differential gene expression detection and sample classification using penalized linear regression models.

PubMed

Wu, Baolin

2006-02-15

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p > n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-differentially expressed genes that can classify the samples very well. The idea of shrinkage is to regularize the model parameters to reduce the effects of noise and produce reliable inferences. Shrinkage has been successfully applied in the microarray data analysis. The SAM statistics proposed by Tusher et al. and the 'nearest shrunken centroid' proposed by Tibshirani et al. are ad hoc shrinkage methods. Both methods are simple, intuitive and prove to be useful in empirical studies. Recently Wu proposed the penalized t/F-statistics with shrinkage by formally using the (1) penalized linear regression models for two-class microarray data, showing good performance. In this paper we systematically discussed the use of penalized regression models for analyzing microarray data. We generalize the two-class penalized t/F-statistics proposed by Wu to multi-class microarray data. We formally derive the ad hoc shrunken centroid used by Tibshirani et al. using the (1) penalized regression models. And we show that the penalized linear regression models provide a rigorous and unified statistical framework for sample classification and differential gene expression detection.
Reduction of interferences in graphite furnace atomic absorption spectrometry by multiple linear regression modelling

NASA Astrophysics Data System (ADS)

Grotti, Marco; Abelmoschi, Maria Luisa; Soggia, Francesco; Tiberiade, Christian; Frache, Roberto

2000-12-01

The multivariate effects of Na, K, Mg and Ca as nitrates on the electrothermal atomisation of manganese, cadmium and iron were studied by multiple linear regression modelling. Since the models proved to efficiently predict the effects of the considered matrix elements in a wide range of concentrations, they were applied to correct the interferences occurring in the determination of trace elements in seawater after pre-concentration of the analytes. In order to obtain a statistically significant number of samples, a large volume of the certified seawater reference materials CASS-3 and NASS-3 was treated with Chelex-100 resin; then, the chelating resin was separated from the solution, divided into several sub-samples, each of them was eluted with nitric acid and analysed by electrothermal atomic absorption spectrometry (for trace element determinations) and inductively coupled plasma optical emission spectrometry (for matrix element determinations). To minimise any other systematic error besides that due to matrix effects, accuracy of the pre-concentration step and contamination levels of the procedure were checked by inductively coupled plasma mass spectrometric measurements. Analytical results obtained by applying the multiple linear regression models were compared with those obtained with other calibration methods, such as external calibration using acid-based standards, external calibration using matrix-matched standards and the analyte addition technique. Empirical models proved to efficiently reduce interferences occurring in the analysis of real samples, allowing an improvement of accuracy better than for other calibration methods.
[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<linear regression P value). The statistical power of CAT test decreased, while the result of linear regression analysis remained the same when population size was reduced by 100 times and AMI incidence rate remained unchanged. The two statistical methods have their advantages and disadvantages. It is necessary to choose statistical method according the fitting degree of data, or comprehensively analyze the results of two methods.
Modeling Pan Evaporation for Kuwait by Multiple Linear Regression

PubMed Central

Almedeij, Jaber

2012-01-01

Evaporation is an important parameter for many projects related to hydrology and water resources systems. This paper constitutes the first study conducted in Kuwait to obtain empirical relations for the estimation of daily and monthly pan evaporation as functions of available meteorological data of temperature, relative humidity, and wind speed. The data used here for the modeling are daily measurements of substantial continuity coverage, within a period of 17 years between January 1993 and December 2009, which can be considered representative of the desert climate of the urban zone of the country. Multiple linear regression technique is used with a procedure of variable selection for fitting the best model forms. The correlations of evaporation with temperature and relative humidity are also transformed in order to linearize the existing curvilinear patterns of the data by using power and exponential functions, respectively. The evaporation models suggested with the best variable combinations were shown to produce results that are in a reasonable agreement with observation values. PMID:23226984
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.
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.
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.
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.
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.
Linear regression analysis and its application to multivariate chromatographic calibration for the quantitative analysis of two-component mixtures.

PubMed

Dinç, Erdal; Ozdemir, Abdil

2005-01-01

Multivariate chromatographic calibration technique was developed for the quantitative analysis of binary mixtures enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets in the presence of losartan potassium (LST). The mathematical algorithm of multivariate chromatographic calibration technique is based on the use of the linear regression equations constructed using relationship between concentration and peak area at the five-wavelength set. The algorithm of this mathematical calibration model having a simple mathematical content was briefly described. This approach is a powerful mathematical tool for an optimum chromatographic multivariate calibration and elimination of fluctuations coming from instrumental and experimental conditions. This multivariate chromatographic calibration contains reduction of multivariate linear regression functions to univariate data set. The validation of model was carried out by analyzing various synthetic binary mixtures and using the standard addition technique. Developed calibration technique was applied to the analysis of the real pharmaceutical tablets containing EA and HCT. The obtained results were compared with those obtained by classical HPLC method. It was observed that the proposed multivariate chromatographic calibration gives better results than classical HPLC.
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.
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.
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
The allometry of coarse root biomass: log-transformed linear regression or nonlinear regression?

PubMed

Lai, Jiangshan; Yang, Bo; Lin, Dunmei; Kerkhoff, Andrew J; Ma, Keping

2013-01-01

Precise estimation of root biomass is important for understanding carbon stocks and dynamics in forests. Traditionally, biomass estimates are based on allometric scaling relationships between stem diameter and coarse root biomass calculated using linear regression (LR) on log-transformed data. Recently, it has been suggested that nonlinear regression (NLR) is a preferable fitting method for scaling relationships. But while this claim has been contested on both theoretical and empirical grounds, and statistical methods have been developed to aid in choosing between the two methods in particular cases, few studies have examined the ramifications of erroneously applying NLR. Here, we use direct measurements of 159 trees belonging to three locally dominant species in east China to compare the LR and NLR models of diameter-root biomass allometry. We then contrast model predictions by estimating stand coarse root biomass based on census data from the nearby 24-ha Gutianshan forest plot and by testing the ability of the models to predict known root biomass values measured on multiple tropical species at the Pasoh Forest Reserve in Malaysia. Based on likelihood estimates for model error distributions, as well as the accuracy of extrapolative predictions, we find that LR on log-transformed data is superior to NLR for fitting diameter-root biomass scaling models. More importantly, inappropriately using NLR leads to grossly inaccurate stand biomass estimates, especially for stands dominated by smaller trees.

A multiple linear regression analysis of hot corrosion attack on a series of nickel base turbine alloys

NASA Technical Reports Server (NTRS)

Barrett, C. A.

1985-01-01

Multiple linear regression analysis was used to determine an equation for estimating hot corrosion attack for a series of Ni base cast turbine alloys. The U transform (i.e., 1/sin (% A/100) to the 1/2) was shown to give the best estimate of the dependent variable, y. A complete second degree equation is described for the centered" weight chemistries for the elements Cr, Al, Ti, Mo, W, Cb, Ta, and Co. In addition linear terms for the minor elements C, B, and Zr were added for a basic 47 term equation. The best reduced equation was determined by the stepwise selection method with essentially 13 terms. The Cr term was found to be the most important accounting for 60 percent of the explained variability hot corrosion attack.
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…
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
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...
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
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.
Predicting flight delay based on multiple linear regression

NASA Astrophysics Data System (ADS)

Ding, Yi

2017-08-01

Delay of flight has been regarded as one of the toughest difficulties in aviation control. How to establish an effective model to handle the delay prediction problem is a significant work. To solve the problem that the flight delay is difficult to predict, this study proposes a method to model the arriving flights and a multiple linear regression algorithm to predict delay, comparing with Naive-Bayes and C4.5 approach. Experiments based on a realistic dataset of domestic airports show that the accuracy of the proposed model approximates 80%, which is further improved than the Naive-Bayes and C4.5 approach approaches. The result testing shows that this method is convenient for calculation, and also can predict the flight delays effectively. It can provide decision basis for airport authorities.
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.
Quantile regression via vector generalized additive models.

PubMed

Yee, Thomas W

2004-07-30

One of the most popular methods for quantile regression is the LMS method of Cole and Green. The method naturally falls within a penalized likelihood framework, and consequently allows for considerable flexible because all three parameters may be modelled by cubic smoothing splines. The model is also very understandable: for a given value of the covariate, the LMS method applies a Box-Cox transformation to the response in order to transform it to standard normality; to obtain the quantiles, an inverse Box-Cox transformation is applied to the quantiles of the standard normal distribution. The purposes of this article are three-fold. Firstly, LMS quantile regression is presented within the framework of the class of vector generalized additive models. This confers a number of advantages such as a unifying theory and estimation process. Secondly, a new LMS method based on the Yeo-Johnson transformation is proposed, which has the advantage that the response is not restricted to be positive. Lastly, this paper describes a software implementation of three LMS quantile regression methods in the S language. This includes the LMS-Yeo-Johnson method, which is estimated efficiently by a new numerical integration scheme. The LMS-Yeo-Johnson method is illustrated by way of a large cross-sectional data set from a New Zealand working population. Copyright 2004 John Wiley & Sons, Ltd.
Analysis of reciprocal creatinine plots by two-phase linear regression.

PubMed

Rowe, P A; Richardson, R E; Burton, P R; Morgan, A G; Burden, R P

1989-01-01

The progression of renal diseases is often monitored by the serial measurement of plasma creatinine. The slope of the linear relation that is frequently found between the reciprocal of creatinine concentration and time delineates the rate of change in renal function. Minor changes in slope, perhaps indicating response to therapeutic intervention, can be difficult to identify and yet be of clinical importance. We describe the application of two-phase linear regression to identify and characterise changes in slope using a microcomputer. The method fits two intersecting lines to the data by computing a least-squares estimate of the position of the slope change and its 95% confidence limits. This avoids the potential bias of fixing the change at a preconceived time corresponding with an alteration in treatment. The program then evaluates the statistical and clinical significance of the slope change and produces a graphical output to aid interpretation.
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…
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.
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
Railway crossing risk area detection using linear regression and terrain drop compensation techniques.

PubMed

Chen, Wen-Yuan; Wang, Mei; Fu, Zhou-Xing

2014-06-16

Most railway accidents happen at railway crossings. Therefore, how to detect humans or objects present in the risk area of a railway crossing and thus prevent accidents are important tasks. In this paper, three strategies are used to detect the risk area of a railway crossing: (1) we use a terrain drop compensation (TDC) technique to solve the problem of the concavity of railway crossings; (2) we use a linear regression technique to predict the position and length of an object from image processing; (3) we have developed a novel strategy called calculating local maximum Y-coordinate object points (CLMYOP) to obtain the ground points of the object. In addition, image preprocessing is also applied to filter out the noise and successfully improve the object detection. From the experimental results, it is demonstrated that our scheme is an effective and corrective method for the detection of railway crossing risk areas.
Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle.

PubMed

Pereira, R J; Bignardi, A B; El Faro, L; Verneque, R S; Vercesi Filho, A E; Albuquerque, L G

2013-01-01

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.
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…
Single Image Super-Resolution Using Global Regression Based on Multiple Local Linear Mappings.

PubMed

Choi, Jae-Seok; Kim, Munchurl

2017-03-01

Super-resolution (SR) has become more vital, because of its capability to generate high-quality ultra-high definition (UHD) high-resolution (HR) images from low-resolution (LR) input images. Conventional SR methods entail high computational complexity, which makes them difficult to be implemented for up-scaling of full-high-definition input images into UHD-resolution images. Nevertheless, our previous super-interpolation (SI) method showed a good compromise between Peak-Signal-to-Noise Ratio (PSNR) performances and computational complexity. However, since SI only utilizes simple linear mappings, it may fail to precisely reconstruct HR patches with complex texture. In this paper, we present a novel SR method, which inherits the large-to-small patch conversion scheme from SI but uses global regression based on local linear mappings (GLM). Thus, our new SR method is called GLM-SI. In GLM-SI, each LR input patch is divided into 25 overlapped subpatches. Next, based on the local properties of these subpatches, 25 different local linear mappings are applied to the current LR input patch to generate 25 HR patch candidates, which are then regressed into one final HR patch using a global regressor. The local linear mappings are learned cluster-wise in our off-line training phase. The main contribution of this paper is as follows: Previously, linear-mapping-based conventional SR methods, including SI only used one simple yet coarse linear mapping to each patch to reconstruct its HR version. On the contrary, for each LR input patch, our GLM-SI is the first to apply a combination of multiple local linear mappings, where each local linear mapping is found according to local properties of the current LR patch. Therefore, it can better approximate nonlinear LR-to-HR mappings for HR patches with complex texture. Experiment results show that the proposed GLM-SI method outperforms most of the state-of-the-art methods, and shows comparable PSNR performance with much lower
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.
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.
Effective Surfactants Blend Concentration Determination for O/W Emulsion Stabilization by Two Nonionic Surfactants by Simple Linear Regression.

PubMed

Hassan, A K

2015-01-01

In this work, O/W emulsion sets were prepared by using different concentrations of two nonionic surfactants. The two surfactants, tween 80(HLB=15.0) and span 80(HLB=4.3) were used in a fixed proportions equal to 0.55:0.45 respectively. HLB value of the surfactants blends were fixed at 10.185. The surfactants blend concentration is starting from 3% up to 19%. For each O/W emulsion set the conductivity was measured at room temperature (25±2°), 40, 50, 60, 70 and 80°. Applying the simple linear regression least squares method statistical analysis to the temperature-conductivity obtained data determines the effective surfactants blend concentration required for preparing the most stable O/W emulsion. These results were confirmed by applying the physical stability centrifugation testing and the phase inversion temperature range measurements. The results indicated that, the relation which represents the most stable O/W emulsion has the strongest direct linear relationship between temperature and conductivity. This relationship is linear up to 80°. This work proves that, the most stable O/W emulsion is determined via the determination of the maximum R² value by applying of the simple linear regression least squares method to the temperature-conductivity obtained data up to 80°, in addition to, the true maximum slope is represented by the equation which has the maximum R² value. Because the conditions would be changed in a more complex formulation, the method of the determination of the effective surfactants blend concentration was verified by applying it for more complex formulations of 2% O/W miconazole nitrate cream and the results indicate its reproducibility.

Robust Head-Pose Estimation Based on Partially-Latent Mixture of Linear Regressions.

PubMed

Drouard, Vincent; Horaud, Radu; Deleforge, Antoine; Ba, Sileye; Evangelidis, Georgios

2017-03-01

Head-pose estimation has many applications, such as social event analysis, human-robot and human-computer interaction, driving assistance, and so forth. Head-pose estimation is challenging, because it must cope with changing illumination conditions, variabilities in face orientation and in appearance, partial occlusions of facial landmarks, as well as bounding-box-to-face alignment errors. We propose to use a mixture of linear regressions with partially-latent output. This regression method learns to map high-dimensional feature vectors (extracted from bounding boxes of faces) onto the joint space of head-pose angles and bounding-box shifts, such that they are robustly predicted in the presence of unobservable phenomena. We describe in detail the mapping method that combines the merits of unsupervised manifold learning techniques and of mixtures of regressions. We validate our method with three publicly available data sets and we thoroughly benchmark four variants of the proposed algorithm with several state-of-the-art head-pose estimation methods.
Railway Crossing Risk Area Detection Using Linear Regression and Terrain Drop Compensation Techniques

PubMed Central

Chen, Wen-Yuan; Wang, Mei; Fu, Zhou-Xing

2014-01-01

Most railway accidents happen at railway crossings. Therefore, how to detect humans or objects present in the risk area of a railway crossing and thus prevent accidents are important tasks. In this paper, three strategies are used to detect the risk area of a railway crossing: (1) we use a terrain drop compensation (TDC) technique to solve the problem of the concavity of railway crossings; (2) we use a linear regression technique to predict the position and length of an object from image processing; (3) we have developed a novel strategy called calculating local maximum Y-coordinate object points (CLMYOP) to obtain the ground points of the object. In addition, image preprocessing is also applied to filter out the noise and successfully improve the object detection. From the experimental results, it is demonstrated that our scheme is an effective and corrective method for the detection of railway crossing risk areas. PMID:24936948
pulver: an R package for parallel ultra-rapid p-value computation for linear regression interaction terms.

PubMed

Molnos, Sophie; Baumbach, Clemens; Wahl, Simone; Müller-Nurasyid, Martina; Strauch, Konstantin; Wang-Sattler, Rui; Waldenberger, Melanie; Meitinger, Thomas; Adamski, Jerzy; Kastenmüller, Gabi; Suhre, Karsten; Peters, Annette; Grallert, Harald; Theis, Fabian J; Gieger, Christian

2017-09-29

Genome-wide association studies allow us to understand the genetics of complex diseases. Human metabolism provides information about the disease-causing mechanisms, so it is usual to investigate the associations between genetic variants and metabolite levels. However, only considering genetic variants and their effects on one trait ignores the possible interplay between different "omics" layers. Existing tools only consider single-nucleotide polymorphism (SNP)-SNP interactions, and no practical tool is available for large-scale investigations of the interactions between pairs of arbitrary quantitative variables. We developed an R package called pulver to compute p-values for the interaction term in a very large number of linear regression models. Comparisons based on simulated data showed that pulver is much faster than the existing tools. This is achieved by using the correlation coefficient to test the null-hypothesis, which avoids the costly computation of inversions. Additional tricks are a rearrangement of the order, when iterating through the different "omics" layers, and implementing this algorithm in the fast programming language C++. Furthermore, we applied our algorithm to data from the German KORA study to investigate a real-world problem involving the interplay among DNA methylation, genetic variants, and metabolite levels. The pulver package is a convenient and rapid tool for screening huge numbers of linear regression models for significant interaction terms in arbitrary pairs of quantitative variables. pulver is written in R and C++, and can be downloaded freely from CRAN at https://cran.r-project.org/web/packages/pulver/ .
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.
Generalized linear and generalized additive models in studies of species distributions: Setting the scene

USGS Publications Warehouse

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

2002-01-01

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

NASA Astrophysics Data System (ADS)

Kaul, Abhishek

This dissertation consists of three chapters. The first chapter introduces the models under consideration and motivates problems of interest. A brief literature review is also provided in this chapter. The second chapter investigates the properties of Lasso under long range dependent model errors. Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p> n) where p can be increasing exponentially with n. Finally, we show the consistency, n½ --d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study. The third chapter proposes and investigates the properties of a penalized quantile based estimator for measurement error models. Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose weighted penalized corrected quantile estimators for the regression parameter vector in linear regression models with additive measurement errors, where unobservable covariates are nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in both the fixed dimension and high dimensional sparse setups, in the latter setup, the
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.
Multiple linear regression analysis

NASA Technical Reports Server (NTRS)

Edwards, T. R.

1980-01-01

Program rapidly selects best-suited set of coefficients. User supplies only vectors of independent and dependent data and specifies confidence level required. Program uses stepwise statistical procedure for relating minimal set of variables to set of observations; final regression contains only most statistically significant coefficients. Program is written in FORTRAN IV for batch execution and has been implemented on NOVA 1200.
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.
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…
Multiple linear regression and regression with time series error models in forecasting PM10 concentrations in Peninsular Malaysia.

PubMed

Ng, Kar Yong; Awang, Norhashidah

2018-01-06

Frequent haze occurrences in Malaysia have made the management of PM 10 (particulate matter with aerodynamic less than 10 μm) pollution a critical task. This requires knowledge on factors associating with PM 10 variation and good forecast of PM 10 concentrations. Hence, this paper demonstrates the prediction of 1-day-ahead daily average PM 10 concentrations based on predictor variables including meteorological parameters and gaseous pollutants. Three different models were built. They were multiple linear regression (MLR) model with lagged predictor variables (MLR1), MLR model with lagged predictor variables and PM 10 concentrations (MLR2) and regression with time series error (RTSE) model. The findings revealed that humidity, temperature, wind speed, wind direction, carbon monoxide and ozone were the main factors explaining the PM 10 variation in Peninsular Malaysia. Comparison among the three models showed that MLR2 model was on a same level with RTSE model in terms of forecasting accuracy, while MLR1 model was the worst.
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…
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.
Causal correlation of foliar biochemical concentrations with AVIRIS spectra using forced entry linear regression

NASA Technical Reports Server (NTRS)

Dawson, Terence P.; Curran, Paul J.; Kupiec, John A.

1995-01-01

A major goal of airborne imaging spectrometry is to estimate the biochemical composition of vegetation canopies from reflectance spectra. Remotely-sensed estimates of foliar biochemical concentrations of forests would provide valuable indicators of ecosystem function at regional and eventually global scales. Empirical research has shown a relationship exists between the amount of radiation reflected from absorption features and the concentration of given biochemicals in leaves and canopies (Matson et al., 1994, Johnson et al., 1994). A technique commonly used to determine which wavelengths have the strongest correlation with the biochemical of interest is unguided (stepwise) multiple regression. Wavelengths are entered into a multivariate regression equation, in their order of importance, each contributing to the reduction of the variance in the measured biochemical concentration. A significant problem with the use of stepwise regression for determining the correlation between biochemical concentration and spectra is that of 'overfitting' as there are significantly more wavebands than biochemical measurements. This could result in the selection of wavebands which may be more accurately attributable to noise or canopy effects. In addition, there is a real problem of collinearity in that the individual biochemical concentrations may covary. A strong correlation between the reflectance at a given wavelength and the concentration of a biochemical of interest, therefore, may be due to the effect of another biochemical which is closely related. Furthermore, it is not always possible to account for potentially suitable waveband omissions in the stepwise selection procedure. This concern about the suitability of stepwise regression has been identified and acknowledged in a number of recent studies (Wessman et al., 1988, Curran, 1989, Curran et al., 1992, Peterson and Hubbard, 1992, Martine and Aber, 1994, Kupiec, 1994). These studies have pointed to the lack of a physical
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
Validating Variational Bayes Linear Regression Method With Multi-Central Datasets.

PubMed

Murata, Hiroshi; Zangwill, Linda M; Fujino, Yuri; Matsuura, Masato; Miki, Atsuya; Hirasawa, Kazunori; Tanito, Masaki; Mizoue, Shiro; Mori, Kazuhiko; Suzuki, Katsuyoshi; Yamashita, Takehiro; Kashiwagi, Kenji; Shoji, Nobuyuki; Asaoka, Ryo

2018-04-01

To validate the prediction accuracy of variational Bayes linear regression (VBLR) with two datasets external to the training dataset. The training dataset consisted of 7268 eyes of 4278 subjects from the University of Tokyo Hospital. The Japanese Archive of Multicentral Databases in Glaucoma (JAMDIG) dataset consisted of 271 eyes of 177 patients, and the Diagnostic Innovations in Glaucoma Study (DIGS) dataset includes 248 eyes of 173 patients, which were used for validation. Prediction accuracy was compared between the VBLR and ordinary least squared linear regression (OLSLR). First, OLSLR and VBLR were carried out using total deviation (TD) values at each of the 52 test points from the second to fourth visual fields (VFs) (VF2-4) to 2nd to 10th VF (VF2-10) of each patient in JAMDIG and DIGS datasets, and the TD values of the 11th VF test were predicted every time. The predictive accuracy of each method was compared through the root mean squared error (RMSE) statistic. OLSLR RMSEs with the JAMDIG and DIGS datasets were between 31 and 4.3 dB, and between 19.5 and 3.9 dB. On the other hand, VBLR RMSEs with JAMDIG and DIGS datasets were between 5.0 and 3.7, and between 4.6 and 3.6 dB. There was statistically significant difference between VBLR and OLSLR for both datasets at every series (VF2-4 to VF2-10) (P < 0.01 for all tests). However, there was no statistically significant difference in VBLR RMSEs between JAMDIG and DIGS datasets at any series of VFs (VF2-2 to VF2-10) (P > 0.05). VBLR outperformed OLSLR to predict future VF progression, and the VBLR has a potential to be a helpful tool at clinical settings.
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…
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.)
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.
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...

Daily Suspended Sediment Discharge Prediction Using Multiple Linear Regression and Artificial Neural Network

NASA Astrophysics Data System (ADS)

Uca; Toriman, Ekhwan; Jaafar, Othman; Maru, Rosmini; Arfan, Amal; Saleh Ahmar, Ansari

2018-01-01

Prediction of suspended sediment discharge in a catchments area is very important because it can be used to evaluation the erosion hazard, management of its water resources, water quality, hydrology project management (dams, reservoirs, and irrigation) and to determine the extent of the damage that occurred in the catchments. Multiple Linear Regression analysis and artificial neural network can be used to predict the amount of daily suspended sediment discharge. Regression analysis using the least square method, whereas artificial neural networks using Radial Basis Function (RBF) and feedforward multilayer perceptron with three learning algorithms namely Levenberg-Marquardt (LM), Scaled Conjugate Descent (SCD) and Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFGS). The number neuron of hidden layer is three to sixteen, while in output layer only one neuron because only one output target. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2 ) and coefficient of efficiency (CE) of the multiple linear regression (MLRg) value Model 2 (6 input variable independent) has the lowest the value of MAE and RMSE (0.0000002 and 13.6039) and highest R2 and CE (0.9971 and 0.9971). When compared between LM, SCG and RBF, the BFGS model structure 3-7-1 is the better and more accurate to prediction suspended sediment discharge in Jenderam catchment. The performance value in testing process, MAE and RMSE (13.5769 and 17.9011) is smallest, meanwhile R2 and CE (0.9999 and 0.9998) is the highest if it compared with the another BFGS Quasi-Newton model (6-3-1, 9-10-1 and 12-12-1). Based on the performance statistics value, MLRg, LM, SCG, BFGS and RBF suitable and accurately for prediction by modeling the non-linear complex behavior of suspended sediment responses to rainfall, water depth and discharge. The comparison between artificial neural network (ANN) and MLRg, the MLRg Model 2 accurately for to prediction suspended sediment discharge (kg
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…
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…
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).
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.
Two Paradoxes in Linear Regression Analysis.

PubMed

Feng, Ge; Peng, Jing; Tu, Dongke; Zheng, Julia Z; Feng, Changyong

2016-12-25

Regression is one of the favorite tools in applied statistics. However, misuse and misinterpretation of results from regression analysis are common in biomedical research. In this paper we use statistical theory and simulation studies to clarify some paradoxes around this popular statistical method. In particular, we show that a widely used model selection procedure employed in many publications in top medical journals is wrong. Formal procedures based on solid statistical theory should be used in model selection.
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
Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models.

PubMed

Wiedermann, Wolfgang; Artner, Richard; von Eye, Alexander

2017-01-01

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.
Two Paradoxes in Linear Regression Analysis

PubMed Central

FENG, Ge; PENG, Jing; TU, Dongke; ZHENG, Julia Z.; FENG, Changyong

2016-01-01

Summary Regression is one of the favorite tools in applied statistics. However, misuse and misinterpretation of results from regression analysis are common in biomedical research. In this paper we use statistical theory and simulation studies to clarify some paradoxes around this popular statistical method. In particular, we show that a widely used model selection procedure employed in many publications in top medical journals is wrong. Formal procedures based on solid statistical theory should be used in model selection. PMID:28638214
DOA Finding with Support Vector Regression Based Forward-Backward Linear Prediction.

PubMed

Pan, Jingjing; Wang, Yide; Le Bastard, Cédric; Wang, Tianzhen

2017-05-27

Direction-of-arrival (DOA) estimation has drawn considerable attention in array signal processing, particularly with coherent signals and a limited number of snapshots. Forward-backward linear prediction (FBLP) is able to directly deal with coherent signals. Support vector regression (SVR) is robust with small samples. This paper proposes the combination of the advantages of FBLP and SVR in the estimation of DOAs of coherent incoming signals with low snapshots. The performance of the proposed method is validated with numerical simulations in coherent scenarios, in terms of different angle separations, numbers of snapshots, and signal-to-noise ratios (SNRs). Simulation results show the effectiveness of the proposed method.
A non-linear regression method for CT brain perfusion analysis

NASA Astrophysics Data System (ADS)

Bennink, E.; Oosterbroek, J.; Viergever, M. A.; Velthuis, B. K.; de Jong, H. W. A. M.

