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Regression with Highly Correlated Predictors: Variable Omission Is Not the Solution.

ABSTRACT: Regression models have been in use for decades to explore and quantify the association between a dependent response and several independent variables in environmental sciences, epidemiology and public health. However, researchers often encounter situations in which some independent variables exhibit high bivariate correlation, or may even be collinear. Improper statistical handling of this situation will most certainly generate models of little or no practical use and misleading interpretations. By means of two example studies, we demonstrate how diagnostic tools for collinearity or near-collinearity may fail in guiding the analyst. Instead, the most appropriate way of handling collinearity should be driven by the research question at hand and, in particular, by the distinction between predictive or explanatory aims.

SUBMITTER: Gregorich M

PROVIDER: S-EPMC8073086 | biostudies-literature | 2021 Apr

REPOSITORIES: biostudies-literature

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Regression with Highly Correlated Predictors: Variable Omission Is Not the Solution.

Gregorich Mariella M Strohmaier Susanne S Dunkler Daniela D Heinze Georg G

International journal of environmental research and public health 20210417 8

Regression models have been in use for decades to explore and quantify the association between a dependent response and several independent variables in environmental sciences, epidemiology and public health. However, researchers often encounter situations in which some independent variables exhibit high bivariate correlation, or may even be collinear. Improper statistical handling of this situation will most certainly generate models of little or no practical use and misleading interpretations. ...[more]

PMID: 33920501

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Project description:BackgroundFor many practical hypothesis testing (H-T) applications, the data are correlated and/or with heterogeneous variance structure. The regression t-test for weighted linear mixed-effects regression (LMER) is a legitimate choice because it accounts for complex covariance structure; however, high computational costs and occasional convergence issues make it impractical for analyzing high-throughput data. In this paper, we propose computationally efficient parametric and semiparametric tests based on a set of specialized matrix techniques dubbed as the PB-transformation. The PB-transformation has two advantages: 1. The PB-transformed data will have a scalar variance-covariance matrix. 2. The original H-T problem will be reduced to an equivalent one-sample H-T problem. The transformed problem can then be approached by either the one-sample Student's t-test or Wilcoxon signed rank test.ResultsIn simulation studies, the proposed methods outperform commonly used alternative methods under both normal and double exponential distributions. In particular, the PB-transformed t-test produces notably better results than the weighted LMER test, especially in the high correlation case, using only a small fraction of computational cost (3 versus 933 s). We apply these two methods to a set of RNA-seq gene expression data collected in a breast cancer study. Pathway analyses show that the PB-transformed t-test reveals more biologically relevant findings in relation to breast cancer than the weighted LMER test.ConclusionsAs fast and numerically stable replacements for the weighted LMER test, the PB-transformed tests are especially suitable for "messy" high-throughput data that include both independent and matched/repeated samples. By using our method, the practitioners no longer have to choose between using partial data (applying paired tests to only the matched samples) or ignoring the correlation in the data (applying two sample tests to data with some correlated samples). Our method is implemented as an R package 'PBtest' and is available at https://github.com/yunzhang813/PBtest-R-Package .

Dataset Information

Regression with Highly Correlated Predictors: Variable Omission Is Not the Solution.

Publications

Regression with Highly Correlated Predictors: Variable Omission Is Not the Solution.

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