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

Author

Listed:
  • Mariella Gregorich

    (Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, 1090 Vienna, Austria)

  • Susanne Strohmaier

    (Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, 1090 Vienna, Austria
    Center for Public Health, Department of Epidemiology, Medical University of Vienna, 1090 Vienna, Austria)

  • Daniela Dunkler

    (Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, 1090 Vienna, Austria)

  • Georg Heinze

    (Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, 1090 Vienna, Austria)

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.

Suggested Citation

  • Mariella Gregorich & Susanne Strohmaier & Daniela Dunkler & Georg Heinze, 2021. "Regression with Highly Correlated Predictors: Variable Omission Is Not the Solution," IJERPH, MDPI, vol. 18(8), pages 1-12, April.
    • Handle: RePEc:gam:jijerp:v:18:y:2021:i:8:p:4259-:d:537958
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    References listed on IDEAS

    as
    1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    2. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).
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