2015-03-01

CT perfusion (CTP) imaging allows for rapid diagnosis of ischemic stroke. Generation of perfusion maps from CTP data usually involves deconvolution algorithms providing estimates for the impulse response function in the tissue. We propose the use of a fast non-linear regression (NLR) method that we postulate has similar performance to the current academic state-of-art method (bSVD), but that has some important advantages, including the estimation of vascular permeability, improved robustness to tracer-delay, and very few tuning parameters, that are all important in stroke assessment. The aim of this study is to evaluate the fast NLR method against bSVD and a commercial clinical state-of-art method. The three methods were tested against a published digital perfusion phantom earlier used to illustrate the superiority of bSVD. In addition, the NLR and clinical methods were also tested against bSVD on 20 clinical scans. Pearson correlation coefficients were calculated for each of the tested methods. All three methods showed high correlation coefficients (>0.9) with the ground truth in the phantom. With respect to the clinical scans, the NLR perfusion maps showed higher correlation with bSVD than the perfusion maps from the clinical method. Furthermore, the perfusion maps showed that the fast NLR estimates are robust to tracer-delay. In conclusion, the proposed fast NLR method provides a simple and flexible way of estimating perfusion parameters from CT perfusion scans, with high correlation coefficients. This suggests that it could be a better alternative to the current clinical and academic state-of-art methods.
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.
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.
Efficient least angle regression for identification of linear-in-the-parameters models

PubMed Central

Beach, Thomas H.; Rezgui, Yacine

2017-01-01

Least angle regression, as a promising model selection method, differentiates itself from conventional stepwise and stagewise methods, in that it is neither too greedy nor too slow. It is closely related to L1 norm optimization, which has the advantage of low prediction variance through sacrificing part of model bias property in order to enhance model generalization capability. In this paper, we propose an efficient least angle regression algorithm for model selection for a large class of linear-in-the-parameters models with the purpose of accelerating the model selection process. The entire algorithm works completely in a recursive manner, where the correlations between model terms and residuals, the evolving directions and other pertinent variables are derived explicitly and updated successively at every subset selection step. The model coefficients are only computed when the algorithm finishes. The direct involvement of matrix inversions is thereby relieved. A detailed computational complexity analysis indicates that the proposed algorithm possesses significant computational efficiency, compared with the original approach where the well-known efficient Cholesky decomposition is involved in solving least angle regression. Three artificial and real-world examples are employed to demonstrate the effectiveness, efficiency and numerical stability of the proposed algorithm. PMID:28293140
Model Checking Techniques for Assessing Functional Form Specifications in Censored Linear Regression Models.

PubMed

León, Larry F; Cai, Tianxi

2012-04-01

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

PubMed

Casero-Alonso, V; López-Fidalgo, J; Torsney, B

2017-01-01

Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space. MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [a, b] will be given for several standard weight functions. The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution. Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights. Copyright Â© 2016 Elsevier Ireland Ltd. All rights reserved.
Method validation using weighted linear regression models for quantification of UV filters in water samples.

PubMed

da Silva, Claudia Pereira; Emídio, Elissandro Soares; de Marchi, Mary Rosa Rodrigues

2015-01-01

This paper describes the validation of a method consisting of solid-phase extraction followed by gas chromatography-tandem mass spectrometry for the analysis of the ultraviolet (UV) filters benzophenone-3, ethylhexyl salicylate, ethylhexyl methoxycinnamate and octocrylene. The method validation criteria included evaluation of selectivity, analytical curve, trueness, precision, limits of detection and limits of quantification. The non-weighted linear regression model has traditionally been used for calibration, but it is not necessarily the optimal model in all cases. Because the assumption of homoscedasticity was not met for the analytical data in this work, a weighted least squares linear regression was used for the calibration method. The evaluated analytical parameters were satisfactory for the analytes and showed recoveries at four fortification levels between 62% and 107%, with relative standard deviations less than 14%. The detection limits ranged from 7.6 to 24.1 ng L(-1). The proposed method was used to determine the amount of UV filters in water samples from water treatment plants in Araraquara and Jau in São Paulo, Brazil. Copyright © 2014 Elsevier B.V. All rights reserved.
Linear and evolutionary polynomial regression models to forecast coastal dynamics: Comparison and reliability assessment

NASA Astrophysics Data System (ADS)

Bruno, Delia Evelina; Barca, Emanuele; Goncalves, Rodrigo Mikosz; de Araujo Queiroz, Heithor Alexandre; Berardi, Luigi; Passarella, Giuseppe

2018-01-01

In this paper, the Evolutionary Polynomial Regression data modelling strategy has been applied to study small scale, short-term coastal morphodynamics, given its capability for treating a wide database of known information, non-linearly. Simple linear and multilinear regression models were also applied to achieve a balance between the computational load and reliability of estimations of the three models. In fact, even though it is easy to imagine that the more complex the model, the more the prediction improves, sometimes a "slight" worsening of estimations can be accepted in exchange for the time saved in data organization and computational load. The models' outcomes were validated through a detailed statistical, error analysis, which revealed a slightly better estimation of the polynomial model with respect to the multilinear model, as expected. On the other hand, even though the data organization was identical for the two models, the multilinear one required a simpler simulation setting and a faster run time. Finally, the most reliable evolutionary polynomial regression model was used in order to make some conjecture about the uncertainty increase with the extension of extrapolation time of the estimation. The overlapping rate between the confidence band of the mean of the known coast position and the prediction band of the estimated position can be a good index of the weakness in producing reliable estimations when the extrapolation time increases too much. The proposed models and tests have been applied to a coastal sector located nearby Torre Colimena in the Apulia region, south Italy.
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...
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.

Estimating integrated variance in the presence of microstructure noise using linear regression

NASA Astrophysics Data System (ADS)

Holý, Vladimír

2017-07-01

Using financial high-frequency data for estimation of integrated variance of asset prices is beneficial but with increasing number of observations so-called microstructure noise occurs. This noise can significantly bias the realized variance estimator. We propose a method for estimation of the integrated variance robust to microstructure noise as well as for testing the presence of the noise. Our method utilizes linear regression in which realized variances estimated from different data subsamples act as dependent variable while the number of observations act as explanatory variable. We compare proposed estimator with other methods on simulated data for several microstructure noise structures.
Face Hallucination with Linear Regression Model in Semi-Orthogonal Multilinear PCA Method

NASA Astrophysics Data System (ADS)

Asavaskulkiet, Krissada

2018-04-01

In this paper, we propose a new face hallucination technique, face images reconstruction in HSV color space with a semi-orthogonal multilinear principal component analysis method. This novel hallucination technique can perform directly from tensors via tensor-to-vector projection by imposing the orthogonality constraint in only one mode. In our experiments, we use facial images from FERET database to test our hallucination approach which is demonstrated by extensive experiments with high-quality hallucinated color faces. The experimental results assure clearly demonstrated that we can generate photorealistic color face images by using the SO-MPCA subspace with a linear regression model.
Structured penalties for functional linear models-partially empirical eigenvectors for regression.

PubMed

Randolph, Timothy W; Harezlak, Jaroslaw; Feng, Ziding

2012-01-01

One of the challenges with functional data is incorporating geometric structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear model is often used to estimate the relationship between the predictor functions and scalar responses. Common approaches to the problem of estimating a coefficient function typically involve two stages: regularization and estimation. Regularization is usually done via dimension reduction, projecting onto a predefined span of basis functions or a reduced set of eigenvectors (principal components). In contrast, we present a unified approach that directly incorporates geometric structure into the estimation process by exploiting the joint eigenproperties of the predictors and a linear penalty operator. In this sense, the components in the regression are 'partially empirical' and the framework is provided by the generalized singular value decomposition (GSVD). The form of the penalized estimation is not new, but the GSVD clarifies the process and informs the choice of penalty by making explicit the joint influence of the penalty and predictors on the bias, variance and performance of the estimated coefficient function. Laboratory spectroscopy data and simulations are used to illustrate the concepts.
Genomic prediction based on data from three layer lines using non-linear regression models.

PubMed

Huang, Heyun; Windig, Jack J; Vereijken, Addie; Calus, Mario P L

2014-11-06

Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values. When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction. Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional
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.
Neural network and multiple linear regression to predict school children dimensions for ergonomic school furniture design.

PubMed

Agha, Salah R; Alnahhal, Mohammed J

2012-11-01

The current study investigates the possibility of obtaining the anthropometric dimensions, critical to school furniture design, without measuring all of them. The study first selects some anthropometric dimensions that are easy to measure. Two methods are then used to check if these easy-to-measure dimensions can predict the dimensions critical to the furniture design. These methods are multiple linear regression and neural networks. Each dimension that is deemed necessary to ergonomically design school furniture is expressed as a function of some other measured anthropometric dimensions. Results show that out of the five dimensions needed for chair design, four can be related to other dimensions that can be measured while children are standing. Therefore, the method suggested here would definitely save time and effort and avoid the difficulty of dealing with students while measuring these dimensions. In general, it was found that neural networks perform better than multiple linear regression in the current study. Copyright © 2012 Elsevier Ltd and The Ergonomics Society. All rights reserved.
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…
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.
Boosted structured additive regression for Escherichia coli fed-batch fermentation modeling.

PubMed

Melcher, Michael; Scharl, Theresa; Luchner, Markus; Striedner, Gerald; Leisch, Friedrich

2017-02-01

The quality of biopharmaceuticals and patients' safety are of highest priority and there are tremendous efforts to replace empirical production process designs by knowledge-based approaches. Main challenge in this context is that real-time access to process variables related to product quality and quantity is severely limited. To date comprehensive on- and offline monitoring platforms are used to generate process data sets that allow for development of mechanistic and/or data driven models for real-time prediction of these important quantities. Ultimate goal is to implement model based feed-back control loops that facilitate online control of product quality. In this contribution, we explore structured additive regression (STAR) models in combination with boosting as a variable selection tool for modeling the cell dry mass, product concentration, and optical density on the basis of online available process variables and two-dimensional fluorescence spectroscopic data. STAR models are powerful extensions of linear models allowing for inclusion of smooth effects or interactions between predictors. Boosting constructs the final model in a stepwise manner and provides a variable importance measure via predictor selection frequencies. Our results show that the cell dry mass can be modeled with a relative error of about ±3%, the optical density with ±6%, the soluble protein with ±16%, and the insoluble product with an accuracy of ±12%. Biotechnol. Bioeng. 2017;114: 321-334. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Exhaustive Search for Sparse Variable Selection in Linear Regression

NASA Astrophysics Data System (ADS)

Igarashi, Yasuhiko; Takenaka, Hikaru; Nakanishi-Ohno, Yoshinori; Uemura, Makoto; Ikeda, Shiro; Okada, Masato

2018-04-01

We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.
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…
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…
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…
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.
U.S. Army Armament Research, Development and Engineering Center Grain Evaluation Software to Numerically Predict Linear Burn Regression for Solid Propellant Grain Geometries

DTIC Science & Technology

2017-10-01

ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID PROPELLANT GRAIN GEOMETRIES Brian...author(s) and should not be construed as an official Department of the Army position, policy, or decision, unless so designated by other documentation...U.S. ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER GRAIN EVALUATION SOFTWARE TO NUMERICALLY PREDICT LINEAR BURN REGRESSION FOR SOLID
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
Linear Regression between CIE-Lab Color Parameters and Organic Matter in Soils of Tea Plantations

NASA Astrophysics Data System (ADS)

Chen, Yonggen; Zhang, Min; Fan, Dongmei; Fan, Kai; Wang, Xiaochang

2018-02-01

To quantify the relationship between the soil organic matter and color parameters using the CIE-Lab system, 62 soil samples (0-10 cm, Ferralic Acrisols) from tea plantations were collected from southern China. After air-drying and sieving, numerical color information and reflectance spectra of soil samples were measured under laboratory conditions using an UltraScan VIS (HunterLab) spectrophotometer equipped with CIE-Lab color models. We found that soil total organic carbon (TOC) and nitrogen (TN) contents were negatively correlated with the L* value (lightness) ( r = -0.84 and -0.80, respectively), a* value (correlation coefficient r = -0.51 and -0.46, respectively) and b* value ( r = -0.76 and -0.70, respectively). There were also linear regressions between TOC and TN contents with the L* value and b* value. Results showed that color parameters from a spectrophotometer equipped with CIE-Lab color models can predict TOC contents well for soils in tea plantations. The linear regression model between color values and soil organic carbon contents showed it can be used as a rapid, cost-effective method to evaluate content of soil organic matter in Chinese tea plantations.
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
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.
Estimating the prevalence of 26 health-related indicators at neighbourhood level in the Netherlands using structured additive regression.

PubMed

van de Kassteele, Jan; Zwakhals, Laurens; Breugelmans, Oscar; Ameling, Caroline; van den Brink, Carolien

2017-07-01

Local policy makers increasingly need information on health-related indicators at smaller geographic levels like districts or neighbourhoods. Although more large data sources have become available, direct estimates of the prevalence of a health-related indicator cannot be produced for neighbourhoods for which only small samples or no samples are available. Small area estimation provides a solution, but unit-level models for binary-valued outcomes that can handle both non-linear effects of the predictors and spatially correlated random effects in a unified framework are rarely encountered. We used data on 26 binary-valued health-related indicators collected on 387,195 persons in the Netherlands. We associated the health-related indicators at the individual level with a set of 12 predictors obtained from national registry data. We formulated a structured additive regression model for small area estimation. The model captured potential non-linear relations between the predictors and the outcome through additive terms in a functional form using penalized splines and included a term that accounted for spatially correlated heterogeneity between neighbourhoods. The registry data were used to predict individual outcomes which in turn are aggregated into higher geographical levels, i.e. neighbourhoods. We validated our method by comparing the estimated prevalences with observed prevalences at the individual level and by comparing the estimated prevalences with direct estimates obtained by weighting methods at municipality level. We estimated the prevalence of the 26 health-related indicators for 415 municipalities, 2599 districts and 11,432 neighbourhoods in the Netherlands. We illustrate our method on overweight data and show that there are distinct geographic patterns in the overweight prevalence. Calibration plots show that the estimated prevalences agree very well with observed prevalences at the individual level. The estimated prevalences agree reasonably well with the

Interaction Models for Functional Regression.

PubMed

Usset, Joseph; Staicu, Ana-Maria; Maity, Arnab

2016-02-01

A functional regression model with a scalar response and multiple functional predictors is proposed that accommodates two-way interactions in addition to their main effects. The proposed estimation procedure models the main effects using penalized regression splines, and the interaction effect by a tensor product basis. Extensions to generalized linear models and data observed on sparse grids or with measurement error are presented. A hypothesis testing procedure for the functional interaction effect is described. The proposed method can be easily implemented through existing software. Numerical studies show that fitting an additive model in the presence of interaction leads to both poor estimation performance and lost prediction power, while fitting an interaction model where there is in fact no interaction leads to negligible losses. The methodology is illustrated on the AneuRisk65 study data.
Causal relationship model between variables using linear regression to improve professional commitment of lecturer

NASA Astrophysics Data System (ADS)

Setyaningsih, S.

2017-01-01

The main element to build a leading university requires lecturer commitment in a professional manner. Commitment is measured through willpower, loyalty, pride, loyalty, and integrity as a professional lecturer. A total of 135 from 337 university lecturers were sampled to collect data. Data were analyzed using validity and reliability test and multiple linear regression. Many studies have found a link on the commitment of lecturers, but the basic cause of the causal relationship is generally neglected. These results indicate that the professional commitment of lecturers affected by variables empowerment, academic culture, and trust. The relationship model between variables is composed of three substructures. The first substructure consists of endogenous variables professional commitment and exogenous three variables, namely the academic culture, empowerment and trust, as well as residue variable ɛ y . The second substructure consists of one endogenous variable that is trust and two exogenous variables, namely empowerment and academic culture and the residue variable ɛ 3. The third substructure consists of one endogenous variable, namely the academic culture and exogenous variables, namely empowerment as well as residue variable ɛ 2. Multiple linear regression was used in the path model for each substructure. The results showed that the hypothesis has been proved and these findings provide empirical evidence that increasing the variables will have an impact on increasing the professional commitment of the lecturers.
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.
Stature Estimation from Lower Limb Anthropometry using Linear Regression Analysis: A Study on the Malaysian Population.

PubMed

Abu Bakar, S N; Aspalilah, A; AbdelNasser, I; Nurliza, A; Hairuliza, M J; Swarhib, M; Das, S; Mohd Nor, F

2017-01-01

Stature is one of the characteristics that could be used to identify human, besides age, sex and racial affiliation. This is useful when the body found is either dismembered, mutilated or even decomposed, and helps in narrowing down the missing person's identity. The main aim of the present study was to construct regression functions for stature estimation by using lower limb bones in the Malaysian population. The sample comprised 87 adult individuals (81 males, 6 females) aged between 20 to 79 years. The parameters such as thigh length, lower leg length, leg length, foot length, foot height and foot breadth were measured. They were measured by a ruler and measuring tape. Statistical analysis involved independent t-test to analyse the difference between lower limbs in male and female. The Pearson's correlation test was used to analyse correlations between lower limb parameters and stature, and the linear regressions were used to form equations. The paired t-test was used to compare between actual stature and estimated stature by using the equations formed. Using independent t-test, there was a significant difference (p< 0.05) in the measurement between males and females with regard to leg length, thigh length, lower leg length, foot length and foot breadth. The thigh length, leg length and foot length were observed to have strong correlations with stature with p= 0.75, p= 0.81 and p= 0.69, respectively. Linear regressions were formulated for stature estimation. Paired t-test showed no significant difference between actual stature and estimated stature. It is concluded that regression functions can be used to estimate stature to identify skeletal remains in the Malaysia population.
Profile local linear estimation of generalized semiparametric regression model for longitudinal data.

PubMed

Sun, Yanqing; Sun, Liuquan; Zhou, Jie

2013-07-01

This paper studies the generalized semiparametric regression model for longitudinal data where the covariate effects are constant for some and time-varying for others. Different link functions can be used to allow more flexible modelling of longitudinal data. The nonparametric components of the model are estimated using a local linear estimating equation and the parametric components are estimated through a profile estimating function. The method automatically adjusts for heterogeneity of sampling times, allowing the sampling strategy to depend on the past sampling history as well as possibly time-dependent covariates without specifically model such dependence. A [Formula: see text]-fold cross-validation bandwidth selection is proposed as a working tool for locating an appropriate bandwidth. A criteria for selecting the link function is proposed to provide better fit of the data. Large sample properties of the proposed estimators are investigated. Large sample pointwise and simultaneous confidence intervals for the regression coefficients are constructed. Formal hypothesis testing procedures are proposed to check for the covariate effects and whether the effects are time-varying. A simulation study is conducted to examine the finite sample performances of the proposed estimation and hypothesis testing procedures. The methods are illustrated with a data example.
Applied Multiple Linear Regression: A General Research Strategy

ERIC Educational Resources Information Center

Smith, Brandon B.

1969-01-01

Illustrates some of the basic concepts and procedures for using regression analysis in experimental design, analysis of variance, analysis of covariance, and curvilinear regression. Applications to evaluation of instruction and vocational education programs are illustrated. (GR)
Regression analysis of informative current status data with the additive hazards model.

PubMed

Zhao, Shishun; Hu, Tao; Ma, Ling; Wang, Peijie; Sun, Jianguo

2015-04-01

This paper discusses regression analysis of current status failure time data arising from the additive hazards model in the presence of informative censoring. Many methods have been developed for regression analysis of current status data under various regression models if the censoring is noninformative, and also there exists a large literature on parametric analysis of informative current status data in the context of tumorgenicity experiments. In this paper, a semiparametric maximum likelihood estimation procedure is presented and in the method, the copula model is employed to describe the relationship between the failure time of interest and the censoring time. Furthermore, I-splines are used to approximate the nonparametric functions involved and the asymptotic consistency and normality of the proposed estimators are established. A simulation study is conducted and indicates that the proposed approach works well for practical situations. An illustrative example is also provided.
Effects of measurement errors on psychometric measurements in ergonomics studies: Implications for correlations, ANOVA, linear regression, factor analysis, and linear discriminant analysis.

PubMed

Liu, Yan; Salvendy, Gavriel

2009-05-01

This paper aims to demonstrate the effects of measurement errors on psychometric measurements in ergonomics studies. A variety of sources can cause random measurement errors in ergonomics studies and these errors can distort virtually every statistic computed and lead investigators to erroneous conclusions. The effects of measurement errors on five most widely used statistical analysis tools have been discussed and illustrated: correlation; ANOVA; linear regression; factor analysis; linear discriminant analysis. It has been shown that measurement errors can greatly attenuate correlations between variables, reduce statistical power of ANOVA, distort (overestimate, underestimate or even change the sign of) regression coefficients, underrate the explanation contributions of the most important factors in factor analysis and depreciate the significance of discriminant function and discrimination abilities of individual variables in discrimination analysis. The discussions will be restricted to subjective scales and survey methods and their reliability estimates. Other methods applied in ergonomics research, such as physical and electrophysiological measurements and chemical and biomedical analysis methods, also have issues of measurement errors, but they are beyond the scope of this paper. As there has been increasing interest in the development and testing of theories in ergonomics research, it has become very important for ergonomics researchers to understand the effects of measurement errors on their experiment results, which the authors believe is very critical to research progress in theory development and cumulative knowledge in the ergonomics field.
Neck-focused panic attacks among Cambodian refugees; a logistic and linear regression analysis.

PubMed

Hinton, Devon E; Chhean, Dara; Pich, Vuth; Um, Khin; Fama, Jeanne M; Pollack, Mark H

2006-01-01

Consecutive Cambodian refugees attending a psychiatric clinic were assessed for the presence and severity of current--i.e., at least one episode in the last month--neck-focused panic. Among the whole sample (N=130), in a logistic regression analysis, the Anxiety Sensitivity Index (ASI; odds ratio=3.70) and the Clinician-Administered PTSD Scale (CAPS; odds ratio=2.61) significantly predicted the presence of current neck panic (NP). Among the neck panic patients (N=60), in the linear regression analysis, NP severity was significantly predicted by NP-associated flashbacks (beta=.42), NP-associated catastrophic cognitions (beta=.22), and CAPS score (beta=.28). Further analysis revealed the effect of the CAPS score to be significantly mediated (Sobel test [Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182]) by both NP-associated flashbacks and catastrophic cognitions. In the care of traumatized Cambodian refugees, NP severity, as well as NP-associated flashbacks and catastrophic cognitions, should be specifically assessed and treated.
Synthesis of linear regression coefficients by recovering the within-study covariance matrix from summary statistics.

PubMed

Yoneoka, Daisuke; Henmi, Masayuki

2017-06-01

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

PubMed

Dong, J Q; Zhang, X Y; Wang, S Z; Jiang, X F; Zhang, K; Ma, G W; Wu, M Q; Li, H; Zhang, H

2018-01-01

Plasma very low-density lipoprotein (VLDL) can be used to select for low body fat or abdominal fat (AF) in broilers, but its correlation with AF is limited. We investigated whether any other biochemical indicator can be used in combination with VLDL for a better selective effect. Nineteen plasma biochemical indicators were measured in male chickens from the Northeast Agricultural University broiler lines divergently selected for AF content (NEAUHLF) in the fed state at 46 and 48 d of age. The average concentration of every parameter for the 2 d was used for statistical analysis. Levels of these 19 plasma biochemical parameters were compared between the lean and fat lines. The phenotypic correlations between these plasma biochemical indicators and AF traits were analyzed. Then, multiple linear regression models were constructed to select the best model used for selecting against AF content. and the heritabilities of plasma indicators contained in the best models were estimated. The results showed that 11 plasma biochemical indicators (triglycerides, total bile acid, total protein, globulin, albumin/globulin, aspartate transaminase, alanine transaminase, gamma-glutamyl transpeptidase, uric acid, creatinine, and VLDL) differed significantly between the lean and fat lines (P < 0.01), and correlated significantly with AF traits (P < 0.05). The best multiple linear regression models based on albumin/globulin, VLDL, triglycerides, globulin, total bile acid, and uric acid, had higher R2 (0.73) than the model based only on VLDL (0.21). The plasma parameters included in the best models had moderate heritability estimates (0.21 ≤ h2 ≤ 0.43). These results indicate that these multiple linear regression models can be used to select for lean broiler chickens. © 2017 Poultry Science Association Inc.
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.
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…
Modified Regression Correlation Coefficient for Poisson Regression Model

NASA Astrophysics Data System (ADS)

Kaengthong, Nattacha; Domthong, Uthumporn

2017-09-01

This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).
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.
SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression *

PubMed Central

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

2014-01-01

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

PubMed

Lin, Feng-Chang; Zhu, Jun

2012-01-01

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

PubMed Central

Williams, D. Keith; Muddiman, David C.

2008-01-01

Fourier transform ion cyclotron resonance mass spectrometry has the ability to achieve unprecedented mass measurement accuracy (MMA); MMA is one of the most significant attributes of mass spectrometric measurements as it affords extraordinary molecular specificity. However, due to space-charge effects, the achievable MMA significantly depends on the total number of ions trapped in the ICR cell for a particular measurement. Even through the use of automatic gain control (AGC), the total ion population is not constant between spectra. Multiple linear regression calibration in conjunction with AGC is utilized in these experiments to formally account for the differences in total ion population in the ICR cell between the external calibration spectra and experimental spectra. This ability allows for the extension of dynamic range of the instrument while allowing mean MMA values to remain less than 1 ppm. In addition, multiple linear regression calibration is used to account for both differences in total ion population in the ICR cell as well as relative ion abundance of a given species, which also affords mean MMA values at the parts-per-billion level. PMID:17539605
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.
Generating linear regression model to predict motor functions by use of laser range finder during TUG.

PubMed

Adachi, Daiki; Nishiguchi, Shu; Fukutani, Naoto; Hotta, Takayuki; Tashiro, Yuto; Morino, Saori; Shirooka, Hidehiko; Nozaki, Yuma; Hirata, Hinako; Yamaguchi, Moe; Yorozu, Ayanori; Takahashi, Masaki; Aoyama, Tomoki

2017-05-01

The purpose of this study was to investigate which spatial and temporal parameters of the Timed Up and Go (TUG) test are associated with motor function in elderly individuals. This study included 99 community-dwelling women aged 72.9 ± 6.3 years. Step length, step width, single support time, variability of the aforementioned parameters, gait velocity, cadence, reaction time from starting signal to first step, and minimum distance between the foot and a marker placed to 3 in front of the chair were measured using our analysis system. The 10-m walk test, five times sit-to-stand (FTSTS) test, and one-leg standing (OLS) test were used to assess motor function. Stepwise multivariate linear regression analysis was used to determine which TUG test parameters were associated with each motor function test. Finally, we calculated a predictive model for each motor function test using each regression coefficient. In stepwise linear regression analysis, step length and cadence were significantly associated with the 10-m walk test, FTSTS and OLS test. Reaction time was associated with the FTSTS test, and step width was associated with the OLS test. Each predictive model showed a strong correlation with the 10-m walk test and OLS test (P < 0.01), which was not significant higher correlation than TUG test time. We showed which TUG test parameters were associated with each motor function test. Moreover, the TUG test time regarded as the lower extremity function and mobility has strong predictive ability in each motor function test. Copyright © 2017 The Japanese Orthopaedic Association. Published by Elsevier B.V. All rights reserved.

Estimation of streamflow, base flow, and nitrate-nitrogen loads in Iowa using multiple linear regression models

USGS Publications Warehouse

Schilling, K.E.; Wolter, C.F.

