Centering categorical predictors in multilevel models: Best practices and interpretation.

Abstract

The topic of centering in multilevel modeling (MLM) has received substantial attention from methodologists, as different centering choices for lower-level predictors present important ramifications for the estimation and interpretation of model parameters. However, the centering literature has focused almost exclusively on continuous predictors, with little attention paid to whether and how categorical predictors should be centered, despite their ubiquity across applied fields. Alongside this gap in the methodological literature, a review of applied articles showed that researchers center categorical predictors infrequently and inconsistently. Algebraically and statistically, continuous and categorical predictors behave the same, but researchers using them do not, and for many, interpreting the effects of categorical predictors is not intuitive. Thus, the goals of this tutorial article are twofold: to clarify why and how categorical predictors should be centered in MLM, and to explain how multilevel regression coefficients resulting from centered categorical predictors should be interpreted. We first provide algebraic support showing that uncentered coding variables result in a conflated blend of the within- and between-cluster effects of a multicategorical predictor, whereas appropriate centering techniques yield level-specific effects. Next, we provide algebraic derivations to illuminate precisely how the within- and between-cluster effects of a multicategorical predictor should be interpreted under dummy, contrast, and effect coding schemes. Finally, we provide a detailed demonstration of our conclusions with an empirical example. Implications for practice, including relevance of our findings to categorical control variables (i.e., covariates), interaction terms with categorical focal predictors, and multilevel latent variable models, are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).