Residualization is not the answer: Rethinking how to address multicollinearity

Abstract

Here I show that a commonly used procedure to address problems stemming from collinearity and multicollinearity among independent variables in regression analysis, “residualization”, leads to biased coefficient and standard error estimates and does not address the fundamental problem of collinearity, which is a lack of information. I demonstrate this using visual representations of collinearity, hypothetical experimental designs, and analyses of both artificial and real world data. I conclude by noting the importance of examining methodological practices to ensure that their validity can be established based on rational criteria.