2005-01-01

Nineteen variables, including precipitation, soils and geology, land use, and basin morphologic characteristics, were evaluated to develop Iowa regression models to predict total streamflow (Q), base flow (Qb), storm flow (Qs) and base flow percentage (%Qb) in gauged and ungauged watersheds in the state. Discharge records from a set of 33 watersheds across the state for the 1980 to 2000 period were separated into Qb and Qs. Multiple linear regression found that 75.5 percent of long term average Q was explained by rainfall, sand content, and row crop percentage variables, whereas 88.5 percent of Qb was explained by these three variables plus permeability and floodplain area variables. Qs was explained by average rainfall and %Qb was a function of row crop percentage, permeability, and basin slope variables. Regional regression models developed for long term average Q and Qb were adapted to annual rainfall and showed good correlation between measured and predicted values. Combining the regression model for Q with an estimate of mean annual nitrate concentration, a map of potential nitrate loads in the state was produced. Results from this study have important implications for understanding geomorphic and land use controls on streamflow and base flow in Iowa watersheds and similar agriculture dominated watersheds in the glaciated Midwest. (JAWRA) (Copyright ?? 2005).
SU-G-BRA-08: Diaphragm Motion Tracking Based On KV CBCT Projections with a Constrained Linear Regression Optimization

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

Wei, J; Chao, M

2016-06-15

Purpose: To develop a novel strategy to extract the respiratory motion of the thoracic diaphragm from kilovoltage cone beam computed tomography (CBCT) projections by a constrained linear regression optimization technique. Methods: A parabolic function was identified as the geometric model and was employed to fit the shape of the diaphragm on the CBCT projections. The search was initialized by five manually placed seeds on a pre-selected projection image. Temporal redundancies, the enabling phenomenology in video compression and encoding techniques, inherent in the dynamic properties of the diaphragm motion together with the geometrical shape of the diaphragm boundary and the associatedmore » algebraic constraint that significantly reduced the searching space of viable parabolic parameters was integrated, which can be effectively optimized by a constrained linear regression approach on the subsequent projections. The innovative algebraic constraints stipulating the kinetic range of the motion and the spatial constraint preventing any unphysical deviations was able to obtain the optimal contour of the diaphragm with minimal initialization. The algorithm was assessed by a fluoroscopic movie acquired at anteriorposterior fixed direction and kilovoltage CBCT projection image sets from four lung and two liver patients. The automatic tracing by the proposed algorithm and manual tracking by a human operator were compared in both space and frequency domains. Results: The error between the estimated and manual detections for the fluoroscopic movie was 0.54mm with standard deviation (SD) of 0.45mm, while the average error for the CBCT projections was 0.79mm with SD of 0.64mm for all enrolled patients. The submillimeter accuracy outcome exhibits the promise of the proposed constrained linear regression approach to track the diaphragm motion on rotational projection images. Conclusion: The new algorithm will provide a potential solution to rendering diaphragm motion and
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.
Estimating mono- and bi-phasic regression parameters using a mixture piecewise linear Bayesian hierarchical model

PubMed Central

Zhao, Rui; Catalano, Paul; DeGruttola, Victor G.; Michor, Franziska

2017-01-01

The dynamics of tumor burden, secreted proteins or other biomarkers over time, is often used to evaluate the effectiveness of therapy and to predict outcomes for patients. Many methods have been proposed to investigate longitudinal trends to better characterize patients and to understand disease progression. However, most approaches assume a homogeneous patient population and a uniform response trajectory over time and across patients. Here, we present a mixture piecewise linear Bayesian hierarchical model, which takes into account both population heterogeneity and nonlinear relationships between biomarkers and time. Simulation results show that our method was able to classify subjects according to their patterns of treatment response with greater than 80% accuracy in the three scenarios tested. We then applied our model to a large randomized controlled phase III clinical trial of multiple myeloma patients. Analysis results suggest that the longitudinal tumor burden trajectories in multiple myeloma patients are heterogeneous and nonlinear, even among patients assigned to the same treatment cohort. In addition, between cohorts, there are distinct differences in terms of the regression parameters and the distributions among categories in the mixture. Those results imply that longitudinal data from clinical trials may harbor unobserved subgroups and nonlinear relationships; accounting for both may be important for analyzing longitudinal data. PMID:28723910
Modeling daily soil temperature over diverse climate conditions in Iran—a comparison of multiple linear regression and support vector regression techniques

NASA Astrophysics Data System (ADS)

Delbari, Masoomeh; Sharifazari, Salman; Mohammadi, Ehsan

2018-02-01

The knowledge of soil temperature at different depths is important for agricultural industry and for understanding climate change. The aim of this study is to evaluate the performance of a support vector regression (SVR)-based model in estimating daily soil temperature at 10, 30 and 100 cm depth at different climate conditions over Iran. The obtained results were compared to those obtained from a more classical multiple linear regression (MLR) model. The correlation sensitivity for the input combinations and periodicity effect were also investigated. Climatic data used as inputs to the models were minimum and maximum air temperature, solar radiation, relative humidity, dew point, and the atmospheric pressure (reduced to see level), collected from five synoptic stations Kerman, Ahvaz, Tabriz, Saghez, and Rasht located respectively in the hyper-arid, arid, semi-arid, Mediterranean, and hyper-humid climate conditions. According to the results, the performance of both MLR and SVR models was quite well at surface layer, i.e., 10-cm depth. However, SVR performed better than MLR in estimating soil temperature at deeper layers especially 100 cm depth. Moreover, both models performed better in humid climate condition than arid and hyper-arid areas. Further, adding a periodicity component into the modeling process considerably improved the models' performance especially in the case of SVR.
Marginal regression approach for additive hazards models with clustered current status data.

PubMed

Su, Pei-Fang; Chi, Yunchan

2014-01-15

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

NASA Astrophysics Data System (ADS)

Passow, Christian; Donner, Reik

2017-04-01

Quantile mapping (QM) is an established concept that allows to correct systematic biases in multiple quantiles of the distribution of a climatic observable. It shows remarkable results in correcting biases in historical simulations through observational data and outperforms simpler correction methods which relate only to the mean or variance. Since it has been shown that bias correction of future predictions or scenario runs with basic QM can result in misleading trends in the projection, adjusted, trend preserving, versions of QM were introduced in the form of detrended quantile mapping (DQM) and quantile delta mapping (QDM) (Cannon, 2015, 2016). Still, all previous versions and applications of QM based bias correction rely on the assumption of time-independent quantiles over the investigated period, which can be misleading in the context of a changing climate. Here, we propose a novel combination of linear quantile regression (QR) with the classical QM method to introduce a consistent, time-dependent and trend preserving approach of bias correction for historical and future projections. Since QR is a regression method, it is possible to estimate quantiles in the same resolution as the given data and include trends or other dependencies. We demonstrate the performance of the new method of linear regression quantile mapping (RQM) in correcting biases of temperature and precipitation products from historical runs (1959 - 2005) of the COSMO model in climate mode (CCLM) from the Euro-CORDEX ensemble relative to gridded E-OBS data of the same spatial and temporal resolution. A thorough comparison with established bias correction methods highlights the strengths and potential weaknesses of the new RQM approach. References: A.J. Cannon, S.R. Sorbie, T.Q. Murdock: Bias Correction of GCM Precipitation by Quantile Mapping - How Well Do Methods Preserve Changes in Quantiles and Extremes? Journal of Climate, 28, 6038, 2015 A.J. Cannon: Multivariate Bias Correction of Climate
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
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.
Chicken barn climate and hazardous volatile compounds control using simple linear regression and PID

NASA Astrophysics Data System (ADS)

Abdullah, A. H.; Bakar, M. A. A.; Shukor, S. A. A.; Saad, F. S. A.; Kamis, M. S.; Mustafa, M. H.; Khalid, N. S.

2016-07-01

The hazardous volatile compounds from chicken manure in chicken barn are potentially to be a health threat to the farm animals and workers. Ammonia (NH3) and hydrogen sulphide (H2S) produced in chicken barn are influenced by climate changes. The Electronic Nose (e-nose) is used for the barn's air, temperature and humidity data sampling. Simple Linear Regression is used to identify the correlation between temperature-humidity, humidity-ammonia and ammonia-hydrogen sulphide. MATLAB Simulink software was used for the sample data analysis using PID controller. Results shows that the performance of PID controller using the Ziegler-Nichols technique can improve the system controller to control climate in chicken barn.
Linear regression models and k-means clustering for statistical analysis of fNIRS data.

PubMed

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

2015-02-01

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

NASA Astrophysics Data System (ADS)

Styborski, Jeremy A.

This project was started in the interest of supplementing existing data on additives to composite solid propellants. The study on the addition of iron and aluminum nanoparticles to composite AP/HTPB propellants was conducted at the Combustion and Energy Systems Laboratory at RPI in the new strand-burner experiment setup. For this study, a large literature review was conducted on history of solid propellant combustion modeling and the empirical results of tests on binders, plasticizers, AP particle size, and additives. The study focused on the addition of nano-scale aluminum and iron in small concentrations to AP/HTPB solid propellants with an average AP particle size of 200 microns. Replacing 1% of the propellant's AP with 40-60 nm aluminum particles produced no change in combustive behavior. The addition of 1% 60-80 nm iron particles produced a significant increase in burn rate, although the increase was lesser at higher pressures. These results are summarized in Table 2. The increase in the burn rate at all pressures due to the addition of iron nanoparticles warranted further study on the effect of concentration of iron. Tests conducted at 10 atm showed that the mean regression rate varied with iron concentration, peaking at 1% and 3%. Regardless of the iron concentration, the regression rate was higher than the baseline AP/HTPB propellants. These results are summarized in Table 3.
Comparison of random regression models with Legendre polynomials and linear splines for production traits and somatic cell score of Canadian Holstein cows.

PubMed

Bohmanova, J; Miglior, F; Jamrozik, J; Misztal, I; Sullivan, P G

2008-09-01

A random regression model with both random and fixed regressions fitted by Legendre polynomials of order 4 was compared with 3 alternative models fitting linear splines with 4, 5, or 6 knots. The effects common for all models were a herd-test-date effect, fixed regressions on days in milk (DIM) nested within region-age-season of calving class, and random regressions for additive genetic and permanent environmental effects. Data were test-day milk, fat and protein yields, and SCS recorded from 5 to 365 DIM during the first 3 lactations of Canadian Holstein cows. A random sample of 50 herds consisting of 96,756 test-day records was generated to estimate variance components within a Bayesian framework via Gibbs sampling. Two sets of genetic evaluations were subsequently carried out to investigate performance of the 4 models. Models were compared by graphical inspection of variance functions, goodness of fit, error of prediction of breeding values, and stability of estimated breeding values. Models with splines gave lower estimates of variances at extremes of lactations than the model with Legendre polynomials. Differences among models in goodness of fit measured by percentages of squared bias, correlations between predicted and observed records, and residual variances were small. The deviance information criterion favored the spline model with 6 knots. Smaller error of prediction and higher stability of estimated breeding values were achieved by using spline models with 5 and 6 knots compared with the model with Legendre polynomials. In general, the spline model with 6 knots had the best overall performance based upon the considered model comparison criteria.
Monopole and dipole estimation for multi-frequency sky maps by linear regression

NASA Astrophysics Data System (ADS)

Wehus, I. K.; Fuskeland, U.; Eriksen, H. K.; Banday, A. J.; Dickinson, C.; Ghosh, T.; Górski, K. M.; Lawrence, C. R.; Leahy, J. P.; Maino, D.; Reich, P.; Reich, W.

2017-01-01

We describe a simple but efficient method for deriving a consistent set of monopole and dipole corrections for multi-frequency sky map data sets, allowing robust parametric component separation with the same data set. The computational core of this method is linear regression between pairs of frequency maps, often called T-T plots. Individual contributions from monopole and dipole terms are determined by performing the regression locally in patches on the sky, while the degeneracy between different frequencies is lifted whenever the dominant foreground component exhibits a significant spatial spectral index variation. Based on this method, we present two different, but each internally consistent, sets of monopole and dipole coefficients for the nine-year WMAP, Planck 2013, SFD 100 μm, Haslam 408 MHz and Reich & Reich 1420 MHz maps. The two sets have been derived with different analysis assumptions and data selection, and provide an estimate of residual systematic uncertainties. In general, our values are in good agreement with previously published results. Among the most notable results are a relative dipole between the WMAP and Planck experiments of 10-15μK (depending on frequency), an estimate of the 408 MHz map monopole of 8.9 ± 1.3 K, and a non-zero dipole in the 1420 MHz map of 0.15 ± 0.03 K pointing towards Galactic coordinates (l,b) = (308°,-36°) ± 14°. These values represent the sum of any instrumental and data processing offsets, as well as any Galactic or extra-Galactic component that is spectrally uniform over the full sky.
Use of non-linear mixed-effects modelling and regression analysis to predict the number of somatic coliphages by plaque enumeration after 3 hours of incubation.

PubMed

Mendez, Javier; Monleon-Getino, Antonio; Jofre, Juan; Lucena, Francisco

2017-10-01

The present study aimed to establish the kinetics of the appearance of coliphage plaques using the double agar layer titration technique to evaluate the feasibility of using traditional coliphage plaque forming unit (PFU) enumeration as a rapid quantification method. Repeated measurements of the appearance of plaques of coliphages titrated according to ISO 10705-2 at different times were analysed using non-linear mixed-effects regression to determine the most suitable model of their appearance kinetics. Although this model is adequate, to simplify its applicability two linear models were developed to predict the numbers of coliphages reliably, using the PFU counts as determined by the ISO after only 3 hours of incubation. One linear model, when the number of plaques detected was between 4 and 26 PFU after 3 hours, had a linear fit of: (1.48 × Counts 3 h + 1.97); and the other, values >26 PFU, had a fit of (1.18 × Counts 3 h + 2.95). If the number of plaques detected was <4 PFU after 3 hours, we recommend incubation for (18 ± 3) hours. The study indicates that the traditional coliphage plating technique has a reasonable potential to provide results in a single working day without the need to invest in additional laboratory equipment.
Penalized nonparametric scalar-on-function regression via principal coordinates

PubMed Central

Reiss, Philip T.; Miller, David L.; Wu, Pei-Shien; Hua, Wen-Yu

2016-01-01

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. PMID:29217963
Use of multivariate linear regression and support vector regression to predict functional outcome after surgery for cervical spondylotic myelopathy.

PubMed

Hoffman, Haydn; Lee, Sunghoon I; Garst, Jordan H; Lu, Derek S; Li, Charles H; Nagasawa, Daniel T; Ghalehsari, Nima; Jahanforouz, Nima; Razaghy, Mehrdad; Espinal, Marie; Ghavamrezaii, Amir; Paak, Brian H; Wu, Irene; Sarrafzadeh, Majid; Lu, Daniel C

2015-09-01

This study introduces the use of multivariate linear regression (MLR) and support vector regression (SVR) models to predict postoperative outcomes in a cohort of patients who underwent surgery for cervical spondylotic myelopathy (CSM). Currently, predicting outcomes after surgery for CSM remains a challenge. We recruited patients who had a diagnosis of CSM and required decompressive surgery with or without fusion. Fine motor function was tested preoperatively and postoperatively with a handgrip-based tracking device that has been previously validated, yielding mean absolute accuracy (MAA) results for two tracking tasks (sinusoidal and step). All patients completed Oswestry disability index (ODI) and modified Japanese Orthopaedic Association questionnaires preoperatively and postoperatively. Preoperative data was utilized in MLR and SVR models to predict postoperative ODI. Predictions were compared to the actual ODI scores with the coefficient of determination (R(2)) and mean absolute difference (MAD). From this, 20 patients met the inclusion criteria and completed follow-up at least 3 months after surgery. With the MLR model, a combination of the preoperative ODI score, preoperative MAA (step function), and symptom duration yielded the best prediction of postoperative ODI (R(2)=0.452; MAD=0.0887; p=1.17 × 10(-3)). With the SVR model, a combination of preoperative ODI score, preoperative MAA (sinusoidal function), and symptom duration yielded the best prediction of postoperative ODI (R(2)=0.932; MAD=0.0283; p=5.73 × 10(-12)). The SVR model was more accurate than the MLR model. The SVR can be used preoperatively in risk/benefit analysis and the decision to operate. Copyright © 2015 Elsevier Ltd. All rights reserved.
Hourly predictive Levenberg-Marquardt ANN and multi linear regression models for predicting of dew point temperature

NASA Astrophysics Data System (ADS)

Zounemat-Kermani, Mohammad

2012-08-01

In this study, the ability of two models of multi linear regression (MLR) and Levenberg-Marquardt (LM) feed-forward neural network was examined to estimate the hourly dew point temperature. Dew point temperature is the temperature at which water vapor in the air condenses into liquid. This temperature can be useful in estimating meteorological variables such as fog, rain, snow, dew, and evapotranspiration and in investigating agronomical issues as stomatal closure in plants. The availability of hourly records of climatic data (air temperature, relative humidity and pressure) which could be used to predict dew point temperature initiated the practice of modeling. Additionally, the wind vector (wind speed magnitude and direction) and conceptual input of weather condition were employed as other input variables. The three quantitative standard statistical performance evaluation measures, i.e. the root mean squared error, mean absolute error, and absolute logarithmic Nash-Sutcliffe efficiency coefficient ( {| {{{Log}}({{NS}})} |} ) were employed to evaluate the performances of the developed models. The results showed that applying wind vector and weather condition as input vectors along with meteorological variables could slightly increase the ANN and MLR predictive accuracy. The results also revealed that LM-NN was superior to MLR model and the best performance was obtained by considering all potential input variables in terms of different evaluation criteria.
TSS concentration in sewers estimated from turbidity measurements by means of linear regression accounting for uncertainties in both variables.

PubMed

Bertrand-Krajewski, J L

2004-01-01

In order to replace traditional sampling and analysis techniques, turbidimeters can be used to estimate TSS concentration in sewers, by means of sensor and site specific empirical equations established by linear regression of on-site turbidity Tvalues with TSS concentrations C measured in corresponding samples. As the ordinary least-squares method is not able to account for measurement uncertainties in both T and C variables, an appropriate regression method is used to solve this difficulty and to evaluate correctly the uncertainty in TSS concentrations estimated from measured turbidity. The regression method is described, including detailed calculations of variances and covariance in the regression parameters. An example of application is given for a calibrated turbidimeter used in a combined sewer system, with data collected during three dry weather days. In order to show how the established regression could be used, an independent 24 hours long dry weather turbidity data series recorded at 2 min time interval is used, transformed into estimated TSS concentrations, and compared to TSS concentrations measured in samples. The comparison appears as satisfactory and suggests that turbidity measurements could replace traditional samples. Further developments, including wet weather periods and other types of sensors, are suggested.
Linear regression models and k-means clustering for statistical analysis of fNIRS data

PubMed Central

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

2015-01-01

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

Tapanuli Organoclay Addition Into Linear Low Density Polyethylene-Pineapple Fiber Composites

NASA Astrophysics Data System (ADS)

Adawiyah, Robiatul; Juwono, Ariadne L.; Roseno, Seto

2010-12-01

Linear low density polyethylene-Tapanuli organoclay-pineapple fiber composites were succesfully synthesized by a melt intercalation method. The clay was modified as an organoclay by a cation exchange reaction using hexadecyl trimethyl ammonium bromide (HDTMABr) surfactant. The X-ray diffraction results of the organoclay exhibited a higher basal spacing of 1.87 nm compared to the unmodified clay of 1.46 nm. The composite tensile strength was enhanced up to 46.4% with the 1 wt% organoclay addition. Both tensile and flexural moduli increased up to 150.6% and 43% with the 3 wt% organoclay addition to the composites. However, the flexural strength of the composites was not improved with the organoclay addition. The addition of organoclay has also decreased the heat deflection temperature of the composites.
A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

PubMed

Brown, A M

2001-06-01

The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.
A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

PubMed

Brown, Angus M

2006-04-01

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.
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
Use of linear regression models to determine influence factors on the concentration levels of radon in occupied houses

NASA Astrophysics Data System (ADS)

Buermeyer, Jonas; Gundlach, Matthias; Grund, Anna-Lisa; Grimm, Volker; Spizyn, Alexander; Breckow, Joachim

2016-09-01

This work is part of the analysis of the effects of constructional energy-saving measures to radon concentration levels in dwellings performed on behalf of the German Federal Office for Radiation Protection. In parallel to radon measurements for five buildings, both meteorological data outside the buildings and the indoor climate factors were recorded. In order to access effects of inhabited buildings, the amount of carbon dioxide (CO2) was measured. For a statistical linear regression model, the data of one object was chosen as an example. Three dummy variables were extracted from the process of the CO2 concentration to provide information on the usage and ventilation of the room. The analysis revealed a highly autoregressive model for the radon concentration with additional influence by the natural environmental factors. The autoregression implies a strong dependency on a radon source since it reflects a backward dependency in time. At this point of the investigation, it cannot be determined whether the influence by outside factors affects the source of radon or the habitant’s ventilation behavior resulting in variation of the occurring concentration levels. In any case, the regression analysis might provide further information that would help to distinguish these effects. In the next step, the influence factors will be weighted according to their impact on the concentration levels. This might lead to a model that enables the prediction of radon concentration levels based on the measurement of CO2 in combination with environmental parameters, as well as the development of advices for ventilation.
Early Parallel Activation of Semantics and Phonology in Picture Naming: Evidence from a Multiple Linear Regression MEG Study

PubMed Central

Miozzo, Michele; Pulvermüller, Friedemann; Hauk, Olaf

2015-01-01

The time course of brain activation during word production has become an area of increasingly intense investigation in cognitive neuroscience. The predominant view has been that semantic and phonological processes are activated sequentially, at about 150 and 200–400 ms after picture onset. Although evidence from prior studies has been interpreted as supporting this view, these studies were arguably not ideally suited to detect early brain activation of semantic and phonological processes. We here used a multiple linear regression approach to magnetoencephalography (MEG) analysis of picture naming in order to investigate early effects of variables specifically related to visual, semantic, and phonological processing. This was combined with distributed minimum-norm source estimation and region-of-interest analysis. Brain activation associated with visual image complexity appeared in occipital cortex at about 100 ms after picture presentation onset. At about 150 ms, semantic variables became physiologically manifest in left frontotemporal regions. In the same latency range, we found an effect of phonological variables in the left middle temporal gyrus. Our results demonstrate that multiple linear regression analysis is sensitive to early effects of multiple psycholinguistic variables in picture naming. Crucially, our results suggest that access to phonological information might begin in parallel with semantic processing around 150 ms after picture onset. PMID:25005037
Folded concave penalized sparse linear regression: sparsity, statistical performance, and algorithmic theory for local solutions.

PubMed

Liu, Hongcheng; Yao, Tao; Li, Runze; Ye, Yinyu

2017-11-01

This paper concerns the folded concave penalized sparse linear regression (FCPSLR), a class of popular sparse recovery methods. Although FCPSLR yields desirable recovery performance when solved globally, computing a global solution is NP-complete. Despite some existing statistical performance analyses on local minimizers or on specific FCPSLR-based learning algorithms, it still remains open questions whether local solutions that are known to admit fully polynomial-time approximation schemes (FPTAS) may already be sufficient to ensure the statistical performance, and whether that statistical performance can be non-contingent on the specific designs of computing procedures. To address the questions, this paper presents the following threefold results: (i) Any local solution (stationary point) is a sparse estimator, under some conditions on the parameters of the folded concave penalties. (ii) Perhaps more importantly, any local solution satisfying a significant subspace second-order necessary condition (S 3 ONC), which is weaker than the second-order KKT condition, yields a bounded error in approximating the true parameter with high probability. In addition, if the minimal signal strength is sufficient, the S 3 ONC solution likely recovers the oracle solution. This result also explicates that the goal of improving the statistical performance is consistent with the optimization criteria of minimizing the suboptimality gap in solving the non-convex programming formulation of FCPSLR. (iii) We apply (ii) to the special case of FCPSLR with minimax concave penalty (MCP) and show that under the restricted eigenvalue condition, any S 3 ONC solution with a better objective value than the Lasso solution entails the strong oracle property. In addition, such a solution generates a model error (ME) comparable to the optimal but exponential-time sparse estimator given a sufficient sample size, while the worst-case ME is comparable to the Lasso in general. Furthermore, to guarantee
Relationship between rice yield and climate variables in southwest Nigeria using multiple linear regression and support vector machine analysis

NASA Astrophysics Data System (ADS)

Oguntunde, Philip G.; Lischeid, Gunnar; Dietrich, Ottfried

2018-03-01

This study examines the variations of climate variables and rice yield and quantifies the relationships among them using multiple linear regression, principal component analysis, and support vector machine (SVM) analysis in southwest Nigeria. The climate and yield data used was for a period of 36 years between 1980 and 2015. Similar to the observed decrease ( P < 0.001) in rice yield, pan evaporation, solar radiation, and wind speed declined significantly. Eight principal components exhibited an eigenvalue > 1 and explained 83.1% of the total variance of predictor variables. The SVM regression function using the scores of the first principal component explained about 75% of the variance in rice yield data and linear regression about 64%. SVM regression between annual solar radiation values and yield explained 67% of the variance. Only the first component of the principal component analysis (PCA) exhibited a clear long-term trend and sometimes short-term variance similar to that of rice yield. Short-term fluctuations of the scores of the PC1 are closely coupled to those of rice yield during the 1986-1993 and the 2006-2013 periods thereby revealing the inter-annual sensitivity of rice production to climate variability. Solar radiation stands out as the climate variable of highest influence on rice yield, and the influence was especially strong during monsoon and post-monsoon periods, which correspond to the vegetative, booting, flowering, and grain filling stages in the study area. The outcome is expected to provide more in-depth regional-specific climate-rice linkage for screening of better cultivars that can positively respond to future climate fluctuations as well as providing information that may help optimized planting dates for improved radiation use efficiency in the study area.
Multiple Linear Regression for Reconstruction of Gene Regulatory Networks in Solving Cascade Error Problems

PubMed Central

Zainudin, Suhaila; Arif, Shereena M.

2017-01-01

Gene regulatory network (GRN) reconstruction is the process of identifying regulatory gene interactions from experimental data through computational analysis. One of the main reasons for the reduced performance of previous GRN methods had been inaccurate prediction of cascade motifs. Cascade error is defined as the wrong prediction of cascade motifs, where an indirect interaction is misinterpreted as a direct interaction. Despite the active research on various GRN prediction methods, the discussion on specific methods to solve problems related to cascade errors is still lacking. In fact, the experiments conducted by the past studies were not specifically geared towards proving the ability of GRN prediction methods in avoiding the occurrences of cascade errors. Hence, this research aims to propose Multiple Linear Regression (MLR) to infer GRN from gene expression data and to avoid wrongly inferring of an indirect interaction (A → B → C) as a direct interaction (A → C). Since the number of observations of the real experiment datasets was far less than the number of predictors, some predictors were eliminated by extracting the random subnetworks from global interaction networks via an established extraction method. In addition, the experiment was extended to assess the effectiveness of MLR in dealing with cascade error by using a novel experimental procedure that had been proposed in this work. The experiment revealed that the number of cascade errors had been very minimal. Apart from that, the Belsley collinearity test proved that multicollinearity did affect the datasets used in this experiment greatly. All the tested subnetworks obtained satisfactory results, with AUROC values above 0.5. PMID:28250767
An Ionospheric Index Model based on Linear Regression and Neural Network Approaches

NASA Astrophysics Data System (ADS)

Tshisaphungo, Mpho; McKinnell, Lee-Anne; Bosco Habarulema, John

2017-04-01

The ionosphere is well known to reflect radio wave signals in the high frequency (HF) band due to the present of electron and ions within the region. To optimise the use of long distance HF communications, it is important to understand the drivers of ionospheric storms and accurately predict the propagation conditions especially during disturbed days. This paper presents the development of an ionospheric storm-time index over the South African region for the application of HF communication users. The model will result into a valuable tool to measure the complex ionospheric behaviour in an operational space weather monitoring and forecasting environment. The development of an ionospheric storm-time index is based on a single ionosonde station data over Grahamstown (33.3°S,26.5°E), South Africa. Critical frequency of the F2 layer (foF2) measurements for a period 1996-2014 were considered for this study. The model was developed based on linear regression and neural network approaches. In this talk validation results for low, medium and high solar activity periods will be discussed to demonstrate model's performance.
Development of statistical linear regression model for metals from transportation land uses.

PubMed

Maniquiz, Marla C; Lee, Soyoung; Lee, Eunju; Kim, Lee-Hyung

2009-01-01

The transportation landuses possessing impervious surfaces such as highways, parking lots, roads, and bridges were recognized as the highly polluted non-point sources (NPSs) in the urban areas. Lots of pollutants from urban transportation are accumulating on the paved surfaces during dry periods and are washed-off during a storm. In Korea, the identification and monitoring of NPSs still represent a great challenge. Since 2004, the Ministry of Environment (MOE) has been engaged in several researches and monitoring to develop stormwater management policies and treatment systems for future implementation. The data over 131 storm events during May 2004 to September 2008 at eleven sites were analyzed to identify correlation relationships between particulates and metals, and to develop simple linear regression (SLR) model to estimate event mean concentration (EMC). Results indicate that there was no significant relationship between metals and TSS EMC. However, the SLR estimation models although not providing useful results are valuable indicators of high uncertainties that NPS pollution possess. Therefore, long term monitoring employing proper methods and precise statistical analysis of the data should be undertaken to eliminate these uncertainties.
Composition-dependence of stacking fault energy in austenitic stainless steels through linear regression with random intercepts

NASA Astrophysics Data System (ADS)

Meric de Bellefon, G.; van Duysen, J. C.; Sridharan, K.

2017-08-01

The stacking fault energy (SFE) plays an important role in deformation behavior and radiation damage of FCC metals and alloys such as austenitic stainless steels. In the present communication, existing expressions to calculate SFE in those steels from chemical composition are reviewed and an improved multivariate linear regression with random intercepts is used to analyze a new database of 144 SFE measurements collected from 30 literature references. It is shown that the use of random intercepts can account for experimental biases in these literature references. A new expression to predict SFE from austenitic stainless steel compositions is proposed.
Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Multi-linear regression of sea level in the south west Pacific as a first step towards local sea level projections

NASA Astrophysics Data System (ADS)

Kumar, Vandhna; Meyssignac, Benoit; Melet, Angélique; Ganachaud, Alexandre

2017-04-01

Rising sea levels are a critical concern in small island nations. The problem is especially serious in the western south Pacific, where the total sea level rise over the last 60 years is up to 3 times the global average. In this study, we attempt to reconstruct sea levels at selected sites in the region (Suva, Lautoka, Noumea - Fiji and New Caledonia) as a mutiple-linear regression of atmospheric and oceanic variables. We focus on interannual-to-decadal scale variability, and lower (including the global mean sea level rise) over the 1979-2014 period. Sea levels are taken from tide gauge records and the ORAS4 reanalysis dataset, and are expressed as a sum of steric and mass changes as a preliminary step. The key development in our methodology is using leading wind stress curl as a proxy for the thermosteric component. This is based on the knowledge that wind stress curl anomalies can modulate the thermocline depth and resultant sea levels via Rossby wave propagation. The analysis is primarily based on correlation between local sea level and selected predictors, the dominant one being wind stress curl. In the first step, proxy boxes for wind stress curl are determined via regions of highest correlation. The proportion of sea level explained via linear regression is then removed, leaving a residual. This residual is then correlated with other locally acting potential predictors: halosteric sea level, the zonal and meridional wind stress components, and sea surface temperature. The statistically significant predictors are used in a multi-linear regression function to simulate the observed sea level. The method is able to reproduce between 40 to 80% of the variance in observed sea level. Based on the skill of the model, it has high potential in sea level projection and downscaling studies.
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…
Application of stepwise multiple regression techniques to inversion of Nimbus 'IRIS' observations.

