Topic
Regression analysis
About: Regression analysis is a research topic. Over the lifetime, 31027 publications have been published within this topic receiving 1744954 citations. The topic is also known as: regression method & regression.
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09 Jan 1997TL;DR: In this article, the authors propose Continuous Outcomes Binary Outcomes Testing and Fit Ordinal Outcomes Numeric Outcomes and Numeric Numeric Count Outcomes (NOCO).
Abstract: Introduction Continuous Outcomes Binary Outcomes Testing and Fit Ordinal Outcomes Nominal Outcomes Limited Outcomes Count Outcomes Conclusions
7,306 citations
01 Jan 2001
TL;DR: In this article, the authors present a case study in least squares fitting and interpretation of a linear model, where they use nonparametric transformations of X and Y to fit a linear regression model.
Abstract: Introduction * General Aspects of Fitting Regression Models * Missing Data * Multivariable Modeling Strategies * Resampling, Validating, Describing, and Simplifying the Model * S-PLUS Software * Case Study in Least Squares Fitting and Interpretation of a Linear Model * Case Study in Imputation and Data Reduction * Overview of Maximum Likelihood Estimation * Binary Logistic Regression * Logistic Model Case Study 1: Predicting Cause of Death * Logistic Model Case Study 2: Survival of Titanic Passengers * Ordinal Logistic Regression * Case Study in Ordinal Regrssion, Data Reduction, and Penalization * Models Using Nonparametic Transformations of X and Y * Introduction to Survival Analysis * Parametric Survival Models * Case Study in Parametric Survival Modeling and Model Approximation * Cox Proportional Hazards Regression Model * Case Study in Cox Regression
7,264 citations
TL;DR: In this article, the authors examined the effect of the variance inflation factor (VIF) on the results of regression analyses, and found that threshold values of the VIF need to be evaluated in the context of several other factors that influence the variance of regression coefficients.
Abstract: The Variance Inflation Factor (VIF) and tolerance are both widely used measures of the degree of multi-collinearity of the ith independent variable with the other independent variables in a regression model. Unfortunately, several rules of thumb – most commonly the rule of 10 – associated with VIF are regarded by many practitioners as a sign of severe or serious multi-collinearity (this rule appears in both scholarly articles and advanced statistical textbooks). When VIF reaches these threshold values researchers often attempt to reduce the collinearity by eliminating one or more variables from their analysis; using Ridge Regression to analyze their data; or combining two or more independent variables into a single index. These techniques for curing problems associated with multi-collinearity can create problems more serious than those they solve. Because of this, we examine these rules of thumb and find that threshold values of the VIF (and tolerance) need to be evaluated in the context of several other factors that influence the variance of regression coefficients. Values of the VIF of 10, 20, 40, or even higher do not, by themselves, discount the results of regression analyses, call for the elimination of one or more independent variables from the analysis, suggest the use of ridge regression, or require combining of independent variable into a single index.
7,165 citations
TL;DR: A class of generalized estimating equations (GEEs) for the regression parameters is proposed, extensions of those used in quasi-likelihood methods which have solutions which are consistent and asymptotically Gaussian even when the time dependence is misspecified as the authors often expect.
Abstract: Longitudinal data sets are comprised of repeated observations of an outcome and a set of covariates for each of many subjects. One objective of statistical analysis is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlation among the repeated observations for a given subject. This paper proposes a unifying approach to such analysis for a variety of discrete and continuous outcomes. A class of generalized estimating equations (GEEs) for the regression parameters is proposed. The equations are extensions of those used in quasi-likelihood (Wedderburn, 1974, Biometrika 61, 439-447) methods. The GEEs have solutions which are consistent and asymptotically Gaussian even when the time dependence is misspecified as we often expect. A consistent variance estimate is presented. We illustrate the use of the GEE approach with longitudinal data from a study of the effect of mothers' stress on children's morbidity.
7,080 citations
TL;DR: Results from a limited simulation study indicate that this approach is very reliable even with total sample sizes as small as 100, and the method is illustrated with two data sets.
Abstract: Relative risk is usually the parameter of interest in epidemiologic and medical studies. In this paper, the author proposes a modified Poisson regression approach (i.e., Poisson regression with a robust error variance) to estimate this effect measure directly. A simple 2-by-2 table is used to justify the validity of this approach. Results from a limited simulation study indicate that this approach is very reliable even with total sample sizes as small as 100. The method is illustrated with two data sets.
7,045 citations