(Multi)Collinearity in Behavioral Sciences Research

Abstract A statistical challenge many researchers face is collinearity (also known as multicollinearity). Collinearity refers to a situation in which predictors - independent variables, covariates, etc. - are linearly related to each other and typically are related strongly enough as to negatively impact one’s statistical analyses, results, and/or substantive interpretations. Collinearity can impact the results of general linear models (e.g., ordinary least squares regression, structural equation modeling) or generalized linear models (e.g., binary logistic regression; Poisson regression). Collinearity can cause (a) estimation/convergence challenges (particularly with iterative estimation methods), (b) inflated standard errors, as well as (c) biased, unstable, and/or uninterpretable parameter estimates. Due to the issues in the results, substantive interpretation of models with collinearity can be inaccurate, sometimes in significant ways (e.g., nonsignificant predictors that are in fact significantly related to the outcome). In standard linear models, researchers can make use of variance inflation factor (VIF) or tolerance (Tol) indices to detect potential collinearity. Although zero-order correlations may be useful for detecting collinearity in rare instances, most researchers will want to use VIF or Tol to capture the potential for collinearity resulting from linear combinations of predictors. For statistical models that use iterative estimation (e.g., generalized linear models), researchers can turn to condition indices. Researchers can address collinearity issues in a myriad of ways. This includes basing models on well-developed a priori theoretical propositions to avoid including empirically or conceptually redundant variables in one’s model—this includes the careful and theoretically appropriate consideration of control variables. In addition, researchers can use data reduction techniques to aggregate correlated covariates (e.g., principal components analysis or exploratory factor analysis), and/or use well-constructed and well-validated measurements so as to ensure that measurement of key variables are not related due to construct overlaps.