NASA Technical Reports Server (NTRS)

Ohring, G.

1972-01-01

Exploratory studies with Nimbus-3 infrared interferometer-spectrometer (IRIS) data indicate that, in addition to temperature, such meteorological parameters as geopotential heights of pressure surfaces, tropopause pressure, and tropopause temperature can be inferred from the observed spectra with the use of simple regression equations. The technique of screening the IRIS spectral data by means of stepwise regression to obtain the best radiation predictors of meteorological parameters is validated. The simplicity of application of the technique and the simplicity of the derived linear regression equations - which contain only a few terms - suggest usefulness for this approach. Based upon the results obtained, suggestions are made for further development and exploitation of the stepwise regression analysis technique.
Successive Projections Algorithm-Multivariable Linear Regression Classifier for the Detection of Contaminants on Chicken Carcasses in Hyperspectral Images

NASA Astrophysics Data System (ADS)

Wu, W.; Chen, G. Y.; Kang, R.; Xia, J. C.; Huang, Y. P.; Chen, K. J.

2017-07-01

During slaughtering and further processing, chicken carcasses are inevitably contaminated by microbial pathogen contaminants. Due to food safety concerns, many countries implement a zero-tolerance policy that forbids the placement of visibly contaminated carcasses in ice-water chiller tanks during processing. Manual detection of contaminants is labor consuming and imprecise. Here, a successive projections algorithm (SPA)-multivariable linear regression (MLR) classifier based on an optimal performance threshold was developed for automatic detection of contaminants on chicken carcasses. Hyperspectral images were obtained using a hyperspectral imaging system. A regression model of the classifier was established by MLR based on twelve characteristic wavelengths (505, 537, 561, 562, 564, 575, 604, 627, 656, 665, 670, and 689 nm) selected by SPA , and the optimal threshold T = 1 was obtained from the receiver operating characteristic (ROC) analysis. The SPA-MLR classifier provided the best detection results when compared with the SPA-partial least squares (PLS) regression classifier and the SPA-least squares supported vector machine (LS-SVM) classifier. The true positive rate (TPR) of 100% and the false positive rate (FPR) of 0.392% indicate that the SPA-MLR classifier can utilize spatial and spectral information to effectively detect contaminants on chicken carcasses.
Bayesian structured additive regression modeling of epidemic data: application to cholera

PubMed Central

2012-01-01

Background A significant interest in spatial epidemiology lies in identifying associated risk factors which enhances the risk of infection. Most studies, however, make no, or limited use of the spatial structure of the data, as well as possible nonlinear effects of the risk factors. Methods We develop a Bayesian Structured Additive Regression model for cholera epidemic data. Model estimation and inference is based on fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulations. The model is applied to cholera epidemic data in the Kumasi Metropolis, Ghana. Proximity to refuse dumps, density of refuse dumps, and proximity to potential cholera reservoirs were modeled as continuous functions; presence of slum settlers and population density were modeled as fixed effects, whereas spatial references to the communities were modeled as structured and unstructured spatial effects. Results We observe that the risk of cholera is associated with slum settlements and high population density. The risk of cholera is equal and lower for communities with fewer refuse dumps, but variable and higher for communities with more refuse dumps. The risk is also lower for communities distant from refuse dumps and potential cholera reservoirs. The results also indicate distinct spatial variation in the risk of cholera infection. Conclusion The study highlights the usefulness of Bayesian semi-parametric regression model analyzing public health data. These findings could serve as novel information to help health planners and policy makers in making effective decisions to control or prevent cholera epidemics. PMID:22866662
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,…
Evaluating differential effects using regression interactions and regression mixture models

PubMed Central

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

2015-01-01

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

A 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.
A new approach to measure visual field progression in glaucoma patients using variational bayes linear regression.

PubMed

Murata, Hiroshi; Araie, Makoto; Asaoka, Ryo

2014-11-20

We generated a variational Bayes model to predict visual field (VF) progression in glaucoma patients. This retrospective study included VF series from 911 eyes of 547 glaucoma patients as test data, and VF series from 5049 eyes of 2858 glaucoma patients as training data. Using training data, variational Bayes linear regression (VBLR) was created to predict VF progression. The performance of VBLR was compared against ordinary least-squares linear regression (OLSLR) by predicting VFs in the test dataset. The total deviation (TD) values of test patients' 11th VFs were predicted using TD values from their second to 10th VFs (VF2-10), the root mean squared error (RMSE) associated with each approach then was calculated. Similarly, mean TD (mTD) of test patients' 11th VFs was predicted using VBLR and OLSLR, and the absolute prediction errors compared. The RMSE resulting from VBLR averaged 3.9 ± 2.1 (SD) and 4.9 ± 2.6 dB for prediction based on the second to 10th VFs (VF2-10) and the second to fourth VFs (VF2-4), respectively. The RMSE resulting from OLSLR was 4.1 ± 2.0 (VF2-10) and 19.9 ± 12.0 (VF2-4) dB. The absolute prediction error (SD) for mTD using VBLR was 1.2 ± 1.3 (VF2-10) and 1.9 ± 2.0 (VF2-4) dB, while the prediction error resulting from OLSLR was 1.2 ± 1.3 (VF2-10) and 6.2 ± 6.6 (VF2-4) dB. The VBLR more accurately predicts future VF progression in glaucoma patients compared to conventional OLSLR, especially in short VF series. © ARVO.
Using Simulation Technique to overcome the multi-collinearity problem for estimating fuzzy linear regression parameters.

NASA Astrophysics Data System (ADS)

Mansoor Gorgees, Hazim; Hilal, Mariam Mohammed

2018-05-01

Fatigue cracking is one of the common types of pavement distresses and is an indicator of structural failure; cracks allow moisture infiltration, roughness, may further deteriorate to a pothole. Some causes of pavement deterioration are: traffic loading; environment influences; drainage deficiencies; materials quality problems; construction deficiencies and external contributors. Many researchers have made models that contain many variables like asphalt content, asphalt viscosity, fatigue life, stiffness of asphalt mixture, temperature and other parameters that affect the fatigue life. For this situation, a fuzzy linear regression model was employed and analyzed by using the traditional methods and our proposed method in order to overcome the multi-collinearity problem. The total spread error was used as a criterion to compare the performance of the studied methods. Simulation program was used to obtain the required results.
Area under the curve predictions of dalbavancin, a new lipoglycopeptide agent, using the end of intravenous infusion concentration data point by regression analyses such as linear, log-linear and power models.

PubMed

Bhamidipati, Ravi Kanth; Syed, Muzeeb; Mullangi, Ramesh; Srinivas, Nuggehally

2018-02-01

1. Dalbavancin, a lipoglycopeptide, is approved for treating gram-positive bacterial infections. Area under plasma concentration versus time curve (AUC inf ) of dalbavancin is a key parameter and AUC inf /MIC ratio is a critical pharmacodynamic marker. 2. Using end of intravenous infusion concentration (i.e. C max ) C max versus AUC inf relationship for dalbavancin was established by regression analyses (i.e. linear, log-log, log-linear and power models) using 21 pairs of subject data. 3. The predictions of the AUC inf were performed using published C max data by application of regression equations. The quotient of observed/predicted values rendered fold difference. The mean absolute error (MAE)/root mean square error (RMSE) and correlation coefficient (r) were used in the assessment. 4. MAE and RMSE values for the various models were comparable. The C max versus AUC inf exhibited excellent correlation (r > 0.9488). The internal data evaluation showed narrow confinement (0.84-1.14-fold difference) with a RMSE < 10.3%. The external data evaluation showed that the models predicted AUC inf with a RMSE of 3.02-27.46% with fold difference largely contained within 0.64-1.48. 5. Regardless of the regression models, a single time point strategy of using C max (i.e. end of 30-min infusion) is amenable as a prospective tool for predicting AUC inf of dalbavancin in patients.
Regression with Small Data Sets: A Case Study using Code Surrogates in Additive Manufacturing

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

Kamath, C.; Fan, Y. J.

There has been an increasing interest in recent years in the mining of massive data sets whose sizes are measured in terabytes. While it is easy to collect such large data sets in some application domains, there are others where collecting even a single data point can be very expensive, so the resulting data sets have only tens or hundreds of samples. For example, when complex computer simulations are used to understand a scientific phenomenon, we want to run the simulation for many different values of the input parameters and analyze the resulting output. The data set relating the simulationmore » inputs and outputs is typically quite small, especially when each run of the simulation is expensive. However, regression techniques can still be used on such data sets to build an inexpensive \\surrogate" that could provide an approximate output for a given set of inputs. A good surrogate can be very useful in sensitivity analysis, uncertainty analysis, and in designing experiments. In this paper, we compare different regression techniques to determine how well they predict melt-pool characteristics in the problem domain of additive manufacturing. Our analysis indicates that some of the commonly used regression methods do perform quite well even on small data sets.« less
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…
Estimating severity of sideways fall using a generic multi linear regression model based on kinematic input variables.

PubMed

van der Zijden, A M; Groen, B E; Tanck, E; Nienhuis, B; Verdonschot, N; Weerdesteyn, V

2017-03-21

Many research groups have studied fall impact mechanics to understand how fall severity can be reduced to prevent hip fractures. Yet, direct impact force measurements with force plates are restricted to a very limited repertoire of experimental falls. The purpose of this study was to develop a generic model for estimating hip impact forces (i.e. fall severity) in in vivo sideways falls without the use of force plates. Twelve experienced judokas performed sideways Martial Arts (MA) and Block ('natural') falls on a force plate, both with and without a mat on top. Data were analyzed to determine the hip impact force and to derive 11 selected (subject-specific and kinematic) variables. Falls from kneeling height were used to perform a stepwise regression procedure to assess the effects of these input variables and build the model. The final model includes four input variables, involving one subject-specific measure and three kinematic variables: maximum upper body deceleration, body mass, shoulder angle at the instant of 'maximum impact' and maximum hip deceleration. The results showed that estimated and measured hip impact forces were linearly related (explained variances ranging from 46 to 63%). Hip impact forces of MA falls onto the mat from a standing position (3650±916N) estimated by the final model were comparable with measured values (3698±689N), even though these data were not used for training the model. In conclusion, a generic linear regression model was developed that enables the assessment of fall severity through kinematic measures of sideways falls, without using force plates. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
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…
Evaluation of multivariate linear regression and artificial neural networks in prediction of water quality parameters

PubMed Central

2014-01-01

This paper examined the efficiency of multivariate linear regression (MLR) and artificial neural network (ANN) models in prediction of two major water quality parameters in a wastewater treatment plant. Biochemical oxygen demand (BOD) and chemical oxygen demand (COD) as well as indirect indicators of organic matters are representative parameters for sewer water quality. Performance of the ANN models was evaluated using coefficient of correlation (r), root mean square error (RMSE) and bias values. The computed values of BOD and COD by model, ANN method and regression analysis were in close agreement with their respective measured values. Results showed that the ANN performance model was better than the MLR model. Comparative indices of the optimized ANN with input values of temperature (T), pH, total suspended solid (TSS) and total suspended (TS) for prediction of BOD was RMSE = 25.1 mg/L, r = 0.83 and for prediction of COD was RMSE = 49.4 mg/L, r = 0.81. It was found that the ANN model could be employed successfully in estimating the BOD and COD in the inlet of wastewater biochemical treatment plants. Moreover, sensitive examination results showed that pH parameter have more effect on BOD and COD predicting to another parameters. Also, both implemented models have predicted BOD better than COD. PMID:24456676
Functional mixture regression.

PubMed

Yao, Fang; Fu, Yuejiao; Lee, Thomas C M

2011-04-01

In functional linear models (FLMs), the relationship between the scalar response and the functional predictor process is often assumed to be identical for all subjects. Motivated by both practical and methodological considerations, we relax this assumption and propose a new class of functional regression models that allow the regression structure to vary for different groups of subjects. By projecting the predictor process onto its eigenspace, the new functional regression model is simplified to a framework that is similar to classical mixture regression models. This leads to the proposed approach named as functional mixture regression (FMR). The estimation of FMR can be readily carried out using existing software implemented for functional principal component analysis and mixture regression. The practical necessity and performance of FMR are illustrated through applications to a longevity analysis of female medflies and a human growth study. Theoretical investigations concerning the consistent estimation and prediction properties of FMR along with simulation experiments illustrating its empirical properties are presented in the supplementary material available at Biostatistics online. Corresponding results demonstrate that the proposed approach could potentially achieve substantial gains over traditional FLMs.
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
Quantification of endocrine disruptors and pesticides in water by gas chromatography-tandem mass spectrometry. Method validation using weighted linear regression schemes.

PubMed

Mansilha, C; Melo, A; Rebelo, H; Ferreira, I M P L V O; Pinho, O; Domingues, V; Pinho, C; Gameiro, P

2010-10-22

A multi-residue methodology based on a solid phase extraction followed by gas chromatography-tandem mass spectrometry was developed for trace analysis of 32 compounds in water matrices, including estrogens and several pesticides from different chemical families, some of them with endocrine disrupting properties. Matrix standard calibration solutions were prepared by adding known amounts of the analytes to a residue-free sample to compensate matrix-induced chromatographic response enhancement observed for certain pesticides. Validation was done mainly according to the International Conference on Harmonisation recommendations, as well as some European and American validation guidelines with specifications for pesticides analysis and/or GC-MS methodology. As the assumption of homoscedasticity was not met for analytical data, weighted least squares linear regression procedure was applied as a simple and effective way to counteract the greater influence of the greater concentrations on the fitted regression line, improving accuracy at the lower end of the calibration curve. The method was considered validated for 31 compounds after consistent evaluation of the key analytical parameters: specificity, linearity, limit of detection and quantification, range, precision, accuracy, extraction efficiency, stability and robustness. Copyright © 2010 Elsevier B.V. All rights reserved.
Differentiating regressed melanoma from regressed lichenoid keratosis.

PubMed

Chan, Aegean H; Shulman, Kenneth J; Lee, Bonnie A

2017-04-01

Distinguishing regressed lichen planus-like keratosis (LPLK) from regressed melanoma can be difficult on histopathologic examination, potentially resulting in mismanagement of patients. We aimed to identify histopathologic features by which regressed melanoma can be differentiated from regressed LPLK. Twenty actively inflamed LPLK, 12 LPLK with regression and 15 melanomas with regression were compared and evaluated by hematoxylin and eosin staining as well as Melan-A, microphthalmia transcription factor (MiTF) and cytokeratin (AE1/AE3) immunostaining. (1) A total of 40% of regressed melanomas showed complete or near complete loss of melanocytes within the epidermis with Melan-A and MiTF immunostaining, while 8% of regressed LPLK exhibited this finding. (2) Necrotic keratinocytes were seen in the epidermis in 33% regressed melanomas as opposed to all of the regressed LPLK. (3) A dense infiltrate of melanophages in the papillary dermis was seen in 40% of regressed melanomas, a feature not seen in regressed LPLK. In summary, our findings suggest that a complete or near complete loss of melanocytes within the epidermis strongly favors a regressed melanoma over a regressed LPLK. In addition, necrotic epidermal keratinocytes and the presence of a dense band-like distribution of dermal melanophages can be helpful in differentiating these lesions. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Non-Linear Relationship between Economic Growth and CO₂ Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models.

PubMed

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-12-13

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO₂ emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO₂ emissions is significantly higher than those of GDPpc and Es on per capita CO₂ emissions.
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.
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.
HT-FRTC: a fast radiative transfer code using kernel regression

NASA Astrophysics Data System (ADS)

Thelen, Jean-Claude; Havemann, Stephan; Lewis, Warren

2016-09-01

The HT-FRTC is a principal component based fast radiative transfer code that can be used across the electromagnetic spectrum from the microwave through to the ultraviolet to calculate transmittance, radiance and flux spectra. The principal components cover the spectrum at a very high spectral resolution, which allows very fast line-by-line, hyperspectral and broadband simulations for satellite-based, airborne and ground-based sensors. The principal components are derived during a code training phase from line-by-line simulations for a diverse set of atmosphere and surface conditions. The derived principal components are sensor independent, i.e. no extra training is required to include additional sensors. During the training phase we also derive the predictors which are required by the fast radiative transfer code to determine the principal component scores from the monochromatic radiances (or fluxes, transmittances). These predictors are calculated for each training profile at a small number of frequencies, which are selected by a k-means cluster algorithm during the training phase. Until recently the predictors were calculated using a linear regression. However, during a recent rewrite of the code the linear regression was replaced by a Gaussian Process (GP) regression which resulted in a significant increase in accuracy when compared to the linear regression. The HT-FRTC has been trained with a large variety of gases, surface properties and scatterers. Rayleigh scattering as well as scattering by frozen/liquid clouds, hydrometeors and aerosols have all been included. The scattering phase function can be fully accounted for by an integrated line-by-line version of the Edwards-Slingo spherical harmonics radiation code or approximately by a modification to the extinction (Chou scaling).
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.
Applicational possibilities of linear and non-linear (polynomial) regression and analysis of variance. III. Stability determination of pharmaceutical preparations: stability of diclofenac-sodium in Diclofen injections.

PubMed

Arambasić, M B; Jatić-Slavković, D

2004-05-01

This paper presents the application of the regression analysis program and the program for comparing linear regressions (modified method for one-way, analysis of variance), writtens in BASIC program language, for instance, determination of content of Diclofenac-Sodium (active ingredient in DIKLOFEN injections, ampules á 75 mg/3 ml). Stability testing of Diclofenac-Sodium was done by isothermic method of accelerated aging at 4 different temperatures (30 degrees, 40 degrees, 50 degrees and 60 degrees C) as a function of time (4 different duration of treatment: (0-155, 0-145, 0-74 and 0-44 days). The decrease in stability (decrease in the mean value of the content of Diclofenac-Sodium (in %), at different temperatures as a function of time, is possible to describe by, linear dependance. According to the value for regression equation values, the times are assessed in which the content of Diclofenac-Sodium (in %) will decrease by 10%, of the initial value. The times are follows at 30 degrees C 761.02 days, at 40 degrees C 397.26 days, at 50 degrees C 201.96 days and at 60 degrees C 58.85 days. The estimated times (in days) in which the mean value for Diclofenac-Sodium content (in %) will by 10% of the initial values, as a junction of time, are most suitably described by 3rd order parabola. Based on the parameter values which describe the 3rd order parabola, the time was estimated in which Diclofenac-Sodium content mean value (in %) will fall by 10% of the initial one at average ambient temperatures of 20 degrees C and 25 degrees C. The times are: 1409.47 days (20 degrees C) and 1042.39 days (25 degrees C). Based on the value for Fischer's coefficien (F), the comparison of trenf of Diclofenac-Sodium content (in %) shows that, under the influence of different temperatures as a function of time, among them, depending on temperature value, there is: statistically very significant difference (P < .05) at 50 degrees C and lower toward 60 degrees C, i.e. statistically

A critical review of the protracted domestication model for Near-Eastern founder crops: linear regression, long-distance gene flow, archaeological, and archaeobotanical evidence.

PubMed

Heun, Manfred; Abbo, Shahal; Lev-Yadun, Simcha; Gopher, Avi

2012-07-01

The recent review by Fuller et al. (2012a) in this journal is part of a series of papers maintaining that plant domestication in the Near East was a slow process lasting circa 4000 years and occurring independently in different locations across the Fertile Crescent. Their protracted domestication scenario is based entirely on linear regression derived from the percentage of domesticated plant remains at specific archaeological sites and the age of these sites themselves. This paper discusses why estimates like haldanes and darwins cannot be applied to the seven founder crops in the Near East (einkorn and emmer wheat, barley, peas, chickpeas, lentils, and bitter vetch). All of these crops are self-fertilizing plants and for this reason they do not fulfil the requirements for performing calculations of this kind. In addition, the percentage of domesticates at any site may be the result of factors other than those that affect the selection for domesticates growing in the surrounding area. These factors are unlikely to have been similar across prehistoric sites of habitation, societies, and millennia. The conclusion here is that single crop analyses are necessary rather than general reviews drawing on regression analyses based on erroneous assumptions. The fact that all seven of these founder crops are self-fertilizers should be incorporated into a comprehensive domestication scenario for the Near East, as self-fertilization naturally isolates domesticates from their wild progenitors.
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.
The use of artificial neural networks and multiple linear regression to predict rate of medical waste generation

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

Jahandideh, Sepideh; Jahandideh, Samad; Asadabadi, Ebrahim Barzegari

2009-11-15

Prediction of the amount of hospital waste production will be helpful in the storage, transportation and disposal of hospital waste management. Based on this fact, two predictor models including artificial neural networks (ANNs) and multiple linear regression (MLR) were applied to predict the rate of medical waste generation totally and in different types of sharp, infectious and general. In this study, a 5-fold cross-validation procedure on a database containing total of 50 hospitals of Fars province (Iran) were used to verify the performance of the models. Three performance measures including MAR, RMSE and R{sup 2} were used to evaluate performancemore » of models. The MLR as a conventional model obtained poor prediction performance measure values. However, MLR distinguished hospital capacity and bed occupancy as more significant parameters. On the other hand, ANNs as a more powerful model, which has not been introduced in predicting rate of medical waste generation, showed high performance measure values, especially 0.99 value of R{sup 2} confirming the good fit of the data. Such satisfactory results could be attributed to the non-linear nature of ANNs in problem solving which provides the opportunity for relating independent variables to dependent ones non-linearly. In conclusion, the obtained results showed that our ANN-based model approach is very promising and may play a useful role in developing a better cost-effective strategy for waste management in future.« less
Understanding logistic regression analysis.

PubMed

Sperandei, Sandro

2014-01-01

Logistic regression is used to obtain odds ratio in the presence of more than one explanatory variable. The procedure is quite similar to multiple linear regression, with the exception that the response variable is binomial. The result is the impact of each variable on the odds ratio of the observed event of interest. The main advantage is to avoid confounding effects by analyzing the association of all variables together. In this article, we explain the logistic regression procedure using examples to make it as simple as possible. After definition of the technique, the basic interpretation of the results is highlighted and then some special issues are discussed.
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.
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.
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.
Plateletpheresis efficiency and mathematical correction of software-derived platelet yield prediction: A linear regression and ROC modeling approach.

PubMed

Jaime-Pérez, José Carlos; Jiménez-Castillo, Raúl Alberto; Vázquez-Hernández, Karina Elizabeth; Salazar-Riojas, Rosario; Méndez-Ramírez, Nereida; Gómez-Almaguer, David

2017-10-01

Advances in automated cell separators have improved the efficiency of plateletpheresis and the possibility of obtaining double products (DP). We assessed cell processor accuracy of predicted platelet (PLT) yields with the goal of a better prediction of DP collections. This retrospective proof-of-concept study included 302 plateletpheresis procedures performed on a Trima Accel v6.0 at the apheresis unit of a hematology department. Donor variables, software predicted yield and actual PLT yield were statistically evaluated. Software prediction was optimized by linear regression analysis and its optimal cut-off to obtain a DP assessed by receiver operating characteristic curve (ROC) modeling. Three hundred and two plateletpheresis procedures were performed; in 271 (89.7%) occasions, donors were men and in 31 (10.3%) women. Pre-donation PLT count had the best direct correlation with actual PLT yield (r = 0.486. P < .001). Means of software machine-derived values differed significantly from actual PLT yield, 4.72 × 10 11 vs.6.12 × 10 11 , respectively, (P < .001). The following equation was developed to adjust these values: actual PLT yield= 0.221 + (1.254 × theoretical platelet yield). ROC curve model showed an optimal apheresis device software prediction cut-off of 4.65 × 10 11 to obtain a DP, with a sensitivity of 82.2%, specificity of 93.3%, and an area under the curve (AUC) of 0.909. Trima Accel v6.0 software consistently underestimated PLT yields. Simple correction derived from linear regression analysis accurately corrected this underestimation and ROC analysis identified a precise cut-off to reliably predict a DP. © 2016 Wiley Periodicals, Inc.
The comparison of robust partial least squares regression with robust principal component regression on a real

NASA Astrophysics Data System (ADS)

Polat, Esra; Gunay, Suleyman

2013-10-01

One of the problems encountered in Multiple Linear Regression (MLR) is multicollinearity, which causes the overestimation of the regression parameters and increase of the variance of these parameters. Hence, in case of multicollinearity presents, biased estimation procedures such as classical Principal Component Regression (CPCR) and Partial Least Squares Regression (PLSR) are then performed. SIMPLS algorithm is the leading PLSR algorithm because of its speed, efficiency and results are easier to interpret. However, both of the CPCR and SIMPLS yield very unreliable results when the data set contains outlying observations. Therefore, Hubert and Vanden Branden (2003) have been presented a robust PCR (RPCR) method and a robust PLSR (RPLSR) method called RSIMPLS. In RPCR, firstly, a robust Principal Component Analysis (PCA) method for high-dimensional data on the independent variables is applied, then, the dependent variables are regressed on the scores using a robust regression method. RSIMPLS has been constructed from a robust covariance matrix for high-dimensional data and robust linear regression. The purpose of this study is to show the usage of RPCR and RSIMPLS methods on an econometric data set, hence, making a comparison of two methods on an inflation model of Turkey. The considered methods have been compared in terms of predictive ability and goodness of fit by using a robust Root Mean Squared Error of Cross-validation (R-RMSECV), a robust R2 value and Robust Component Selection (RCS) statistic.
Fungible weights in logistic regression.

PubMed

Jones, Jeff A; Waller, Niels G

2016-06-01

In this article we develop methods for assessing parameter sensitivity in logistic regression models. To set the stage for this work, we first review Waller's (2008) equations for computing fungible weights in linear regression. Next, we describe 2 methods for computing fungible weights in logistic regression. To demonstrate the utility of these methods, we compute fungible logistic regression weights using data from the Centers for Disease Control and Prevention's (2010) Youth Risk Behavior Surveillance Survey, and we illustrate how these alternate weights can be used to evaluate parameter sensitivity. To make our work accessible to the research community, we provide R code (R Core Team, 2015) that will generate both kinds of fungible logistic regression weights. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
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.
Non-Linear Relationship between Economic Growth and CO2 Emissions in China: An Empirical Study Based on Panel Smooth Transition Regression Models

PubMed Central

Wang, Zheng-Xin; Hao, Peng; Yao, Pei-Yi

2017-01-01

The non-linear relationship between provincial economic growth and carbon emissions is investigated by using panel smooth transition regression (PSTR) models. The research indicates that, on the condition of separately taking Gross Domestic Product per capita (GDPpc), energy structure (Es), and urbanisation level (Ul) as transition variables, three models all reject the null hypothesis of a linear relationship, i.e., a non-linear relationship exists. The results show that the three models all contain only one transition function but different numbers of location parameters. The model taking GDPpc as the transition variable has two location parameters, while the other two models separately considering Es and Ul as the transition variables both contain one location parameter. The three models applied in the study all favourably describe the non-linear relationship between economic growth and CO2 emissions in China. It also can be seen that the conversion rate of the influence of Ul on per capita CO2 emissions is significantly higher than those of GDPpc and Es on per capita CO2 emissions. PMID:29236083
Predicting the aquatic toxicity mode of action using logistic regression and linear discriminant analysis.

PubMed

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

2016-09-01

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

PubMed

Vaeth, Michael; Skovlund, Eva

2004-06-15

For a given regression problem it is possible to identify a suitably defined equivalent two-sample problem such that the power or sample size obtained for the two-sample problem also applies to the regression problem. For a standard linear regression model the equivalent two-sample problem is easily identified, but for generalized linear models and for Cox regression models the situation is more complicated. An approximately equivalent two-sample problem may, however, also be identified here. In particular, we show that for logistic regression and Cox regression models the equivalent two-sample problem is obtained by selecting two equally sized samples for which the parameters differ by a value equal to the slope times twice the standard deviation of the independent variable and further requiring that the overall expected number of events is unchanged. In a simulation study we examine the validity of this approach to power calculations in logistic regression and Cox regression models. Several different covariate distributions are considered for selected values of the overall response probability and a range of alternatives. For the Cox regression model we consider both constant and non-constant hazard rates. The results show that in general the approach is remarkably accurate even in relatively small samples. Some discrepancies are, however, found in small samples with few events and a highly skewed covariate distribution. Comparison with results based on alternative methods for logistic regression models with a single continuous covariate indicates that the proposed method is at least as good as its competitors. The method is easy to implement and therefore provides a simple way to extend the range of problems that can be covered by the usual formulas for power and sample size determination. Copyright 2004 John Wiley & Sons, Ltd.
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.
Linear-regression convolutional neural network for fully automated coronary lumen segmentation in intravascular optical coherence tomography

NASA Astrophysics Data System (ADS)

Yong, Yan Ling; Tan, Li Kuo; McLaughlin, Robert A.; Chee, Kok Han; Liew, Yih Miin

2017-12-01

Intravascular optical coherence tomography (OCT) is an optical imaging modality commonly used in the assessment of coronary artery diseases during percutaneous coronary intervention. Manual segmentation to assess luminal stenosis from OCT pullback scans is challenging and time consuming. We propose a linear-regression convolutional neural network to automatically perform vessel lumen segmentation, parameterized in terms of radial distances from the catheter centroid in polar space. Benchmarked against gold-standard manual segmentation, our proposed algorithm achieves average locational accuracy of the vessel wall of 22 microns, and 0.985 and 0.970 in Dice coefficient and Jaccard similarity index, respectively. The average absolute error of luminal area estimation is 1.38%. The processing rate is 40.6 ms per image, suggesting the potential to be incorporated into a clinical workflow and to provide quantitative assessment of vessel lumen in an intraoperative time frame.
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…
Non-linear auto-regressive models for cross-frequency coupling in neural time series

PubMed Central

Tallot, Lucille; Grabot, Laetitia; Doyère, Valérie; Grenier, Yves; Gramfort, Alexandre

2017-01-01

We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling. PMID:29227989
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.
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.

Logic regression and its extensions.

PubMed

Schwender, Holger; Ruczinski, Ingo

2010-01-01

Logic regression is an adaptive classification and regression procedure, initially developed to reveal interacting single nucleotide polymorphisms (SNPs) in genetic association studies. In general, this approach can be used in any setting with binary predictors, when the interaction of these covariates is of primary interest. Logic regression searches for Boolean (logic) combinations of binary variables that best explain the variability in the outcome variable, and thus, reveals variables and interactions that are associated with the response and/or have predictive capabilities. The logic expressions are embedded in a generalized linear regression framework, and thus, logic regression can handle a variety of outcome types, such as binary responses in case-control studies, numeric responses, and time-to-event data. In this chapter, we provide an introduction to the logic regression methodology, list some applications in public health and medicine, and summarize some of the direct extensions and modifications of logic regression that have been proposed in the literature. Copyright © 2010 Elsevier Inc. All rights reserved.
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
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.
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…
Linear Regression Links Transcriptomic Data and Cellular Raman Spectra.

PubMed

Kobayashi-Kirschvink, Koseki J; Nakaoka, Hidenori; Oda, Arisa; Kamei, Ken-Ichiro F; Nosho, Kazuki; Fukushima, Hiroko; Kanesaki, Yu; Yajima, Shunsuke; Masaki, Haruhiko; Ohta, Kunihiro; Wakamoto, Yuichi

2018-06-08

Raman microscopy is an imaging technique that has been applied to assess molecular compositions of living cells to characterize cell types and states. However, owing to the diverse molecular species in cells and challenges of assigning peaks to specific molecules, it has not been clear how to interpret cellular Raman spectra. Here, we provide firm evidence that cellular Raman spectra and transcriptomic profiles of Schizosaccharomyces pombe and Escherichia coli can be computationally connected and thus interpreted. We find that the dimensions of high-dimensional Raman spectra and transcriptomes measured by RNA sequencing can be reduced and connected linearly through a shared low-dimensional subspace. Accordingly, we were able to predict global gene expression profiles by applying the calculated transformation matrix to Raman spectra, and vice versa. Highly expressed non-coding RNAs contributed to the Raman-transcriptome linear correspondence more significantly than mRNAs in S. pombe. This demonstration of correspondence between cellular Raman spectra and transcriptomes is a promising step toward establishing spectroscopic live-cell omics studies. Copyright © 2018 Elsevier Inc. All rights reserved.
Is it the intervention or the students? using linear regression to control for student characteristics in undergraduate STEM education research.

PubMed

Theobald, Roddy; Freeman, Scott

2014-01-01

Although researchers in undergraduate science, technology, engineering, and mathematics education are currently using several methods to analyze learning gains from pre- and posttest data, the most commonly used approaches have significant shortcomings. Chief among these is the inability to distinguish whether differences in learning gains are due to the effect of an instructional intervention or to differences in student characteristics when students cannot be assigned to control and treatment groups at random. Using pre- and posttest scores from an introductory biology course, we illustrate how the methods currently in wide use can lead to erroneous conclusions, and how multiple linear regression offers an effective framework for distinguishing the impact of an instructional intervention from the impact of student characteristics on test score gains. In general, we recommend that researchers always use student-level regression models that control for possible differences in student ability and preparation to estimate the effect of any nonrandomized instructional intervention on student performance.
Is It the Intervention or the Students? Using Linear Regression to Control for Student Characteristics in Undergraduate STEM Education Research

PubMed Central

Theobald, Roddy; Freeman, Scott

2014-01-01

Although researchers in undergraduate science, technology, engineering, and mathematics education are currently using several methods to analyze learning gains from pre- and posttest data, the most commonly used approaches have significant shortcomings. Chief among these is the inability to distinguish whether differences in learning gains are due to the effect of an instructional intervention or to differences in student characteristics when students cannot be assigned to control and treatment groups at random. Using pre- and posttest scores from an introductory biology course, we illustrate how the methods currently in wide use can lead to erroneous conclusions, and how multiple linear regression offers an effective framework for distinguishing the impact of an instructional intervention from the impact of student characteristics on test score gains. In general, we recommend that researchers always use student-level regression models that control for possible differences in student ability and preparation to estimate the effect of any nonrandomized instructional intervention on student performance. PMID:24591502
Estimating Dbh of Trees Employing Multiple Linear Regression of the best Lidar-Derived Parameter Combination Automated in Python in a Natural Broadleaf Forest in the Philippines

NASA Astrophysics Data System (ADS)

Ibanez, C. A. G.; Carcellar, B. G., III; Paringit, E. C.; Argamosa, R. J. L.; Faelga, R. A. G.; Posilero, M. A. V.; Zaragosa, G. P.; Dimayacyac, N. A.

2016-06-01

Diameter-at-Breast-Height Estimation is a prerequisite in various allometric equations estimating important forestry indices like stem volume, basal area, biomass and carbon stock. LiDAR Technology has a means of directly obtaining different forest parameters, except DBH, from the behavior and characteristics of point cloud unique in different forest classes. Extensive tree inventory was done on a two-hectare established sample plot in Mt. Makiling, Laguna for a natural growth forest. Coordinates, height, and canopy cover were measured and types of species were identified to compare to LiDAR derivatives. Multiple linear regression was used to get LiDAR-derived DBH by integrating field-derived DBH and 27 LiDAR-derived parameters at 20m, 10m, and 5m grid resolutions. To know the best combination of parameters in DBH Estimation, all possible combinations of parameters were generated and automated using python scripts and additional regression related libraries such as Numpy, Scipy, and Scikit learn were used. The combination that yields the highest r-squared or coefficient of determination and lowest AIC (Akaike's Information Criterion) and BIC (Bayesian Information Criterion) was determined to be the best equation. The equation is at its best using 11 parameters at 10mgrid size and at of 0.604 r-squared, 154.04 AIC and 175.08 BIC. Combination of parameters may differ among forest classes for further studies. Additional statistical tests can be supplemented to help determine the correlation among parameters such as Kaiser- Meyer-Olkin (KMO) Coefficient and the Barlett's Test for Spherecity (BTS).
Quantile regression for the statistical analysis of immunological data with many non-detects.

PubMed

Eilers, Paul H C; Röder, Esther; Savelkoul, Huub F J; van Wijk, Roy Gerth

2012-07-07

Immunological parameters are hard to measure. A well-known problem is the occurrence of values below the detection limit, the non-detects. Non-detects are a nuisance, because classical statistical analyses, like ANOVA and regression, cannot be applied. The more advanced statistical techniques currently available for the analysis of datasets with non-detects can only be used if a small percentage of the data are non-detects. Quantile regression, a generalization of percentiles to regression models, models the median or higher percentiles and tolerates very high numbers of non-detects. We present a non-technical introduction and illustrate it with an implementation to real data from a clinical trial. We show that by using quantile regression, groups can be compared and that meaningful linear trends can be computed, even if more than half of the data consists of non-detects. Quantile regression is a valuable addition to the statistical methods that can be used for the analysis of immunological datasets with non-detects.
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.
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
An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

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

NASA Astrophysics Data System (ADS)

Al-Daffaie, Kadhem; Khan, Shahjahan

2017-05-01

This paper considers the relationship between a binary response and a circular predictor. It develops the logistic regression model by employing the linear-circular regression approach. The maximum likelihood method is used to estimate the parameters. The Newton-Raphson numerical method is used to find the estimated values of the parameters. A data set from weather records of Toowoomba city is analysed by the proposed methods. Moreover, a simulation study is considered. The R software is used for all computations and simulations.
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;…
Linear-regression convolutional neural network for fully automated coronary lumen segmentation in intravascular optical coherence tomography.

PubMed

Yong, Yan Ling; Tan, Li Kuo; McLaughlin, Robert A; Chee, Kok Han; Liew, Yih Miin

2017-12-01

Intravascular optical coherence tomography (OCT) is an optical imaging modality commonly used in the assessment of coronary artery diseases during percutaneous coronary intervention. Manual segmentation to assess luminal stenosis from OCT pullback scans is challenging and time consuming. We propose a linear-regression convolutional neural network to automatically perform vessel lumen segmentation, parameterized in terms of radial distances from the catheter centroid in polar space. Benchmarked against gold-standard manual segmentation, our proposed algorithm achieves average locational accuracy of the vessel wall of 22 microns, and 0.985 and 0.970 in Dice coefficient and Jaccard similarity index, respectively. The average absolute error of luminal area estimation is 1.38%. The processing rate is 40.6 ms per image, suggesting the potential to be incorporated into a clinical workflow and to provide quantitative assessment of vessel lumen in an intraoperative time frame. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).
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.

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.
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.
The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

NASA Technical Reports Server (NTRS)

Parker, Peter A.; Geoffrey, Vining G.; Wilson, Sara R.; Szarka, John L., III; Johnson, Nels G.

2010-01-01

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.
Survival Data and Regression Models

NASA Astrophysics Data System (ADS)

Grégoire, G.

2014-12-01

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

NASA Astrophysics Data System (ADS)

Beh, W. L.; Yong, M. K. Au

2017-04-01

This study is to give an insight on the doubt of the important of macroeconomic variables that affecting the total volumes of Malaysia's imports and exports by using multiple linear regression (MLR) analysis. The time frame for this study will be determined by using quarterly data of the total volumes of Malaysia's imports and exports covering the period between 2000-2015. The macroeconomic variables will be limited to eleven variables which are the exchange rate of US Dollar with Malaysia Ringgit (USD-MYR), exchange rate of China Yuan with Malaysia Ringgit (RMB-MYR), exchange rate of European Euro with Malaysia Ringgit (EUR-MYR), exchange rate of Singapore Dollar with Malaysia Ringgit (SGD-MYR), crude oil prices, gold prices, producer price index (PPI), interest rate, consumer price index (CPI), industrial production index (IPI) and gross domestic product (GDP). This study has applied the Johansen Co-integration test to investigate the relationship among the total volumes to Malaysia's imports and exports. The result shows that crude oil prices, RMB-MYR, EUR-MYR and IPI play important roles in the total volumes of Malaysia's imports. Meanwhile crude oil price, USD-MYR and GDP play important roles in the total volumes of Malaysia's exports.
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
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…
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.
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…
Regression Analysis of Mixed Recurrent-Event and Panel-Count Data with Additive Rate Models

PubMed Central

Zhu, Liang; Zhao, Hui; Sun, Jianguo; Leisenring, Wendy; Robison, Leslie L.

2015-01-01

Summary Event-history studies of recurrent events are often conducted in fields such as demography, epidemiology, medicine, and social sciences (Cook and Lawless, 2007; Zhao et al., 2011). For such analysis, two types of data have been extensively investigated: recurrent-event data and panel-count data. However, in practice, one may face a third type of data, mixed recurrent-event and panel-count data or mixed event-history data. Such data occur if some study subjects are monitored or observed continuously and thus provide recurrent-event data, while the others are observed only at discrete times and hence give only panel-count data. A more general situation is that each subject is observed continuously over certain time periods but only at discrete times over other time periods. There exists little literature on the analysis of such mixed data except that published by Zhu et al. (2013). In this paper, we consider the regression analysis of mixed data using the additive rate model and develop some estimating equation-based approaches to estimate the regression parameters of interest. Both finite sample and asymptotic properties of the resulting estimators are established, and the numerical studies suggest that the proposed methodology works well for practical situations. The approach is applied to a Childhood Cancer Survivor Study that motivated this study. PMID:25345405
Prediction of unwanted pregnancies using logistic regression, probit regression and discriminant analysis

PubMed Central

Ebrahimzadeh, Farzad; Hajizadeh, Ebrahim; Vahabi, Nasim; Almasian, Mohammad; Bakhteyar, Katayoon

2015-01-01

Background: Unwanted pregnancy not intended by at least one of the parents has undesirable consequences for the family and the society. In the present study, three classification models were used and compared to predict unwanted pregnancies in an urban population. Methods: In this cross-sectional study, 887 pregnant mothers referring to health centers in Khorramabad, Iran, in 2012 were selected by the stratified and cluster sampling; relevant variables were measured and for prediction of unwanted pregnancy, logistic regression, discriminant analysis, and probit regression models and SPSS software version 21 were used. To compare these models, indicators such as sensitivity, specificity, the area under the ROC curve, and the percentage of correct predictions were used. Results: The prevalence of unwanted pregnancies was 25.3%. The logistic and probit regression models indicated that parity and pregnancy spacing, contraceptive methods, household income and number of living male children were related to unwanted pregnancy. The performance of the models based on the area under the ROC curve was 0.735, 0.733, and 0.680 for logistic regression, probit regression, and linear discriminant analysis, respectively. Conclusion: Given the relatively high prevalence of unwanted pregnancies in Khorramabad, it seems necessary to revise family planning programs. Despite the similar accuracy of the models, if the researcher is interested in the interpretability of the results, the use of the logistic regression model is recommended. PMID:26793655
Prediction of unwanted pregnancies using logistic regression, probit regression and discriminant analysis.

PubMed

Ebrahimzadeh, Farzad; Hajizadeh, Ebrahim; Vahabi, Nasim; Almasian, Mohammad; Bakhteyar, Katayoon

2015-01-01

Unwanted pregnancy not intended by at least one of the parents has undesirable consequences for the family and the society. In the present study, three classification models were used and compared to predict unwanted pregnancies in an urban population. In this cross-sectional study, 887 pregnant mothers referring to health centers in Khorramabad, Iran, in 2012 were selected by the stratified and cluster sampling; relevant variables were measured and for prediction of unwanted pregnancy, logistic regression, discriminant analysis, and probit regression models and SPSS software version 21 were used. To compare these models, indicators such as sensitivity, specificity, the area under the ROC curve, and the percentage of correct predictions were used. The prevalence of unwanted pregnancies was 25.3%. The logistic and probit regression models indicated that parity and pregnancy spacing, contraceptive methods, household income and number of living male children were related to unwanted pregnancy. The performance of the models based on the area under the ROC curve was 0.735, 0.733, and 0.680 for logistic regression, probit regression, and linear discriminant analysis, respectively. Given the relatively high prevalence of unwanted pregnancies in Khorramabad, it seems necessary to revise family planning programs. Despite the similar accuracy of the models, if the researcher is interested in the interpretability of the results, the use of the logistic regression model is recommended.
Simulation of groundwater level variations using wavelet combined with neural network, linear regression and support vector machine

NASA Astrophysics Data System (ADS)

Ebrahimi, Hadi; Rajaee, Taher

2017-01-01

Simulation of groundwater level (GWL) fluctuations is an important task in management of groundwater resources. In this study, the effect of wavelet analysis on the training of the artificial neural network (ANN), multi linear regression (MLR) and support vector regression (SVR) approaches was investigated, and the ANN, MLR and SVR along with the wavelet-ANN (WNN), wavelet-MLR (WLR) and wavelet-SVR (WSVR) models were compared in simulating one-month-ahead of GWL. The only variable used to develop the models was the monthly GWL data recorded over a period of 11 years from two wells in the Qom plain, Iran. The results showed that decomposing GWL time series into several sub-time series, extremely improved the training of the models. For both wells 1 and 2, the Meyer and Db5 wavelets produced better results compared to the other wavelets; which indicated wavelet types had similar behavior in similar case studies. The optimal number of delays was 6 months, which seems to be due to natural phenomena. The best WNN model, using Meyer mother wavelet with two decomposition levels, simulated one-month-ahead with RMSE values being equal to 0.069 m and 0.154 m for wells 1 and 2, respectively. The RMSE values for the WLR model were 0.058 m and 0.111 m, and for WSVR model were 0.136 m and 0.060 m for wells 1 and 2, respectively.
A Comparative Assessment of the Influences of Human Impacts on Soil Cd Concentrations Based on Stepwise Linear Regression, Classification and Regression Tree, and Random Forest Models

PubMed Central

Qiu, Lefeng; Wang, Kai; Long, Wenli; Wang, Ke; Hu, Wei; Amable, Gabriel S.

2016-01-01

Soil cadmium (Cd) contamination has attracted a great deal of attention because of its detrimental effects on animals and humans. This study aimed to develop and compare the performances of stepwise linear regression (SLR), classification and regression tree (CART) and random forest (RF) models in the prediction and mapping of the spatial distribution of soil Cd and to identify likely sources of Cd accumulation in Fuyang County, eastern China. Soil Cd data from 276 topsoil (0–20 cm) samples were collected and randomly divided into calibration (222 samples) and validation datasets (54 samples). Auxiliary data, including detailed land use information, soil organic matter, soil pH, and topographic data, were incorporated into the models to simulate the soil Cd concentrations and further identify the main factors influencing soil Cd variation. The predictive models for soil Cd concentration exhibited acceptable overall accuracies (72.22% for SLR, 70.37% for CART, and 75.93% for RF). The SLR model exhibited the largest predicted deviation, with a mean error (ME) of 0.074 mg/kg, a mean absolute error (MAE) of 0.160 mg/kg, and a root mean squared error (RMSE) of 0.274 mg/kg, and the RF model produced the results closest to the observed values, with an ME of 0.002 mg/kg, an MAE of 0.132 mg/kg, and an RMSE of 0.198 mg/kg. The RF model also exhibited the greatest R2 value (0.772). The CART model predictions closely followed, with ME, MAE, RMSE, and R2 values of 0.013 mg/kg, 0.154 mg/kg, 0.230 mg/kg and 0.644, respectively. The three prediction maps generally exhibited similar and realistic spatial patterns of soil Cd contamination. The heavily Cd-affected areas were primarily located in the alluvial valley plain of the Fuchun River and its tributaries because of the dramatic industrialization and urbanization processes that have occurred there. The most important variable for explaining high levels of soil Cd accumulation was the presence of metal smelting industries. The
A Comparative Assessment of the Influences of Human Impacts on Soil Cd Concentrations Based on Stepwise Linear Regression, Classification and Regression Tree, and Random Forest Models.

PubMed

Qiu, Lefeng; Wang, Kai; Long, Wenli; Wang, Ke; Hu, Wei; Amable, Gabriel S

2016-01-01

Soil cadmium (Cd) contamination has attracted a great deal of attention because of its detrimental effects on animals and humans. This study aimed to develop and compare the performances of stepwise linear regression (SLR), classification and regression tree (CART) and random forest (RF) models in the prediction and mapping of the spatial distribution of soil Cd and to identify likely sources of Cd accumulation in Fuyang County, eastern China. Soil Cd data from 276 topsoil (0-20 cm) samples were collected and randomly divided into calibration (222 samples) and validation datasets (54 samples). Auxiliary data, including detailed land use information, soil organic matter, soil pH, and topographic data, were incorporated into the models to simulate the soil Cd concentrations and further identify the main factors influencing soil Cd variation. The predictive models for soil Cd concentration exhibited acceptable overall accuracies (72.22% for SLR, 70.37% for CART, and 75.93% for RF). The SLR model exhibited the largest predicted deviation, with a mean error (ME) of 0.074 mg/kg, a mean absolute error (MAE) of 0.160 mg/kg, and a root mean squared error (RMSE) of 0.274 mg/kg, and the RF model produced the results closest to the observed values, with an ME of 0.002 mg/kg, an MAE of 0.132 mg/kg, and an RMSE of 0.198 mg/kg. The RF model also exhibited the greatest R2 value (0.772). The CART model predictions closely followed, with ME, MAE, RMSE, and R2 values of 0.013 mg/kg, 0.154 mg/kg, 0.230 mg/kg and 0.644, respectively. The three prediction maps generally exhibited similar and realistic spatial patterns of soil Cd contamination. The heavily Cd-affected areas were primarily located in the alluvial valley plain of the Fuchun River and its tributaries because of the dramatic industrialization and urbanization processes that have occurred there. The most important variable for explaining high levels of soil Cd accumulation was the presence of metal smelting industries. The
Assessing risk factors for periodontitis using regression

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

NASA Astrophysics Data System (ADS)

Sahoo, Sasmita; Jha, Madan K.

2013-12-01

The potential of multiple linear regression (MLR) and artificial neural network (ANN) techniques in predicting transient water levels over a groundwater basin were compared. MLR and ANN modeling was carried out at 17 sites in Japan, considering all significant inputs: rainfall, ambient temperature, river stage, 11 seasonal dummy variables, and influential lags of rainfall, ambient temperature, river stage and groundwater level. Seventeen site-specific ANN models were developed, using multi-layer feed-forward neural networks trained with Levenberg-Marquardt backpropagation algorithms. The performance of the models was evaluated using statistical and graphical indicators. Comparison of the goodness-of-fit statistics of the MLR models with those of the ANN models indicated that there is better agreement between the ANN-predicted groundwater levels and the observed groundwater levels at all the sites, compared to the MLR. This finding was supported by the graphical indicators and the residual analysis. Thus, it is concluded that the ANN technique is superior to the MLR technique in predicting spatio-temporal distribution of groundwater levels in a basin. However, considering the practical advantages of the MLR technique, it is recommended as an alternative and cost-effective groundwater modeling tool.
Use of empirical likelihood to calibrate auxiliary information in partly linear monotone regression models.

PubMed

Chen, Baojiang; Qin, Jing

2014-05-10

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

Ridge Regression for Interactive Models.

ERIC Educational Resources Information Center

Tate, Richard L.

1988-01-01

An exploratory study of the value of ridge regression for interactive models is reported. Assuming that the linear terms in a simple interactive model are centered to eliminate non-essential multicollinearity, a variety of common models, representing both ordinal and disordinal interactions, are shown to have "orientations" that are…
The Geometry of Enhancement in Multiple Regression

ERIC Educational Resources Information Center

Waller, Niels G.

2011-01-01

In linear multiple regression, "enhancement" is said to occur when R[superscript 2] = b[prime]r greater than r[prime]r, where b is a p x 1 vector of standardized regression coefficients and r is a p x 1 vector of correlations between a criterion y and a set of standardized regressors, x. When p = 1 then b [is congruent to] r and…
Tumour regression of uveal melanoma after ruthenium-106 brachytherapy or stereotactic radiotherapy with gamma knife or linear accelerator.

PubMed

Georgopoulos, Michael; Zehetmayer, Martin; Ruhswurm, Irene; Toma-Bstaendig, Sabine; Ségur-Eltz, Nikolaus; Sacu, Stefan; Menapace, Rupert

2003-01-01

This study assesses differences in relative tumour regression and internal acoustic reflectivity after 3 methods of radiotherapy for uveal melanoma: (1) brachytherapy with ruthenium-106 radioactive plaques (RU), (2) fractionated high-dose gamma knife stereotactic irradiation in 2-3 fractions (GK) or (3) fractionated linear-accelerator-based stereotactic teletherapy in 5 fractions (Linac). Ultrasound measurements of tumour thickness and internal reflectivity were performed with standardised A scan pre-operatively and 3, 6, 9, 12, 18, 24 and 36 months postoperatively. Of 211 patients included in the study, 111 had a complete 3-year follow-up (RU: 41, GK: 37, Linac: 33). Differences in tumour thickness and internal reflectivity were assessed with analysis of variance, and post hoc multiple comparisons were calculated with Tukey's honestly significant difference test. Local tumour control was excellent with all 3 methods (>93%). At 36 months, relative tumour height reduction was 69, 50 and 30% after RU, GK and Linac, respectively. In all 3 treatment groups, internal reflectivity increased from about 30% initially to 60-70% 3 years after treatment. Brachytherapy with ruthenium-106 plaques results in a faster tumour regression as compared to teletherapy with gamma knife or Linac. Internal reflectivity increases comparably in all 3 groups. Besides tumour growth arrest, increasing internal reflectivity is considered as an important factor indicating successful treatment. Copyright 2003 S. Karger AG, Basel
A Comparative Study of Pairwise Learning Methods Based on Kernel Ridge Regression.

PubMed

Stock, Michiel; Pahikkala, Tapio; Airola, Antti; De Baets, Bernard; Waegeman, Willem

2018-06-12

Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction, or network inference problems. During the past decade, kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression, and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency, and spectral filtering properties. Our theoretical results provide valuable insights into assessing the advantages and limitations of existing pairwise learning methods.
Structured Additive Quantile Regression for Assessing the Determinants of Childhood Anemia in Rwanda.

PubMed

Habyarimana, Faustin; Zewotir, Temesgen; Ramroop, Shaun

2017-06-17

Childhood anemia is among the most significant health problems faced by public health departments in developing countries. This study aims at assessing the determinants and possible spatial effects associated with childhood anemia in Rwanda. The 2014/2015 Rwanda Demographic and Health Survey (RDHS) data was used. The analysis was done using the structured spatial additive quantile regression model. The findings of this study revealed that the child's age; the duration of breastfeeding; gender of the child; the nutritional status of the child (whether underweight and/or wasting); whether the child had a fever; had a cough in the two weeks prior to the survey or not; whether the child received vitamin A supplementation in the six weeks before the survey or not; the household wealth index; literacy of the mother; mother's anemia status; mother's age at the birth are all significant factors associated with childhood anemia in Rwanda. Furthermore, significant structured spatial location effects on childhood anemia was found.
Functional Additive Mixed Models

PubMed Central

Scheipl, Fabian; Staicu, Ana-Maria; Greven, Sonja

2014-01-01

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. It accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms. We provide easy-to-use open source software in the pffr() function for the R-package refund. Simulations show that the proposed method recovers relevant effects reliably, handles small sample sizes well and also scales to larger data sets. Applications with spatially and longitudinally observed functional data demonstrate the flexibility in modeling and interpretability of results of our approach. PMID:26347592
Functional Additive Mixed Models.

PubMed

Scheipl, Fabian; Staicu, Ana-Maria; Greven, Sonja

2015-04-01

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. It accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms. We provide easy-to-use open source software in the pffr() function for the R-package refund. Simulations show that the proposed method recovers relevant effects reliably, handles small sample sizes well and also scales to larger data sets. Applications with spatially and longitudinally observed functional data demonstrate the flexibility in modeling and interpretability of results of our approach.
Regression modeling of ground-water flow

USGS Publications Warehouse

Cooley, R.L.; Naff, R.L.

1985-01-01

Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)
Quantile regression models of animal habitat relationships

USGS Publications Warehouse

Cade, Brian S.

2003-01-01

Typically, all factors that limit an organism are not measured and included in statistical models used to investigate relationships with their environment. If important unmeasured variables interact multiplicatively with the measured variables, the statistical models often will have heterogeneous response distributions with unequal variances. Quantile regression is an approach for estimating the conditional quantiles of a response variable distribution in the linear model, providing a more complete view of possible causal relationships between variables in ecological processes. Chapter 1 introduces quantile regression and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of estimates for homogeneous and heterogeneous regression models. Chapter 2 evaluates performance of quantile rankscore tests used for hypothesis testing and constructing confidence intervals for linear quantile regression estimates (0 ≤ τ ≤ 1). A permutation F test maintained better Type I errors than the Chi-square T test for models with smaller n, greater number of parameters p, and more extreme quantiles τ. Both versions of the test required weighting to maintain correct Type I errors when there was heterogeneity under the alternative model. An example application related trout densities to stream channel width:depth. Chapter 3 evaluates a drop in dispersion, F-ratio like permutation test for hypothesis testing and constructing confidence intervals for linear quantile regression estimates (0 ≤ τ ≤ 1). Chapter 4 simulates from a large (N = 10,000) finite population representing grid areas on a landscape to demonstrate various forms of hidden bias that might occur when the effect of a measured habitat variable on some animal was confounded with the effect of another unmeasured variable (spatially and not spatially structured). Depending on whether interactions of the measured habitat and unmeasured variable were negative
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…
An Application of Robust Method in Multiple Linear Regression Model toward Credit Card Debt

NASA Astrophysics Data System (ADS)

Amira Azmi, Nur; Saifullah Rusiman, Mohd; Khalid, Kamil; Roslan, Rozaini; Sufahani, Suliadi; Mohamad, Mahathir; Salleh, Rohayu Mohd; Hamzah, Nur Shamsidah Amir

2018-04-01

Credit card is a convenient alternative replaced cash or cheque, and it is essential component for electronic and internet commerce. In this study, the researchers attempt to determine the relationship and significance variables between credit card debt and demographic variables such as age, household income, education level, years with current employer, years at current address, debt to income ratio and other debt. The provided data covers 850 customers information. There are three methods that applied to the credit card debt data which are multiple linear regression (MLR) models, MLR models with least quartile difference (LQD) method and MLR models with mean absolute deviation method. After comparing among three methods, it is found that MLR model with LQD method became the best model with the lowest value of mean square error (MSE). According to the final model, it shows that the years with current employer, years at current address, household income in thousands and debt to income ratio are positively associated with the amount of credit debt. Meanwhile variables for age, level of education and other debt are negatively associated with amount of credit debt. This study may serve as a reference for the bank company by using robust methods, so that they could better understand their options and choice that is best aligned with their goals for inference regarding to the credit card debt.
Artificial neural networks and multiple linear regression model using principal components to estimate rainfall over South America

NASA Astrophysics Data System (ADS)

Soares dos Santos, T.; Mendes, D.; Rodrigues Torres, R.

2016-01-01

Several studies have been devoted to dynamic and statistical downscaling for analysis of both climate variability and climate change. This paper introduces an application of artificial neural networks (ANNs) and multiple linear regression (MLR) by principal components to estimate rainfall in South America. This method is proposed for downscaling monthly precipitation time series over South America for three regions: the Amazon; northeastern Brazil; and the La Plata Basin, which is one of the regions of the planet that will be most affected by the climate change projected for the end of the 21st century. The downscaling models were developed and validated using CMIP5 model output and observed monthly precipitation. We used general circulation model (GCM) experiments for the 20th century (RCP historical; 1970-1999) and two scenarios (RCP 2.6 and 8.5; 2070-2100). The model test results indicate that the ANNs significantly outperform the MLR downscaling of monthly precipitation variability.
Artificial neural networks and multiple linear regression model using principal components to estimate rainfall over South America

NASA Astrophysics Data System (ADS)

dos Santos, T. S.; Mendes, D.; Torres, R. R.

2015-08-01

Several studies have been devoted to dynamic and statistical downscaling for analysis of both climate variability and climate change. This paper introduces an application of artificial neural networks (ANN) and multiple linear regression (MLR) by principal components to estimate rainfall in South America. This method is proposed for downscaling monthly precipitation time series over South America for three regions: the Amazon, Northeastern Brazil and the La Plata Basin, which is one of the regions of the planet that will be most affected by the climate change projected for the end of the 21st century. The downscaling models were developed and validated using CMIP5 model out- put and observed monthly precipitation. We used GCMs experiments for the 20th century (RCP Historical; 1970-1999) and two scenarios (RCP 2.6 and 8.5; 2070-2100). The model test results indicate that the ANN significantly outperforms the MLR downscaling of monthly precipitation variability.
Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

PubMed

Meng, Yilin; Roux, Benoît

2015-08-11

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost.
Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression

PubMed Central

2015-01-01

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost. PMID:26574437
Regression analysis of mixed recurrent-event and panel-count data with additive rate models.

PubMed

Zhu, Liang; Zhao, Hui; Sun, Jianguo; Leisenring, Wendy; Robison, Leslie L

2015-03-01

Event-history studies of recurrent events are often conducted in fields such as demography, epidemiology, medicine, and social sciences (Cook and Lawless, 2007, The Statistical Analysis of Recurrent Events. New York: Springer-Verlag; Zhao et al., 2011, Test 20, 1-42). For such analysis, two types of data have been extensively investigated: recurrent-event data and panel-count data. However, in practice, one may face a third type of data, mixed recurrent-event and panel-count data or mixed event-history data. Such data occur if some study subjects are monitored or observed continuously and thus provide recurrent-event data, while the others are observed only at discrete times and hence give only panel-count data. A more general situation is that each subject is observed continuously over certain time periods but only at discrete times over other time periods. There exists little literature on the analysis of such mixed data except that published by Zhu et al. (2013, Statistics in Medicine 32, 1954-1963). In this article, we consider the regression analysis of mixed data using the additive rate model and develop some estimating equation-based approaches to estimate the regression parameters of interest. Both finite sample and asymptotic properties of the resulting estimators are established, and the numerical studies suggest that the proposed methodology works well for practical situations. The approach is applied to a Childhood Cancer Survivor Study that motivated this study. © 2014, The International Biometric Society.
Random regression analyses using B-spline functions to model growth of Nellore cattle.

PubMed

Boligon, A A; Mercadante, M E Z; Lôbo, R B; Baldi, F; Albuquerque, L G

2012-02-01

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions
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…
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.
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.

The comparison between several robust ridge regression estimators in the presence of multicollinearity and multiple outliers

NASA Astrophysics Data System (ADS)

Zahari, Siti Meriam; Ramli, Norazan Mohamed; Moktar, Balkiah; Zainol, Mohammad Said

2014-09-01

In the presence of multicollinearity and multiple outliers, statistical inference of linear regression model using ordinary least squares (OLS) estimators would be severely affected and produces misleading results. To overcome this, many approaches have been investigated. These include robust methods which were reported to be less sensitive to the presence of outliers. In addition, ridge regression technique was employed to tackle multicollinearity problem. In order to mitigate both problems, a combination of ridge regression and robust methods was discussed in this study. The superiority of this approach was examined when simultaneous presence of multicollinearity and multiple outliers occurred in multiple linear regression. This study aimed to look at the performance of several well-known robust estimators; M, MM, RIDGE and robust ridge regression estimators, namely Weighted Ridge M-estimator (WRM), Weighted Ridge MM (WRMM), Ridge MM (RMM), in such a situation. Results of the study showed that in the presence of simultaneous multicollinearity and multiple outliers (in both x and y-direction), the RMM and RIDGE are more or less similar in terms of superiority over the other estimators, regardless of the number of observation, level of collinearity and percentage of outliers used. However, when outliers occurred in only single direction (y-direction), the WRMM estimator is the most superior among the robust ridge regression estimators, by producing the least variance. In conclusion, the robust ridge regression is the best alternative as compared to robust and conventional least squares estimators when dealing with simultaneous presence of multicollinearity and outliers.
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…
Assessment of triglyceride and cholesterol in overweight people based on multiple linear regression and artificial intelligence model.

PubMed

Ma, Jing; Yu, Jiong; Hao, Guangshu; Wang, Dan; Sun, Yanni; Lu, Jianxin; Cao, Hongcui; Lin, Feiyan

2017-02-20

The prevalence of high hyperlipemia is increasing around the world. Our aims are to analyze the relationship of triglyceride (TG) and cholesterol (TC) with indexes of liver function and kidney function, and to develop a prediction model of TG, TC in overweight people. A total of 302 adult healthy subjects and 273 overweight subjects were enrolled in this study. The levels of fasting indexes of TG (fs-TG), TC (fs-TC), blood glucose, liver function, and kidney function were measured and analyzed by correlation analysis and multiple linear regression (MRL). The back propagation artificial neural network (BP-ANN) was applied to develop prediction models of fs-TG and fs-TC. The results showed there was significant difference in biochemical indexes between healthy people and overweight people. The correlation analysis showed fs-TG was related to weight, height, blood glucose, and indexes of liver and kidney function; while fs-TC was correlated with age, indexes of liver function (P < 0.01). The MRL analysis indicated regression equations of fs-TG and fs-TC both had statistic significant (P < 0.01) when included independent indexes. The BP-ANN model of fs-TG reached training goal at 59 epoch, while fs-TC model achieved high prediction accuracy after training 1000 epoch. In conclusions, there was high relationship of fs-TG and fs-TC with weight, height, age, blood glucose, indexes of liver function and kidney function. Based on related variables, the indexes of fs-TG and fs-TC can be predicted by BP-ANN models in overweight people.
An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and t-distributed deviations

NASA Astrophysics Data System (ADS)

Kargoll, Boris; Omidalizarandi, Mohammad; Loth, Ina; Paffenholz, Jens-André; Alkhatib, Hamza

2018-03-01

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student's) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.
On the linear programming bound for linear Lee codes.

PubMed

Astola, Helena; Tabus, Ioan

2016-01-01

Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.
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.
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
Artificial neural networks environmental forecasting in comparison with multiple linear regression technique: From heavy metals to organic micropollutants screening in agricultural soils

NASA Astrophysics Data System (ADS)

Bonelli, Maria Grazia; Ferrini, Mauro; Manni, Andrea

2016-12-01

The assessment of metals and organic micropollutants contamination in agricultural soils is a difficult challenge due to the extensive area used to collect and analyze a very large number of samples. With Dioxins and dioxin-like PCBs measurement methods and subsequent the treatment of data, the European Community advises the develop low-cost and fast methods allowing routing analysis of a great number of samples, providing rapid measurement of these compounds in the environment, feeds and food. The aim of the present work has been to find a method suitable to describe the relations occurring between organic and inorganic contaminants and use the value of the latter in order to forecast the former. In practice, the use of a metal portable soil analyzer coupled with an efficient statistical procedure enables the required objective to be achieved. Compared to Multiple Linear Regression, the Artificial Neural Networks technique has shown to be an excellent forecasting method, though there is no linear correlation between the variables to be analyzed.
Estimation of perceptible water vapor of atmosphere using artificial neural network, support vector machine and multiple linear regression algorithm and their comparative study

NASA Astrophysics Data System (ADS)

Shastri, Niket; Pathak, Kamlesh

2018-05-01

The water vapor content in atmosphere plays very important role in climate. In this paper the application of GPS signal in meteorology is discussed, which is useful technique that is used to estimate the perceptible water vapor of atmosphere. In this paper various algorithms like artificial neural network, support vector machine and multiple linear regression are use to predict perceptible water vapor. The comparative studies in terms of root mean square error and mean absolute errors are also carried out for all the algorithms.
Assessment of cortical bone fracture resistance curves by fusing artificial neural networks and linear regression.

PubMed

Vukicevic, Arso M; Jovicic, Gordana R; Jovicic, Milos N; Milicevic, Vladimir L; Filipovic, Nenad D

2018-02-01

Bone injures (BI) represents one of the major health problems, together with cancer and cardiovascular diseases. Assessment of the risks associated with BI is nontrivial since fragility of human cortical bone is varying with age. Due to restrictions for performing experiments on humans, only a limited number of fracture resistance curves (R-curves) for particular ages have been reported in the literature. This study proposes a novel decision support system for the assessment of bone fracture resistance by fusing various artificial intelligence algorithms. The aim was to estimate the R-curve slope, toughness threshold and stress intensity factor using the two input parameters commonly available during a routine clinical examination: patients age and crack length. Using the data from the literature, the evolutionary assembled Artificial Neural Network was developed and used for the derivation of Linear regression (LR) models of R-curves for arbitrary age. Finally, by using the patient (age)-specific LR models and diagnosed crack size one could estimate the risk of bone fracture under given physiological conditions. Compared to the literature, we demonstrated improved performances for estimating nonlinear changes of R-curve slope (R 2 = 0.82 vs. R 2 = 0.76) and Toughness threshold with ageing (R 2 = 0.73 vs. R 2 = 0.66).
Cascade Optimization for Aircraft Engines With Regression and Neural Network Analysis - Approximators

NASA Technical Reports Server (NTRS)

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

2000-01-01

The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and deficiencies in the Newton-Raphson solver during engine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through a cascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neural network and linear regression methods. An approximation-interspersed cascade strategy was used to optimize the engine's operation over its flight envelope. Replacement of Powell's algorithm by the cascade strategy improved the optimization segment of the NEPP code. The performance of the linear regression and neural network methods as alternative engine analyzers was found to be satisfactory. This report considers two examples-a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine-to illustrate the results, and it discusses insights gained from the improved version of the NEPP code.
Using structured additive regression models to estimate risk factors of malaria: analysis of 2010 Malawi malaria indicator survey data.

PubMed

Chirombo, James; Lowe, Rachel; Kazembe, Lawrence

2014-01-01

After years of implementing Roll Back Malaria (RBM) interventions, the changing landscape of malaria in terms of risk factors and spatial pattern has not been fully investigated. This paper uses the 2010 malaria indicator survey data to investigate if known malaria risk factors remain relevant after many years of interventions. We adopted a structured additive logistic regression model that allowed for spatial correlation, to more realistically estimate malaria risk factors. Our model included child and household level covariates, as well as climatic and environmental factors. Continuous variables were modelled by assuming second order random walk priors, while spatial correlation was specified as a Markov random field prior, with fixed effects assigned diffuse priors. Inference was fully Bayesian resulting in an under five malaria risk map for Malawi. Malaria risk increased with increasing age of the child. With respect to socio-economic factors, the greater the household wealth, the lower the malaria prevalence. A general decline in malaria risk was observed as altitude increased. Minimum temperatures and average total rainfall in the three months preceding the survey did not show a strong association with disease risk. The structured additive regression model offered a flexible extension to standard regression models by enabling simultaneous modelling of possible nonlinear effects of continuous covariates, spatial correlation and heterogeneity, while estimating usual fixed effects of categorical and continuous observed variables. Our results confirmed that malaria epidemiology is a complex interaction of biotic and abiotic factors, both at the individual, household and community level and that risk factors are still relevant many years after extensive implementation of RBM activities.
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…
Meta-regression analysis of the effect of trans fatty acids on low-density lipoprotein cholesterol.

PubMed

Allen, Bruce C; Vincent, Melissa J; Liska, DeAnn; Haber, Lynne T

2016-12-01

We conducted a meta-regression of controlled clinical trial data to investigate quantitatively the relationship between dietary intake of industrial trans fatty acids (iTFA) and increased low-density lipoprotein cholesterol (LDL-C). Previous regression analyses included insufficient data to determine the nature of the dose response in the low-dose region and have nonetheless assumed a linear relationship between iTFA intake and LDL-C levels. This work contributes to the previous work by 1) including additional studies examining low-dose intake (identified using an evidence mapping procedure); 2) investigating a range of curve shapes, including both linear and nonlinear models; and 3) using Bayesian meta-regression to combine results across trials. We found that, contrary to previous assumptions, the linear model does not acceptably fit the data, while the nonlinear, S-shaped Hill model fits the data well. Based on a conservative estimate of the degree of intra-individual variability in LDL-C (0.1 mmoL/L), as an estimate of a change in LDL-C that is not adverse, a change in iTFA intake of 2.2% of energy intake (%en) (corresponding to a total iTFA intake of 2.2-2.9%en) does not cause adverse effects on LDL-C. The iTFA intake associated with this change in LDL-C is substantially higher than the average iTFA intake (0.5%en). Copyright Â© 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.
Correlation Weights in Multiple Regression

ERIC Educational Resources Information Center

Waller, Niels G.; Jones, Jeff A.

2010-01-01

A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting…
A comparison of model-based imputation methods for handling missing predictor values in a linear regression model: A simulation study

NASA Astrophysics Data System (ADS)

Hasan, Haliza; Ahmad, Sanizah; Osman, Balkish Mohd; Sapri, Shamsiah; Othman, Nadirah

2017-08-01

In regression analysis, missing covariate data has been a common problem. Many researchers use ad hoc methods to overcome this problem due to the ease of implementation. However, these methods require assumptions about the data that rarely hold in practice. Model-based methods such as Maximum Likelihood (ML) using the expectation maximization (EM) algorithm and Multiple Imputation (MI) are more promising when dealing with difficulties caused by missing data. Then again, inappropriate methods of missing value imputation can lead to serious bias that severely affects the parameter estimates. The main objective of this study is to provide a better understanding regarding missing data concept that can assist the researcher to select the appropriate missing data imputation methods. A simulation study was performed to assess the effects of different missing data techniques on the performance of a regression model. The covariate data were generated using an underlying multivariate normal distribution and the dependent variable was generated as a combination of explanatory variables. Missing values in covariate were simulated using a mechanism called missing at random (MAR). Four levels of missingness (10%, 20%, 30% and 40%) were imposed. ML and MI techniques available within SAS software were investigated. A linear regression analysis was fitted and the model performance measures; MSE, and R-Squared were obtained. Results of the analysis showed that MI is superior in handling missing data with highest R-Squared and lowest MSE when percent of missingness is less than 30%. Both methods are unable to handle larger than 30% level of missingness.
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.
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
Two-Dimensional, Supersonic, Linearized Flow with Heat Addition

NASA Technical Reports Server (NTRS)

Lomax, Harvard

1959-01-01

Calculations are presented for the forces on a thin supersonic wing underneath which the air is heated. The analysis is limited principally to linearized theory but nonlinear effects are considered. It is shown that significant advantages to external heating would exist if the heat were added well below and ahead of the wing.
Selection of higher order regression models in the analysis of multi-factorial transcription data.

PubMed

Prazeres da Costa, Olivia; Hoffman, Arthur; Rey, Johannes W; Mansmann, Ulrich; Buch, Thorsten; Tresch, Achim

2014-01-01

Many studies examine gene expression data that has been obtained under the influence of multiple factors, such as genetic background, environmental conditions, or exposure to diseases. The interplay of multiple factors may lead to effect modification and confounding. Higher order linear regression models can account for these effects. We present a new methodology for linear model selection and apply it to microarray data of bone marrow-derived macrophages. This experiment investigates the influence of three variable factors: the genetic background of the mice from which the macrophages were obtained, Yersinia enterocolitica infection (two strains, and a mock control), and treatment/non-treatment with interferon-γ. We set up four different linear regression models in a hierarchical order. We introduce the eruption plot as a new practical tool for model selection complementary to global testing. It visually compares the size and significance of effect estimates between two nested models. Using this methodology we were able to select the most appropriate model by keeping only relevant factors showing additional explanatory power. Application to experimental data allowed us to qualify the interaction of factors as either neutral (no interaction), alleviating (co-occurring effects are weaker than expected from the single effects), or aggravating (stronger than expected). We find a biologically meaningful gene cluster of putative C2TA target genes that appear to be co-regulated with MHC class II genes. We introduced the eruption plot as a tool for visual model comparison to identify relevant higher order interactions in the analysis of expression data obtained under the influence of multiple factors. We conclude that model selection in higher order linear regression models should generally be performed for the analysis of multi-factorial microarray data.

Linear regression analysis of Hospital Episode Statistics predicts a large increase in demand for elective hand surgery in England.

PubMed

Bebbington, Emily; Furniss, Dominic

2015-02-01

We integrated two factors, demographic population shifts and changes in prevalence of disease, to predict future trends in demand for hand surgery in England, to facilitate workforce planning. We analysed Hospital Episode Statistics data for Dupuytren's disease, carpal tunnel syndrome, cubital tunnel syndrome, and trigger finger from 1998 to 2011. Using linear regression, we estimated trends in both diagnosis and surgery until 2030. We integrated this regression with age specific population data from the Office for National Statistics in order to estimate how this will contribute to a change in workload over time. There has been a significant increase in both absolute numbers of diagnoses and surgery for all four conditions. Combined with future population data, we calculate that the total operative burden for these four conditions will increase from 87,582 in 2011 to 170,166 (95% confidence interval 144,517-195,353) in 2030. The prevalence of these diseases in the ageing population, and increasing prevalence of predisposing factors such as obesity and diabetes, may account for the predicted increase in workload. The most cost effective treatments must be sought, which requires high quality clinical trials. Our methodology can be applied to other sub-specialties to help anticipate the need for future service provision. Copyright © 2014 British Association of Plastic, Reconstructive and Aesthetic Surgeons. Published by Elsevier Ltd. All rights reserved.
Assessing the risk of bovine fasciolosis using linear regression analysis for the state of Rio Grande do Sul, Brazil.

PubMed

Silva, Ana Elisa Pereira; Freitas, Corina da Costa; Dutra, Luciano Vieira; Molento, Marcelo Beltrão

2016-02-15

Fasciola hepatica is the causative agent of fasciolosis, a disease that triggers a chronic inflammatory process in the liver affecting mainly ruminants and other animals including humans. In Brazil, F. hepatica occurs in larger numbers in the most Southern state of Rio Grande do Sul. The objective of this study was to estimate areas at risk using an eight-year (2002-2010) time series of climatic and environmental variables that best relate to the disease using a linear regression method to municipalities in the state of Rio Grande do Sul. The positivity index of the disease, which is the rate of infected animal per slaughtered animal, was divided into three risk classes: low, medium and high. The accuracy of the known sample classification on the confusion matrix for the low, medium and high rates produced by the estimated model presented values between 39 and 88% depending of the year. The regression analysis showed the importance of the time-based data for the construction of the model, considering the two variables of the previous year of the event (positivity index and maximum temperature). The generated data is important for epidemiological and parasite control studies mainly because F. hepatica is an infection that can last from months to years. Copyright © 2015 Elsevier B.V. All rights reserved.
Kendall-Theil Robust Line (KTRLine--version 1.0)-A Visual Basic Program for Calculating and Graphing Robust Nonparametric Estimates of Linear-Regression Coefficients Between Two Continuous Variables

USGS Publications Warehouse

Granato, Gregory E.

2006-01-01

The Kendall-Theil Robust Line software (KTRLine-version 1.0) is a Visual Basic program that may be used with the Microsoft Windows operating system to calculate parameters for robust, nonparametric estimates of linear-regression coefficients between two continuous variables. The KTRLine software was developed by the U.S. Geological Survey, in cooperation with the Federal Highway Administration, for use in stochastic data modeling with local, regional, and national hydrologic data sets to develop planning-level estimates of potential effects of highway runoff on the quality of receiving waters. The Kendall-Theil robust line was selected because this robust nonparametric method is resistant to the effects of outliers and nonnormality in residuals that commonly characterize hydrologic data sets. The slope of the line is calculated as the median of all possible pairwise slopes between points. The intercept is calculated so that the line will run through the median of input data. A single-line model or a multisegment model may be specified. The program was developed to provide regression equations with an error component for stochastic data generation because nonparametric multisegment regression tools are not available with the software that is commonly used to develop regression models. The Kendall-Theil robust line is a median line and, therefore, may underestimate total mass, volume, or loads unless the error component or a bias correction factor is incorporated into the estimate. Regression statistics such as the median error, the median absolute deviation, the prediction error sum of squares, the root mean square error, the confidence interval for the slope, and the bias correction factor for median estimates are calculated by use of nonparametric methods. These statistics, however, may be used to formulate estimates of mass, volume, or total loads. The program is used to read a two- or three-column tab-delimited input file with variable names in the first row and
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.
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)…
Method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1972-01-01

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
Isolating and Examining Sources of Suppression and Multicollinearity in Multiple Linear Regression.

PubMed

Beckstead, Jason W

2012-03-30

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 strategy to isolate, examine, and remove suppression effects has been offered. In this article such an approach, rooted in confirmatory factor analysis theory and employing matrix algebra, is developed. Suppression is viewed as the result of criterion-irrelevant variance operating among predictors. Decomposition of predictor variables into criterion-relevant and criterion-irrelevant components using structural equation modeling permits derivation of regression weights with the effects of criterion-irrelevant variance omitted. Three examples with data from applied research are used to illustrate the approach: the first assesses child and parent characteristics to explain why some parents of children with obsessive-compulsive disorder accommodate their child's compulsions more so than do others, the second examines various dimensions of personal health to explain individual differences in global quality of life among patients following heart surgery, and the third deals with quantifying the relative importance of various aptitudes for explaining academic performance in a sample of nursing students. The approach is offered as an analytic tool for investigators interested in understanding predictor-criterion relationships when complex patterns of intercorrelation among predictors are present and is shown to augment dominance analysis.
Poisson Mixture Regression Models for Heart Disease Prediction.

PubMed

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.
Poisson Mixture Regression Models for Heart Disease Prediction

PubMed Central

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611
Wheat bran reduces concentrations of digestible, metabolizable, and net energy in diets fed to pigs, but energy values in wheat bran determined by the difference procedure are not different from values estimated from a linear regression procedure.

PubMed

Jaworski, N W; Liu, D W; Li, D F; Stein, H H

2016-07-01

An experiment was conducted to determine effects on DE, ME, and NE for growing pigs of adding 15 or 30% wheat bran to a corn-soybean meal diet and to compare values for DE, ME, and NE calculated using the difference procedure with values obtained using linear regression. Eighteen barrows (54.4 ± 4.3 kg initial BW) were individually housed in metabolism crates. The experiment had 3 diets and 6 replicate pigs per diet. The control diet contained corn, soybean meal, and no wheat bran. Two additional diets were formulated by mixing 15 or 30% wheat bran with 85 or 70% of the control diet, respectively. The experimental period lasted 15 d. During the initial 7 d, pigs were adapted to their experimental diets and housed in metabolism crates and fed 573 kcal ME/kg BW per day. On d 8, metabolism crates with the pigs were moved into open-circuit respiration chambers for measurement of O consumption and CO and CH production. The feeding level was the same as in the adaptation period, and feces and urine were collected during this period. On d 13 and 14, pigs were fed 225 kcal ME/kg BW per day, and pigs were then fasted for 24 h to obtain fasting heat production. Results of the experiment indicated that the apparent total tract digestibility of DM, GE, crude fiber, ADF, and NDF linearly decreased ( ≤ 0.05) as wheat bran inclusion increased in the diets. The daily O consumption and CO and CH production by pigs fed increasing concentrations of wheat bran linearly decreased ( ≤ 0.05), resulting in a linear decrease ( ≤ 0.05) in heat production. The DE (3,454, 3,257, and 3,161 kcal/kg for diets containing 0, 15, and 30% wheat bran, respectively for diets containing 0, 15, and 30% wheat bran, respectively), ME (3,400, 3,209, and 3,091 kcal/kg for diets containing 0, 15, and 30% wheat bran, respectively), and NE (1,808, 1,575, and 1,458 kcal/kg for diets containing 0, 15, and 30% wheat bran, respectively) of diets decreased (linear, ≤ 0.05) as wheat bran inclusion increased
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…
Investigating bias in squared regression structure coefficients

PubMed Central

Nimon, Kim F.; Zientek, Linda R.; Thompson, Bruce

2015-01-01

The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients. PMID:26217273
Multiple linear regression to estimate time-frequency electrophysiological responses in single trials

PubMed Central

Hu, L.; Zhang, Z.G.; Mouraux, A.; Iannetti, G.D.

2015-01-01

Transient sensory, motor or cognitive event elicit not only phase-locked event-related potentials (ERPs) in the ongoing electroencephalogram (EEG), but also induce non-phase-locked modulations of ongoing EEG oscillations. These modulations can be detected when single-trial waveforms are analysed in the time-frequency domain, and consist in stimulus-induced decreases (event-related desynchronization, ERD) or increases (event-related synchronization, ERS) of synchrony in the activity of the underlying neuronal populations. ERD and ERS reflect changes in the parameters that control oscillations in neuronal networks and, depending on the frequency at which they occur, represent neuronal mechanisms involved in cortical activation, inhibition and binding. ERD and ERS are commonly estimated by averaging the time-frequency decomposition of single trials. However, their trial-to-trial variability that can reflect physiologically-important information is lost by across-trial averaging. Here, we aim to (1) develop novel approaches to explore single-trial parameters (including latency, frequency and magnitude) of ERP/ERD/ERS; (2) disclose the relationship between estimated single-trial parameters and other experimental factors (e.g., perceived intensity). We found that (1) stimulus-elicited ERP/ERD/ERS can be correctly separated using principal component analysis (PCA) decomposition with Varimax rotation on the single-trial time-frequency distributions; (2) time-frequency multiple linear regression with dispersion term (TF-MLRd) enhances the signal-to-noise ratio of ERP/ERD/ERS in single trials, and provides an unbiased estimation of their latency, frequency, and magnitude at single-trial level; (3) these estimates can be meaningfully correlated with each other and with other experimental factors at single-trial level (e.g., perceived stimulus intensity and ERP magnitude). The methods described in this article allow exploring fully non-phase-locked stimulus-induced cortical
Using Structured Additive Regression Models to Estimate Risk Factors of Malaria: Analysis of 2010 Malawi Malaria Indicator Survey Data

PubMed Central

Chirombo, James; Lowe, Rachel; Kazembe, Lawrence

2014-01-01

Background After years of implementing Roll Back Malaria (RBM) interventions, the changing landscape of malaria in terms of risk factors and spatial pattern has not been fully investigated. This paper uses the 2010 malaria indicator survey data to investigate if known malaria risk factors remain relevant after many years of interventions. Methods We adopted a structured additive logistic regression model that allowed for spatial correlation, to more realistically estimate malaria risk factors. Our model included child and household level covariates, as well as climatic and environmental factors. Continuous variables were modelled by assuming second order random walk priors, while spatial correlation was specified as a Markov random field prior, with fixed effects assigned diffuse priors. Inference was fully Bayesian resulting in an under five malaria risk map for Malawi. Results Malaria risk increased with increasing age of the child. With respect to socio-economic factors, the greater the household wealth, the lower the malaria prevalence. A general decline in malaria risk was observed as altitude increased. Minimum temperatures and average total rainfall in the three months preceding the survey did not show a strong association with disease risk. Conclusions The structured additive regression model offered a flexible extension to standard regression models by enabling simultaneous modelling of possible nonlinear effects of continuous covariates, spatial correlation and heterogeneity, while estimating usual fixed effects of categorical and continuous observed variables. Our results confirmed that malaria epidemiology is a complex interaction of biotic and abiotic factors, both at the individual, household and community level and that risk factors are still relevant many years after extensive implementation of RBM activities. PMID:24991915
Frequency doubling technology perimetry for detection of visual field progression in glaucoma: a pointwise linear regression analysis.

PubMed

Liu, Shu; Yu, Marco; Weinreb, Robert N; Lai, Gilda; Lam, Dennis Shun-Chiu; Leung, Christopher Kai-Shun

2014-05-02

We compared the detection of visual field progression and its rate of change between standard automated perimetry (SAP) and Matrix frequency doubling technology perimetry (FDTP) in glaucoma. We followed prospectively 217 eyes (179 glaucoma and 38 normal eyes) for SAP and FDTP testing at 4-month intervals for ≥36 months. Pointwise linear regression analysis was performed. A test location was considered progressing when the rate of change of visual sensitivity was ≤-1 dB/y for nonedge and ≤-2 dB/y for edge locations. Three criteria were used to define progression in an eye: ≥3 adjacent nonedge test locations (conservative), any three locations (moderate), and any two locations (liberal) progressed. The rate of change of visual sensitivity was calculated with linear mixed models. Of the 217 eyes, 6.1% and 3.9% progressed with the conservative criteria, 14.5% and 5.6% of eyes progressed with the moderate criteria, and 20.1% and 11.7% of eyes progressed with the liberal criteria by FDTP and SAP, respectively. Taking all test locations into consideration (total, 54 × 179 locations), FDTP detected more progressing locations (176) than SAP (103, P < 0.001). The rate of change of visual field mean deviation (MD) was significantly faster for FDTP (all with P < 0.001). No eyes showed progression in the normal group using the conservative and the moderate criteria. With a faster rate of change of visual sensitivity, FDTP detected more progressing eyes than SAP at a comparable level of specificity. Frequency doubling technology perimetry can provide a useful alternative to monitor glaucoma progression.
Identifying predictors of physics item difficulty: A linear regression approach

NASA Astrophysics Data System (ADS)

Mesic, Vanes; Muratovic, Hasnija

2011-06-01

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 difficult and very easy items. Knowing the factors that influence physics item difficulty makes it possible to model the item difficulty even before the first pilot study is conducted. Thus, by identifying predictors of physics item difficulty, we can improve the test-design process. Furthermore, we get additional qualitative feedback regarding the basic aspects of student cognitive achievement in physics that are directly responsible for the obtained, quantitative test results. In this study, we conducted a secondary analysis of data that came from two large-scale assessments of student physics achievement at the end of compulsory education in Bosnia and Herzegovina. Foremost, we explored the concept of “physics competence” and performed a content analysis of 123 physics items that were included within the above-mentioned assessments. Thereafter, an item database was created. Items were described by variables which reflect some basic cognitive aspects of physics competence. For each of the assessments, Rasch item difficulties were calculated in separate analyses. In order to make the item difficulties from different assessments comparable, a virtual test equating procedure had to be implemented. Finally, a regression model of physics item difficulty was created. It has been shown that 61.2% of item difficulty variance can be explained by factors which reflect the automaticity, complexity, and modality of the knowledge structure that is relevant for generating the most probable correct solution, as well as by the divergence of required thinking and interference effects between intuitive and formal physics knowledge
Multi-linear regression models predict the effects of water chemistry on acute lead toxicity to Ceriodaphnia dubia and Pimephales promelas.

PubMed

Esbaugh, A J; Brix, K V; Mager, E M; Grosell, M

2011-09-01

The current study examined the acute toxicity of lead (Pb) to Ceriodaphnia dubia and Pimephales promelas in a variety of natural waters. The natural waters were selected to range in pertinent water chemistry parameters such as calcium, pH, total CO(2) and dissolved organic carbon (DOC). Acute toxicity was determined for C. dubia and P. promelas using standard 48h and 96h protocols, respectively. For both organisms acute toxicity varied markedly according to water chemistry, with C. dubia LC50s ranging from 29 to 180μg/L and P. promelas LC50s ranging from 41 to 3598μg/L. Additionally, no Pb toxicity was observed for P. promelas in three alkaline natural waters. With respect to water chemistry parameters, DOC had the strongest protective impact for both organisms. A multi-linear regression (MLR) approach combining previous lab data and the current data was used to identify the relative importance of individual water chemistry components in predicting acute Pb toxicity for both species. As anticipated, the P. promelas best-fit MLR model combined DOC, calcium and pH. Unexpectedly, in the C. dubiaMLR model the importance of pH, TCO(2) and calcium was minimal while DOC and ionic strength were the controlling water quality variables. Adjusted R(2) values of 0.82 and 0.64 for the P. promelas and C. dubia models, respectively, are comparable to previously developed biotic ligand models for other metals. Copyright © 2011 Elsevier Inc. All rights reserved.
Random regression models using different functions to model milk flow in dairy cows.

PubMed

Laureano, M M M; Bignardi, A B; El Faro, L; Cardoso, V L; Tonhati, H; Albuquerque, L G

2014-09-12

We analyzed 75,555 test-day milk flow records from 2175 primiparous Holstein cows that calved between 1997 and 2005. Milk flow was obtained by dividing the mean milk yield (kg) of the 3 daily milking by the total milking time (min) and was expressed as kg/min. Milk flow was grouped into 43 weekly classes. The analyses were performed using a single-trait Random Regression Models that included direct additive genetic, permanent environmental, and residual random effects. In addition, the contemporary group and linear and quadratic effects of cow age at calving were included as fixed effects. Fourth-order orthogonal Legendre polynomial of days in milk was used to model the mean trend in milk flow. The additive genetic and permanent environmental covariance functions were estimated using random regression Legendre polynomials and B-spline functions of days in milk. The model using a third-order Legendre polynomial for additive genetic effects and a sixth-order polynomial for permanent environmental effects, which contained 7 residual classes, proved to be the most adequate to describe variations in milk flow, and was also the most parsimonious. The heritability in milk flow estimated by the most parsimonious model was of moderate to high magnitude.
Linear Regression with a Randomly Censored Covariate: Application to an Alzheimer's Study.

PubMed

Atem, Folefac D; Qian, Jing; Maye, Jacqueline E; Johnson, Keith A; Betensky, Rebecca A

2017-01-01

The association between maternal age of onset of dementia and amyloid deposition (measured by in vivo positron emission tomography (PET) imaging) in cognitively normal older offspring is of interest. In a regression model for amyloid, special methods are required due to the random right censoring of the covariate of maternal age of onset of dementia. Prior literature has proposed methods to address the problem of censoring due to assay limit of detection, but not random censoring. We propose imputation methods and a survival regression method that do not require parametric assumptions about the distribution of the censored covariate. Existing imputation methods address missing covariates, but not right censored covariates. In simulation studies, we compare these methods to the simple, but inefficient complete case analysis, and to thresholding approaches. We apply the methods to the Alzheimer's study.
Reflexion on linear regression trip production modelling method for ensuring good model quality

NASA Astrophysics Data System (ADS)

Suprayitno, Hitapriya; Ratnasari, Vita

2017-11-01

Transport Modelling is important. For certain cases, the conventional model still has to be used, in which having a good trip production model is capital. A good model can only be obtained from a good sample. Two of the basic principles of a good sampling is having a sample capable to represent the population characteristics and capable to produce an acceptable error at a certain confidence level. It seems that this principle is not yet quite understood and used in trip production modeling. Therefore, investigating the Trip Production Modelling practice in Indonesia and try to formulate a better modeling method for ensuring the Model Quality is necessary. This research result is presented as follows. Statistics knows a method to calculate span of prediction value at a certain confidence level for linear regression, which is called Confidence Interval of Predicted Value. The common modeling practice uses R2 as the principal quality measure, the sampling practice varies and not always conform to the sampling principles. An experiment indicates that small sample is already capable to give excellent R2 value and sample composition can significantly change the model. Hence, good R2 value, in fact, does not always mean good model quality. These lead to three basic ideas for ensuring good model quality, i.e. reformulating quality measure, calculation procedure, and sampling method. A quality measure is defined as having a good R2 value and a good Confidence Interval of Predicted Value. Calculation procedure must incorporate statistical calculation method and appropriate statistical tests needed. A good sampling method must incorporate random well distributed stratified sampling with a certain minimum number of samples. These three ideas need to be more developed and tested.

Introduction to the use of regression models in epidemiology.

PubMed

Bender, Ralf

2009-01-01

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

USGS Publications Warehouse

Kokaly, R.F.; Clark, R.N.

1999-01-01

We develop a new method for estimating the biochemistry of plant material using spectroscopy. Normalized band depths calculated from the continuum-removed reflectance spectra of dried and ground leaves were used to estimate their concentrations of nitrogen, lignin, and cellulose. Stepwise multiple linear regression was used to select wavelengths in the broad absorption features centered at 1.73 ??m, 2.10 ??m, and 2.30 ??m that were highly correlated with the chemistry of samples from eastern U.S. forests. Band depths of absorption features at these wavelengths were found to also be highly correlated with the chemistry of four other sites. A subset of data from the eastern U.S. forest sites was used to derive linear equations that were applied to the remaining data to successfully estimate their nitrogen, lignin, and cellulose concentrations. Correlations were highest for nitrogen (R2 from 0.75 to 0.94). The consistent results indicate the possibility of establishing a single equation capable of estimating the chemical concentrations in a wide variety of species from the reflectance spectra of dried leaves. The extension of this method to remote sensing was investigated. The effects of leaf water content, sensor signal-to-noise and bandpass, atmospheric effects, and background soil exposure were examined. Leaf water was found to be the greatest challenge to extending this empirical method to the analysis of fresh whole leaves and complete vegetation canopies. The influence of leaf water on reflectance spectra must be removed to within 10%. Other effects were reduced by continuum removal and normalization of band depths. If the effects of leaf water can be compensated for, it might be possible to extend this method to remote sensing data acquired by imaging spectrometers to give estimates of nitrogen, lignin, and cellulose concentrations over large areas for use in ecosystem studies.We develop a new method for estimating the biochemistry of plant material using
Using ridge regression in systematic pointing error corrections

NASA Technical Reports Server (NTRS)

Guiar, C. N.

1988-01-01

A pointing error model is used in the antenna calibration process. Data from spacecraft or radio star observations are used to determine the parameters in the model. However, the regression variables are not truly independent, displaying a condition known as multicollinearity. Ridge regression, a biased estimation technique, is used to combat the multicollinearity problem. Two data sets pertaining to Voyager 1 spacecraft tracking (days 105 and 106 of 1987) were analyzed using both linear least squares and ridge regression methods. The advantages and limitations of employing the technique are presented. The problem is not yet fully resolved.
Understanding poisson regression.

PubMed

Hayat, Matthew J; Higgins, Melinda

2014-04-01

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

NASA Astrophysics Data System (ADS)

Singh, S.; Jaishi, H. P.; Tiwari, R. P.; Tiwari, R. C.

2017-07-01

This paper reports the analysis of soil radon data recorded in the seismic zone-V, located in the northeastern part of India (latitude 23.73N, longitude 92.73E). Continuous measurements of soil-gas emission along Chite fault in Mizoram (India) were carried out with the replacement of solid-state nuclear track detectors at weekly interval. The present study was done for the period from March 2013 to May 2015 using LR-115 Type II detectors, manufactured by Kodak Pathe, France. In order to reduce the influence of meteorological parameters, statistical analysis tools such as multiple linear regression and artificial neural network have been used. Decrease in radon concentration was recorded prior to some earthquakes that occurred during the observation period. Some false anomalies were also recorded which may be attributed to the ongoing crustal deformation which was not major enough to produce an earthquake.
Modelling long-term fire occurrence factors in Spain by accounting for local variations with geographically weighted regression

NASA Astrophysics Data System (ADS)

Martínez-Fernández, J.; Chuvieco, E.; Koutsias, N.

2013-02-01

Humans are responsible for most forest fires in Europe, but anthropogenic factors behind these events are still poorly understood. We tried to identify the driving factors of human-caused fire occurrence in Spain by applying two different statistical approaches. Firstly, assuming stationary processes for the whole country, we created models based on multiple linear regression and binary logistic regression to find factors associated with fire density and fire presence, respectively. Secondly, we used geographically weighted regression (GWR) to better understand and explore the local and regional variations of those factors behind human-caused fire occurrence. The number of human-caused fires occurring within a 25-yr period (1983-2007) was computed for each of the 7638 Spanish mainland municipalities, creating a binary variable (fire/no fire) to develop logistic models, and a continuous variable (fire density) to build standard linear regression models. A total of 383 657 fires were registered in the study dataset. The binary logistic model, which estimates the probability of having/not having a fire, successfully classified 76.4% of the total observations, while the ordinary least squares (OLS) regression model explained 53% of the variation of the fire density patterns (adjusted R2 = 0.53). Both approaches confirmed, in addition to forest and climatic variables, the importance of variables related with agrarian activities, land abandonment, rural population exodus and developmental processes as underlying factors of fire occurrence. For the GWR approach, the explanatory power of the GW linear model for fire density using an adaptive bandwidth increased from 53% to 67%, while for the GW logistic model the correctly classified observations improved only slightly, from 76.4% to 78.4%, but significantly according to the corrected Akaike Information Criterion (AICc), from 3451.19 to 3321.19. The results from GWR indicated a significant spatial variation in the local
Deriving the Regression Line with Algebra

ERIC Educational Resources Information Center

Quintanilla, John A.

2017-01-01

Exploration with spreadsheets and reliance on previous skills can lead students to determine the line of best fit. To perform linear regression on a set of data, students in Algebra 2 (or, in principle, Algebra 1) do not have to settle for using the mysterious "black box" of their graphing calculators (or other classroom technologies).…
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
Two biased estimation techniques in linear regression: Application to aircraft

NASA Technical Reports Server (NTRS)

Klein, Vladislav

1988-01-01

Several ways for detection and assessment of collinearity in measured data are discussed. Because data collinearity usually results in poor least squares estimates, two estimation techniques which can limit a damaging effect of collinearity are presented. These two techniques, the principal components regression and mixed estimation, belong to a class of biased estimation techniques. Detection and assessment of data collinearity and the two biased estimation techniques are demonstrated in two examples using flight test data from longitudinal maneuvers of an experimental aircraft. The eigensystem analysis and parameter variance decomposition appeared to be a promising tool for collinearity evaluation. The biased estimators had far better accuracy than the results from the ordinary least squares technique.
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.
Inferring gene regression networks with model trees

PubMed Central

2010-01-01

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

PubMed

Held, Elizabeth; Cape, Joshua; Tintle, Nathan

2016-01-01

Machine learning methods continue to show promise in the analysis of data from genetic association studies because of the high number of variables relative to the number of observations. However, few best practices exist for the application of these methods. We extend a recently proposed supervised machine learning approach for predicting disease risk by genotypes to be able to incorporate gene expression data and rare variants. We then apply 2 different versions of the approach (radial and linear support vector machines) to simulated data from Genetic Analysis Workshop 19 and compare performance to logistic regression. Method performance was not radically different across the 3 methods, although the linear support vector machine tended to show small gains in predictive ability relative to a radial support vector machine and logistic regression. Importantly, as the number of genes in the models was increased, even when those genes contained causal rare variants, model predictive ability showed a statistically significant decrease in performance for both the radial support vector machine and logistic regression. The linear support vector machine showed more robust performance to the inclusion of additional genes. Further work is needed to evaluate machine learning approaches on larger samples and to evaluate the relative improvement in model prediction from the incorporation of gene expression data.
Application of artificial neural network to fMRI regression analysis.

PubMed

Misaki, Masaya; Miyauchi, Satoru

2006-01-15

We used an artificial neural network (ANN) to detect correlations between event sequences and fMRI (functional magnetic resonance imaging) signals. The layered feed-forward neural network, given a series of events as inputs and the fMRI signal as a supervised signal, performed a non-linear regression analysis. This type of ANN is capable of approximating any continuous function, and thus this analysis method can detect any fMRI signals that correlated with corresponding events. Because of the flexible nature of ANNs, fitting to autocorrelation noise is a problem in fMRI analyses. We avoided this problem by using cross-validation and an early stopping procedure. The results showed that the ANN could detect various responses with different time courses. The simulation analysis also indicated an additional advantage of ANN over non-parametric methods in detecting parametrically modulated responses, i.e., it can detect various types of parametric modulations without a priori assumptions. The ANN regression analysis is therefore beneficial for exploratory fMRI analyses in detecting continuous changes in responses modulated by changes in input values.
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.
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…
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
Divergent estimation error in portfolio optimization and in linear regression

NASA Astrophysics Data System (ADS)

Kondor, I.; Varga-Haszonits, I.

2008-08-01

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifestation of an algorithmic phase transition, it is accompanied by a number of critical phenomena, and displays universality. As the structure of a large number of multidimensional regression and modelling problems is very similar to portfolio optimization, the scope of the above observations extends far beyond finance, and covers a large number of problems in operations research, machine learning, bioinformatics, medical science, economics, and technology.
Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle.

PubMed

Baldi, F; Alencar, M M; Albuquerque, L G

2010-12-01

The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions. © 2010 Blackwell Verlag GmbH.
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…
Ecologic regression analysis and the study of the influence of air quality on mortality.

PubMed Central

Selvin, S; Merrill, D; Wong, L; Sacks, S T

1984-01-01

This presentation focuses entirely on the use and evaluation of regression analysis applied to ecologic data as a method to study the effects of ambient air pollution on mortality rates. Using extensive national data on mortality, air quality and socio-economic status regression analyses are used to study the influence of air quality on mortality. The analytic methods and data are selected in such a way that direct comparisons can be made with other ecologic regression studies of mortality and air quality. Analyses are performed by use of two types of geographic areas, age-specific mortality of both males and females and three pollutants (total suspended particulates, sulfur dioxide and nitrogen dioxide). The overall results indicate no persuasive evidence exists of a link between air quality and general mortality levels. Additionally, a lack of consistency between the present results and previous published work is noted. Overall, it is concluded that linear regression analysis applied to nationally collected ecologic data cannot be used to usefully infer a causal relationship between air quality and mortality which is in direct contradiction to other major published studies. PMID:6734568

Modeling ionospheric foF 2 response during geomagnetic storms using neural network and linear regression techniques

NASA Astrophysics Data System (ADS)

Tshisaphungo, Mpho; Habarulema, John Bosco; McKinnell, Lee-Anne

2018-06-01

In this paper, the modeling of the ionospheric foF 2 changes during geomagnetic storms by means of neural network (NN) and linear regression (LR) techniques is presented. The results will lead to a valuable tool to model the complex ionospheric changes during disturbed days in an operational space weather monitoring and forecasting environment. The storm-time foF 2 data during 1996-2014 from Grahamstown (33.3°S, 26.5°E), South Africa ionosonde station was used in modeling. In this paper, six storms were reserved to validate the models and hence not used in the modeling process. We found that the performance of both NN and LR models is comparable during selected storms which fell within the data period (1996-2014) used in modeling. However, when validated on storm periods beyond 1996-2014, the NN model gives a better performance (R = 0.62) compared to LR model (R = 0.56) for a storm that reached a minimum Dst index of -155 nT during 19-23 December 2015. We also found that both NN and LR models are capable of capturing the ionospheric foF 2 responses during two great geomagnetic storms (28 October-1 November 2003 and 6-12 November 2004) which have been demonstrated to be difficult storms to model in previous studies.
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.
Strengthen forensic entomology in court--the need for data exploration and the validation of a generalised additive mixed model.

PubMed

Baqué, Michèle; Amendt, Jens

2013-01-01

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

NASA Astrophysics Data System (ADS)

Herminiati, A.; Rahman, T.; Turmala, E.; Fitriany, C. G.

2017-12-01

The purpose of this study was to determine the correlation of different concentrations of modified cassava flour that was processed for banana fritter flour. The research method consists of two stages: (1) to determine the different types of flour: cassava flour, modified cassava flour-A (using the method of the lactid acid bacteria), and modified cassava flour-B (using the method of the autoclaving cooling cycle), then conducted on organoleptic test and physicochemical analysis; (2) to determine the correlation of concentration of modified cassava flour for banana fritter flour, by design was used simple linear regression. The factors were used different concentrations of modified cassava flour-B (y1) 40%, (y2) 50%, and (y3) 60%. The response in the study includes physical analysis (whiteness of flour, water holding capacity-WHC, oil holding capacity-OHC), chemical analysis (moisture content, ash content, crude fiber content, starch content), and organoleptic (color, aroma, taste, texture). The results showed that the type of flour selected from the organoleptic test was modified cassava flour-B. Analysis results of modified cassava flour-B component containing whiteness of flour 60.42%; WHC 41.17%; OHC 21.15%; moisture content 4.4%; ash content 1.75%; crude fiber content 1.86%; starch content 67.31%. The different concentrations of modified cassava flour-B with the results of the analysis provides correlation to the whiteness of flour, WHC, OHC, moisture content, ash content, crude fiber content, and starch content. The different concentrations of modified cassava flour-B does not affect the color, aroma, taste, and texture.
A gentle introduction to quantile regression for ecologists

USGS Publications Warehouse

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

2003-01-01

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

PubMed

Jiang, Yuan; He, Yunxiao; Zhang, Heping

LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This paper proposes an extension of LASSO, namely, prior LASSO (pLASSO), to incorporate that prior information into penalized generalized linear models. The goal is achieved by adding in the LASSO criterion function an additional measure of the discrepancy between the prior information and the model. For linear regression, the whole solution path of the pLASSO estimator can be found with a procedure similar to the Least Angle Regression (LARS). Asymptotic theories and simulation results show that pLASSO provides significant improvement over LASSO when the prior information is relatively accurate. When the prior information is less reliable, pLASSO shows great robustness to the misspecification. We illustrate the application of pLASSO using a real data set from a genome-wide association study.
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.
Learning accurate and interpretable models based on regularized random forests regression

PubMed Central

2014-01-01

Background Many biology related research works combine data from multiple sources in an effort to understand the underlying problems. It is important to find and interpret the most important information from these sources. Thus it will be beneficial to have an effective algorithm that can simultaneously extract decision rules and select critical features for good interpretation while preserving the prediction performance. Methods In this study, we focus on regression problems for biological data where target outcomes are continuous. In general, models constructed from linear regression approaches are relatively easy to interpret. However, many practical biological applications are nonlinear in essence where we can hardly find a direct linear relationship between input and output. Nonlinear regression techniques can reveal nonlinear relationship of data, but are generally hard for human to interpret. We propose a rule based regression algorithm that uses 1-norm regularized random forests. The proposed approach simultaneously extracts a small number of rules from generated random forests and eliminates unimportant features. Results We tested the approach on some biological data sets. The proposed approach is able to construct a significantly smaller set of regression rules using a subset of attributes while achieving prediction performance comparable to that of random forests regression. Conclusion It demonstrates high potential in aiding prediction and interpretation of nonlinear relationships of the subject being studied. PMID:25350120
Regression and multivariate models for predicting particulate matter concentration level.

PubMed

Nazif, Amina; Mohammed, Nurul Izma; Malakahmad, Amirhossein; Abualqumboz, Motasem S

2018-01-01

The devastating health effects of particulate matter (PM 10 ) exposure by susceptible populace has made it necessary to evaluate PM 10 pollution. Meteorological parameters and seasonal variation increases PM 10 concentration levels, especially in areas that have multiple anthropogenic activities. Hence, stepwise regression (SR), multiple linear regression (MLR) and principal component regression (PCR) analyses were used to analyse daily average PM 10 concentration levels. The analyses were carried out using daily average PM 10 concentration, temperature, humidity, wind speed and wind direction data from 2006 to 2010. The data was from an industrial air quality monitoring station in Malaysia. The SR analysis established that meteorological parameters had less influence on PM 10 concentration levels having coefficient of determination (R 2 ) result from 23 to 29% based on seasoned and unseasoned analysis. While, the result of the prediction analysis showed that PCR models had a better R 2 result than MLR methods. The results for the analyses based on both seasoned and unseasoned data established that MLR models had R 2 result from 0.50 to 0.60. While, PCR models had R 2 result from 0.66 to 0.89. In addition, the validation analysis using 2016 data also recognised that the PCR model outperformed the MLR model, with the PCR model for the seasoned analysis having the best result. These analyses will aid in achieving sustainable air quality management strategies.
Linear models: permutation methods

USGS Publications Warehouse

Cade, B.S.; Everitt, B.S.; Howell, D.C.

2005-01-01

Permutation tests (see Permutation Based Inference) for the linear model have applications in behavioral studies when traditional parametric assumptions about the error term in a linear model are not tenable. Improved validity of Type I error rates can be achieved with properly constructed permutation tests. Perhaps more importantly, increased statistical power, improved robustness to effects of outliers, and detection of alternative distributional differences can be achieved by coupling permutation inference with alternative linear model estimators. For example, it is well-known that estimates of the mean in linear model are extremely sensitive to even a single outlying value of the dependent variable compared to estimates of the median [7, 19]. Traditionally, linear modeling focused on estimating changes in the center of distributions (means or medians). However, quantile regression allows distributional changes to be estimated in all or any selected part of a distribution or responses, providing a more complete statistical picture that has relevance to many biological questions [6]...
Regression Analysis of Top of Descent Location for Idle-thrust Descents

NASA Technical Reports Server (NTRS)

Stell, Laurel; Bronsvoort, Jesper; McDonald, Greg

2013-01-01

In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. The independent variables cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also recorded or computed post-operations. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajec- tory parameters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowl- edge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace. In particular, a model for TOD location that is linear in the independent variables would enable decision support tool human-machine interfaces for which a kinetic approach would be computationally too slow.
Spatial measurement error and correction by spatial SIMEX in linear regression models when using predicted air pollution exposures.

PubMed

Alexeeff, Stacey E; Carroll, Raymond J; Coull, Brent

2016-04-01

Spatial modeling of air pollution exposures is widespread in air pollution epidemiology research as a way to improve exposure assessment. However, there are key sources of exposure model uncertainty when air pollution is modeled, including estimation error and model misspecification. We examine the use of predicted air pollution levels in linear health effect models under a measurement error framework. For the prediction of air pollution exposures, we consider a universal Kriging framework, which may include land-use regression terms in the mean function and a spatial covariance structure for the residuals. We derive the bias induced by estimation error and by model misspecification in the exposure model, and we find that a misspecified exposure model can induce asymptotic bias in the effect estimate of air pollution on health. We propose a new spatial simulation extrapolation (SIMEX) procedure, and we demonstrate that the procedure has good performance in correcting this asymptotic bias. We illustrate spatial SIMEX in a study of air pollution and birthweight in Massachusetts. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
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...
Crude oil price forecasting based on hybridizing wavelet multiple linear regression model, particle swarm optimization techniques, and principal component analysis.

PubMed

Shabri, Ani; Samsudin, Ruhaidah

2014-01-01

Crude oil prices do play significant role in the global economy and are a key input into option pricing formulas, portfolio allocation, and risk measurement. In this paper, a hybrid model integrating wavelet and multiple linear regressions (MLR) is proposed for crude oil price forecasting. In this model, Mallat wavelet transform is first selected to decompose an original time series into several subseries with different scale. Then, the principal component analysis (PCA) is used in processing subseries data in MLR for crude oil price forecasting. The particle swarm optimization (PSO) is used to adopt the optimal parameters of the MLR model. To assess the effectiveness of this model, daily crude oil market, West Texas Intermediate (WTI), has been used as the case study. Time series prediction capability performance of the WMLR model is compared with the MLR, ARIMA, and GARCH models using various statistics measures. The experimental results show that the proposed model outperforms the individual models in forecasting of the crude oil prices series.
Crude Oil Price Forecasting Based on Hybridizing Wavelet Multiple Linear Regression Model, Particle Swarm Optimization Techniques, and Principal Component Analysis

PubMed Central

Shabri, Ani; Samsudin, Ruhaidah

2014-01-01

Crude oil prices do play significant role in the global economy and are a key input into option pricing formulas, portfolio allocation, and risk measurement. In this paper, a hybrid model integrating wavelet and multiple linear regressions (MLR) is proposed for crude oil price forecasting. In this model, Mallat wavelet transform is first selected to decompose an original time series into several subseries with different scale. Then, the principal component analysis (PCA) is used in processing subseries data in MLR for crude oil price forecasting. The particle swarm optimization (PSO) is used to adopt the optimal parameters of the MLR model. To assess the effectiveness of this model, daily crude oil market, West Texas Intermediate (WTI), has been used as the case study. Time series prediction capability performance of the WMLR model is compared with the MLR, ARIMA, and GARCH models using various statistics measures. The experimental results show that the proposed model outperforms the individual models in forecasting of the crude oil prices series. PMID:24895666
Meta-Regression Approximations to Reduce Publication Selection Bias

ERIC Educational Resources Information Center

Stanley, T. D.; Doucouliagos, Hristos

2014-01-01

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…
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.
A linear regression approach to evaluate the green supply chain management impact on industrial organizational performance.

PubMed

Mumtaz, Ubaidullah; Ali, Yousaf; Petrillo, Antonella

2018-05-15

The increase in the environmental pollution is one of the most important topic in today's world. In this context, the industrial activities can pose a significant threat to the environment. To manage problems associate to industrial activities several methods, techniques and approaches have been developed. Green supply chain management (GSCM) is considered one of the most important "environmental management approach". In developing countries such as Pakistan the implementation of GSCM practices is still in its initial stages. Lack of knowledge about its effects on economic performance is the reason because of industries fear to implement these practices. The aim of this research is to perceive the effects of GSCM practices on organizational performance in Pakistan. In this research the GSCM practices considered are: internal practices, external practices, investment recovery and eco-design. While, the performance parameters considered are: environmental pollution, operational cost and organizational flexibility. A set of hypothesis propose the effect of each GSCM practice on the performance parameters. Factor analysis and linear regression are used to analyze the survey data of Pakistani industries, in order to authenticate these hypotheses. The findings of this research indicate a decrease in environmental pollution and operational cost with the implementation of GSCM practices, whereas organizational flexibility has not improved for Pakistani industries. These results aim to help managers regarding their decision of implementing GSCM practices in the industrial sector of Pakistan. Copyright © 2017 Elsevier B.V. All rights reserved.

Multivariate linear regression analysis to identify general factors for quantitative predictions of implant stability quotient values

PubMed Central

Huang, Hairong; Xu, Zanzan; Shao, Xianhong; Wismeijer, Daniel; Sun, Ping; Wang, Jingxiao

2017-01-01

Objectives This study identified potential general influencing factors for a mathematical prediction of implant stability quotient (ISQ) values in clinical practice. Methods We collected the ISQ values of 557 implants from 2 different brands (SICace and Osstem) placed by 2 surgeons in 336 patients. Surgeon 1 placed 329 SICace implants, and surgeon 2 placed 113 SICace implants and 115 Osstem implants. ISQ measurements were taken at T1 (immediately after implant placement) and T2 (before dental restoration). A multivariate linear regression model was used to analyze the influence of the following 11 candidate factors for stability prediction: sex, age, maxillary/mandibular location, bone type, immediate/delayed implantation, bone grafting, insertion torque, I-stage or II-stage healing pattern, implant diameter, implant length and T1-T2 time interval. Results The need for bone grafting as a predictor significantly influenced ISQ values in all three groups at T1 (weight coefficients ranging from -4 to -5). In contrast, implant diameter consistently influenced the ISQ values in all three groups at T2 (weight coefficients ranging from 3.4 to 4.2). Other factors, such as sex, age, I/II-stage implantation and bone type, did not significantly influence ISQ values at T2, and implant length did not significantly influence ISQ values at T1 or T2. Conclusions These findings provide a rational basis for mathematical models to quantitatively predict the ISQ values of implants in clinical practice. PMID:29084260
Prediction of Depression in Cancer Patients With Different Classification Criteria, Linear Discriminant Analysis versus Logistic Regression.

PubMed

Shayan, Zahra; Mohammad Gholi Mezerji, Naser; Shayan, Leila; Naseri, Parisa

2015-11-03

Logistic regression (LR) and linear discriminant analysis (LDA) are two popular statistical models for prediction of group membership. Although they are very similar, the LDA makes more assumptions about the data. When categorical and continuous variables used simultaneously, the optimal choice between the two models is questionable. In most studies, classification error (CE) is used to discriminate between subjects in several groups, but this index is not suitable to predict the accuracy of the outcome. The present study compared LR and LDA models using classification indices. This cross-sectional study selected 243 cancer patients. Sample sets of different sizes (n = 50, 100, 150, 200, 220) were randomly selected and the CE, B, and Q classification indices were calculated by the LR and LDA models. CE revealed the a lack of superiority for one model over the other, but the results showed that LR performed better than LDA for the B and Q indices in all situations. No significant effect for sample size on CE was noted for selection of an optimal model. Assessment of the accuracy of prediction of real data indicated that the B and Q indices are appropriate for selection of an optimal model. The results of this study showed that LR performs better in some cases and LDA in others when based on CE. The CE index is not appropriate for classification, although the B and Q indices performed better and offered more efficient criteria for comparison and discrimination between groups.
Regression analysis of clustered failure time data with informative cluster size under the additive transformation models.

PubMed

Chen, Ling; Feng, Yanqin; Sun, Jianguo

2017-10-01

This paper discusses regression analysis of clustered failure time data, which occur when the failure times of interest are collected from clusters. In particular, we consider the situation where the correlated failure times of interest may be related to cluster sizes. For inference, we present two estimation procedures, the weighted estimating equation-based method and the within-cluster resampling-based method, when the correlated failure times of interest arise from a class of additive transformation models. The former makes use of the inverse of cluster sizes as weights in the estimating equations, while the latter can be easily implemented by using the existing software packages for right-censored failure time data. An extensive simulation study is conducted and indicates that the proposed approaches work well in both the situations with and without informative cluster size. They are applied to a dental study that motivated this study.
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.
Finite-sample and asymptotic sign-based tests for parameters of non-linear quantile regression with Markov noise

NASA Astrophysics Data System (ADS)

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

2017-01-01

One of the most noticeable features of sign-based statistical procedures is an opportunity to build an exact test for simple hypothesis testing of parameters in a regression model. In this article, we expanded a sing-based approach to the nonlinear case with dependent noise. The examined model is a multi-quantile regression, which makes it possible to test hypothesis not only of regression parameters, but of noise parameters as well.
Robust mislabel logistic regression without modeling mislabel probabilities.

PubMed

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

2018-03-01

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

ERIC Educational Resources Information Center

Brooks, Gordon P.; Barcikowski, Robert S.

The focus of this research was to determine the efficacy of a new method of selecting sample sizes for multiple linear regression. A Monte Carlo simulation was used to study both empirical predictive power rates and empirical statistical power rates of the new method and seven other methods: those of C. N. Park and A. L. Dudycha (1974); J. Cohen…
Experimental variability and data pre-processing as factors affecting the discrimination power of some chemometric approaches (PCA, CA and a new algorithm based on linear regression) applied to (+/-)ESI/MS and RPLC/UV data: Application on green tea extracts.

PubMed

Iorgulescu, E; Voicu, V A; Sârbu, C; Tache, F; Albu, F; Medvedovici, A

2016-08-01

The influence of the experimental variability (instrumental repeatability, instrumental intermediate precision and sample preparation variability) and data pre-processing (normalization, peak alignment, background subtraction) on the discrimination power of multivariate data analysis methods (Principal Component Analysis -PCA- and Cluster Analysis -CA-) as well as a new algorithm based on linear regression was studied. Data used in the study were obtained through positive or negative ion monitoring electrospray mass spectrometry (+/-ESI/MS) and reversed phase liquid chromatography/UV spectrometric detection (RPLC/UV) applied to green tea extracts. Extractions in ethanol and heated water infusion were used as sample preparation procedures. The multivariate methods were directly applied to mass spectra and chromatograms, involving strictly a holistic comparison of shapes, without assignment of any structural identity to compounds. An alternative data interpretation based on linear regression analysis mutually applied to data series is also discussed. Slopes, intercepts and correlation coefficients produced by the linear regression analysis applied on pairs of very large experimental data series successfully retain information resulting from high frequency instrumental acquisition rates, obviously better defining the profiles being compared. Consequently, each type of sample or comparison between samples produces in the Cartesian space an ellipsoidal volume defined by the normal variation intervals of the slope, intercept and correlation coefficient. Distances between volumes graphically illustrates (dis)similarities between compared data. The instrumental intermediate precision had the major effect on the discrimination power of the multivariate data analysis methods. Mass spectra produced through ionization from liquid state in atmospheric pressure conditions of bulk complex mixtures resulting from extracted materials of natural origins provided an excellent data
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
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…
Comparison of Adaline and Multiple Linear Regression Methods for Rainfall Forecasting

NASA Astrophysics Data System (ADS)

Sutawinaya, IP; Astawa, INGA; Hariyanti, NKD

2018-01-01

Heavy rainfall can cause disaster, therefore need a forecast to predict rainfall intensity. Main factor that cause flooding is there is a high rainfall intensity and it makes the river become overcapacity. This will cause flooding around the area. Rainfall factor is a dynamic factor, so rainfall is very interesting to be studied. In order to support the rainfall forecasting, there are methods that can be used from Artificial Intelligence (AI) to statistic. In this research, we used Adaline for AI method and Regression for statistic method. The more accurate forecast result shows the method that used is good for forecasting the rainfall. Through those methods, we expected which is the best method for rainfall forecasting here.
PARAMETRIC AND NON PARAMETRIC (MARS: MULTIVARIATE ADDITIVE REGRESSION SPLINES) LOGISTIC REGRESSIONS FOR PREDICTION OF A DICHOTOMOUS RESPONSE VARIABLE WITH AN EXAMPLE FOR PRESENCE/ABSENCE OF AMPHIBIANS

EPA Science Inventory

The purpose of this report is to provide a reference manual that could be used by investigators for making informed use of logistic regression using two methods (standard logistic regression and MARS). The details for analyses of relationships between a dependent binary response ...
Learning curve of single port laparoscopic cholecystectomy determined using the non-linear ordinary least squares method based on a non-linear regression model: An analysis of 150 consecutive patients.

PubMed

Han, Hyung Joon; Choi, Sae Byeol; Park, Man Sik; Lee, Jin Suk; Kim, Wan Bae; Song, Tae Jin; Choi, Sang Yong

2011-07-01

Single port laparoscopic surgery has come to the forefront of minimally invasive surgery. For those familiar with conventional techniques, however, this type of operation demands a different type of eye/hand coordination and involves unfamiliar working instruments. Herein, the authors describe the learning curve and the clinical outcomes of single port laparoscopic cholecystectomy for 150 consecutive patients with benign gallbladder disease. All patients underwent single port laparoscopic cholecystectomy using a homemade glove port by one of five operators with different levels of experiences of laparoscopic surgery. The learning curve for each operator was fitted using the non-linear ordinary least squares method based on a non-linear regression model. Mean operating time was 77.6 ± 28.5 min. Fourteen patients (6.0%) were converted to conventional laparoscopic cholecystectomy. Complications occurred in 15 patients (10.0%), as follows: bile duct injury (n = 2), surgical site infection (n = 8), seroma (n = 2), and wound pain (n = 3). One operator achieved a learning curve plateau at 61.4 min per procedure after 8.5 cases and his time improved by 95.3 min as compared with initial operation time. Younger surgeons showed significant decreases in mean operation time and achieved stable mean operation times. In particular, younger surgeons showed significant decreases in operation times after 20 cases. Experienced laparoscopic surgeons can safely perform single port laparoscopic cholecystectomy using conventional or angled laparoscopic instruments. The present study shows that an operator can overcome the single port laparoscopic cholecystectomy learning curve in about eight cases.
Regression Models For Multivariate Count Data.

PubMed

Zhang, Yiwen; Zhou, Hua; Zhou, Jin; Sun, Wei

2017-01-01

Data with multivariate count responses frequently occur in modern applications. The commonly used multinomial-logit model is limiting due to its restrictive mean-variance structure. For instance, analyzing count data from the recent RNA-seq technology by the multinomial-logit model leads to serious errors in hypothesis testing. The ubiquity of over-dispersion and complicated correlation structures among multivariate counts calls for more flexible regression models. In this article, we study some generalized linear models that incorporate various correlation structures among the counts. Current literature lacks a treatment of these models, partly due to the fact that they do not belong to the natural exponential family. We study the estimation, testing, and variable selection for these models in a unifying framework. The regression models are compared on both synthetic and real RNA-seq data.
Testcross additive and dominance effects in best linear unbiased prediction of maize single-cross performance.

PubMed

Bernardo, R

1996-11-01

Best linear unbiased prediction (BLUP) has been found to be useful in maize (Zea mays L.) breeding. The advantage of including both testcross additive and dominance effects (Intralocus Model) in BLUP, rather than only testcross additive effects (Additive Model), has not been clearly demonstrated. The objective of this study was to compare the usefulness of Intralocus and Additive Models for BLUP of maize single-cross performance. Multilocation data from 1990 to 1995 were obtained from the hybrid testing program of Limagrain Genetics. Grain yield, moisture, stalk lodging, and root lodging of untested single crosses were predicted from (1) the performance of tested single crosses and (2) known genetic relationships among the parental inbreds. Correlations between predicted and observed performance were obtained with a delete-one cross-validation procedure. For the Intralocus Model, the correlations ranged from 0.50 to 0.66 for yield, 0.88 to 0.94 for moisture, 0.47 to 0.69 for stalk lodging, and 0.31 to 0.45 for root lodging. The BLUP procedure was consistently more effective with the Intralocus Model than with the Additive Model. When the Additive Model was used instead of the Intralocus Model, the reductions in the correlation were largest for root lodging (0.06-0.35), smallest for moisture (0.00-0.02), and intermediate for yield (0.02-0.06) and stalk lodging (0.02-0.08). The ratio of dominance variance (v D) to total genetic variance (v G) was highest for root lodging (0.47) and lowest for moisture (0.10). The Additive Model may be used if prior information indicates that VD for a given trait has little contribution to VG. Otherwise, the continued use of the Intralocus Model for BLUP of single-cross performance is recommended.
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.
A flexible count data regression model for risk analysis.

PubMed

Guikema, Seth D; Coffelt, Jeremy P; Goffelt, Jeremy P

2008-02-01

In many cases, risk and reliability analyses involve estimating the probabilities of discrete events such as hardware failures and occurrences of disease or death. There is often additional information in the form of explanatory variables that can be used to help estimate the likelihood of different numbers of events in the future through the use of an appropriate regression model, such as a generalized linear model. However, existing generalized linear models (GLM) are limited in their ability to handle the types of variance structures often encountered in using count data in risk and reliability analysis. In particular, standard models cannot handle both underdispersed data (variance less than the mean) and overdispersed data (variance greater than the mean) in a single coherent modeling framework. This article presents a new GLM based on a reformulation of the Conway-Maxwell Poisson (COM) distribution that is useful for both underdispersed and overdispersed count data and demonstrates this model by applying it to the assessment of electric power system reliability. The results show that the proposed COM GLM can provide as good of fits to data as the commonly used existing models for overdispered data sets while outperforming these commonly used models for underdispersed data sets.
Weighted SGD for ℓ p Regression with Randomized Preconditioning.

PubMed

Yang, Jiyan; Chow, Yin-Lam; Ré, Christopher; Mahoney, Michael W

2016-01-01

In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. SGD methods are easy to implement and applicable to a wide range of convex optimization problems. In contrast, RLA algorithms provide much stronger performance guarantees but are applicable to a narrower class of problems. We aim to bridge the gap between these two methods in solving constrained overdetermined linear regression problems-e.g., ℓ 2 and ℓ 1 regression problems. We propose a hybrid algorithm named pwSGD that uses RLA techniques for preconditioning and constructing an importance sampling distribution, and then performs an SGD-like iterative process with weighted sampling on the preconditioned system.By rewriting a deterministic ℓ p regression problem as a stochastic optimization problem, we connect pwSGD to several existing ℓ p solvers including RLA methods with algorithmic leveraging (RLA for short).We prove that pwSGD inherits faster convergence rates that only depend on the lower dimension of the linear system, while maintaining low computation complexity. Such SGD convergence rates are superior to other related SGD algorithm such as the weighted randomized Kaczmarz algorithm.Particularly, when solving ℓ 1 regression with size n by d , pwSGD returns an approximate solution with ε relative error in the objective value in (log n ·nnz( A )+poly( d )/ ε 2 ) time. This complexity is uniformly better than that of RLA methods in terms of both ε and d when the problem is unconstrained. In the presence of constraints, pwSGD only has to solve a sequence of much simpler and smaller optimization problem over the same constraints. In general this is more efficient than solving the constrained subproblem required in RLA.For ℓ 2 regression, pwSGD returns an approximate solution with ε relative error in the objective value and the solution vector measured in
A regression-adjusted approach can estimate competing biomass

Treesearch

James H. Miller

1983-01-01

A method is presented for estimating above-ground herbaceous and woody biomass on competition research plots. On a set of destructively-sampled plots, an ocular estimate of biomass by vegetative component is first made, after which vegetation is clipped, dried, and weighed. Linear regressions are then calculated for each component between estimated and actual weights...

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

ERIC Educational Resources Information Center

Wing, Coady; Cook, Thomas D.

2013-01-01

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

ERIC Educational Resources Information Center

Auchlin, Antoine; And Others

1981-01-01

Examines the phenomenon of regressive moves (retro-interpretation) in the light of a hypothesis according to which the formation of complex and hierarchically organized conversation units is subordinated to the linearity of discourse. Analyzes a transactional exchange, describing the interplay of integration, anticipation, and retro-interpretation…
Statistical sex determination from craniometrics: Comparison of linear discriminant analysis, logistic regression, and support vector machines.

PubMed

Santos, Frédéric; Guyomarc'h, Pierre; Bruzek, Jaroslav

2014-12-01

Accuracy of identification tools in forensic anthropology primarily rely upon the variations inherent in the data upon which they are built. Sex determination methods based on craniometrics are widely used and known to be specific to several factors (e.g. sample distribution, population, age, secular trends, measurement technique, etc.). The goal of this study is to discuss the potential variations linked to the statistical treatment of the data. Traditional craniometrics of four samples extracted from documented osteological collections (from Portugal, France, the U.S.A., and Thailand) were used to test three different classification methods: linear discriminant analysis (LDA), logistic regression (LR), and support vector machines (SVM). The Portuguese sample was set as a training model on which the other samples were applied in order to assess the validity and reliability of the different models. The tests were performed using different parameters: some included the selection of the best predictors; some included a strict decision threshold (sex assessed only if the related posterior probability was high, including the notion of indeterminate result); and some used an unbalanced sex-ratio. Results indicated that LR tends to perform slightly better than the other techniques and offers a better selection of predictors. Also, the use of a decision threshold (i.e. p>0.95) is essential to ensure an acceptable reliability of sex determination methods based on craniometrics. Although the Portuguese, French, and American samples share a similar sexual dimorphism, application of Western models on the Thai sample (that displayed a lower degree of dimorphism) was unsuccessful. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Wrong Signs in Regression Coefficients

NASA Technical Reports Server (NTRS)

McGee, Holly

1999-01-01

When using parametric cost estimation, it is important to note the possibility of the regression coefficients having the wrong sign. A wrong sign is defined as a sign on the regression coefficient opposite to the researcher's intuition and experience. Some possible causes for the wrong sign discussed in this paper are a small range of x's, leverage points, missing variables, multicollinearity, and computational error. Additionally, techniques for determining the cause of the wrong sign are given.
Identifying Keystone Species in the Human Gut Microbiome from Metagenomic Timeseries Using Sparse Linear Regression

PubMed Central

Fisher, Charles K.; Mehta, Pankaj

2014-01-01

Human associated microbial communities exert tremendous influence over human health and disease. With modern metagenomic sequencing methods it is now possible to follow the relative abundance of microbes in a community over time. These microbial communities exhibit rich ecological dynamics and an important goal of microbial ecology is to infer the ecological interactions between species directly from sequence data. Any algorithm for inferring ecological interactions must overcome three major obstacles: 1) a correlation between the abundances of two species does not imply that those species are interacting, 2) the sum constraint on the relative abundances obtained from metagenomic studies makes it difficult to infer the parameters in timeseries models, and 3) errors due to experimental uncertainty, or mis-assignment of sequencing reads into operational taxonomic units, bias inferences of species interactions due to a statistical problem called “errors-in-variables”. Here we introduce an approach, Learning Interactions from MIcrobial Time Series (LIMITS), that overcomes these obstacles. LIMITS uses sparse linear regression with boostrap aggregation to infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested LIMITS on synthetic data and showed that it could reliably infer the topology of the inter-species ecological interactions. We then used LIMITS to characterize the species interactions in the gut microbiomes of two individuals and found that the interaction networks varied significantly between individuals. Furthermore, we found that the interaction networks of the two individuals are dominated by distinct “keystone species”, Bacteroides fragilis and Bacteroided stercosis, that have a disproportionate influence on the structure of the gut microbiome even though they are only found in moderate abundance. Based on our results, we hypothesize that the abundances of certain keystone species may be responsible for individuality in the human
Ranking contributing areas of salt and selenium in the Lower Gunnison River Basin, Colorado, using multiple linear regression models

USGS Publications Warehouse

Linard, Joshua I.

2013-01-01

Mitigating the effects of salt and selenium on water quality in the Grand Valley and lower Gunnison River Basin in western Colorado is a major concern for land managers. Previous modeling indicated means to improve the models by including more detailed geospatial data and a more rigorous method for developing the models. After evaluating all possible combinations of geospatial variables, four multiple linear regression models resulted that could estimate irrigation-season salt yield, nonirrigation-season salt yield, irrigation-season selenium yield, and nonirrigation-season selenium yield. The adjusted r-squared and the residual standard error (in units of log-transformed yield) of the models were, respectively, 0.87 and 2.03 for the irrigation-season salt model, 0.90 and 1.25 for the nonirrigation-season salt model, 0.85 and 2.94 for the irrigation-season selenium model, and 0.93 and 1.75 for the nonirrigation-season selenium model. The four models were used to estimate yields and loads from contributing areas corresponding to 12-digit hydrologic unit codes in the lower Gunnison River Basin study area. Each of the 175 contributing areas was ranked according to its estimated mean seasonal yield of salt and selenium.
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
Linear Modeling and Evaluation of Controls on Flow Response in Western Post-Fire Watersheds

NASA Astrophysics Data System (ADS)

Saxe, S.; Hogue, T. S.; Hay, L.

2015-12-01

This research investigates the impact of wildfires on watershed flow regimes throughout the western United States, specifically focusing on evaluation of fire events within specified subregions and determination of the impact of climate and geophysical variables in post-fire flow response. Fire events were collected through federal and state-level databases and streamflow data were collected from U.S. Geological Survey stream gages. 263 watersheds were identified with at least 10 years of continuous pre-fire daily streamflow records and 5 years of continuous post-fire daily flow records. For each watershed, percent changes in runoff ratio (RO), annual seven day low-flows (7Q2) and annual seven day high-flows (7Q10) were calculated from pre- to post-fire. Numerous independent variables were identified for each watershed and fire event, including topographic, land cover, climate, burn severity, and soils data. The national watersheds were divided into five regions through K-clustering and a lasso linear regression model, applying the Leave-One-Out calibration method, was calculated for each region. Nash-Sutcliffe Efficiency (NSE) was used to determine the accuracy of the resulting models. The regions encompassing the United States along and west of the Rocky Mountains, excluding the coastal watersheds, produced the most accurate linear models. The Pacific coast region models produced poor and inconsistent results, indicating that the regions need to be further subdivided. Presently, RO and HF response variables appear to be more easily modeled than LF. Results of linear regression modeling showed varying importance of watershed and fire event variables, with conflicting correlation between land cover types and soil types by region. The addition of further independent variables and constriction of current variables based on correlation indicators is ongoing and should allow for more accurate linear regression modeling.
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
On the use of log-transformation vs. nonlinear regression for analyzing biological power laws.

PubMed

Xiao, Xiao; White, Ethan P; Hooten, Mevin B; Durham, Susan L

2011-10-01

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.
Prediction of octanol-water partition coefficients of organic compounds by multiple linear regression, partial least squares, and artificial neural network.

PubMed

Golmohammadi, Hassan

2009-11-30

A quantitative structure-property relationship (QSPR) study was performed to develop models those relate the structure of 141 organic compounds to their octanol-water partition coefficients (log P(o/w)). A genetic algorithm was applied as a variable selection tool. Modeling of log P(o/w) of these compounds as a function of theoretically derived descriptors was established by multiple linear regression (MLR), partial least squares (PLS), and artificial neural network (ANN). The best selected descriptors that appear in the models are: atomic charge weighted partial positively charged surface area (PPSA-3), fractional atomic charge weighted partial positive surface area (FPSA-3), minimum atomic partial charge (Qmin), molecular volume (MV), total dipole moment of molecule (mu), maximum antibonding contribution of a molecule orbital in the molecule (MAC), and maximum free valency of a C atom in the molecule (MFV). The result obtained showed the ability of developed artificial neural network to prediction of partition coefficients of organic compounds. Also, the results revealed the superiority of ANN over the MLR and PLS models. Copyright 2009 Wiley Periodicals, Inc.
Creating a non-linear total sediment load formula using polynomial best subset regression model

NASA Astrophysics Data System (ADS)

Okcu, Davut; Pektas, Ali Osman; Uyumaz, Ali

2016-08-01

The aim of this study is to derive a new total sediment load formula which is more accurate and which has less application constraints than the well-known formulae of the literature. 5 most known stream power concept sediment formulae which are approved by ASCE are used for benchmarking on a wide range of datasets that includes both field and flume (lab) observations. The dimensionless parameters of these widely used formulae are used as inputs in a new regression approach. The new approach is called Polynomial Best subset regression (PBSR) analysis. The aim of the PBRS analysis is fitting and testing all possible combinations of the input variables and selecting the best subset. Whole the input variables with their second and third powers are included in the regression to test the possible relation between the explanatory variables and the dependent variable. While selecting the best subset a multistep approach is used that depends on significance values and also the multicollinearity degrees of inputs. The new formula is compared to others in a holdout dataset and detailed performance investigations are conducted for field and lab datasets within this holdout data. Different goodness of fit statistics are used as they represent different perspectives of the model accuracy. After the detailed comparisons are carried out we figured out the most accurate equation that is also applicable on both flume and river data. Especially, on field dataset the prediction performance of the proposed formula outperformed the benchmark formulations.
Background stratified Poisson regression analysis of cohort data.

PubMed

Richardson, David B; Langholz, Bryan

2012-03-01

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

NASA Astrophysics Data System (ADS)

Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

2016-03-01

From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States

PubMed Central

Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

2016-01-01

From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states. PMID:26996254
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.
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.
Prediction of dynamical systems by symbolic regression

NASA Astrophysics Data System (ADS)

Quade, Markus; Abel, Markus; Shafi, Kamran; Niven, Robert K.; Noack, Bernd R.

2016-07-01

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.
Diurnal salivary cortisol and regression status in MECP2 Duplication syndrome

PubMed Central

Peters, Sarika U.; Byiers, Breanne J.; Symons, Frank J.

2015-01-01

MECP2 duplication syndrome is an X-linked genomic disorder that is characterized by infantile hypotonia, intellectual disability, and recurrent respiratory infections. Regression affects a subset of individuals, and the etiology of regression has yet to be examined. In this study, alterations in the hypothalamus-pituitary-adrenal axis, including diurnal patterns in salivary cortisol, were examined in four males with MECP2 duplication syndrome who had regression, and four males with the same syndrome without regression (ages 3–22 years). Individuals who had experienced regression do not exhibit typical diurnal cortisol rhythms, and their profiles were flatter through the day. In contrast, individuals with MECP2 duplication syndrome who had not experienced regression showed more typical patterns of higher cortisol levels in the morning with linear decreases throughout the day. This study is the first to suggest a link between atypical diurnal cortisol rhythms and regression status in MECP2 duplication syndrome, and may have implications for treatment. PMID:25999300

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