Centering Categorical Predictors in Multilevel Models: Best Practices and Interpretation

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. Translational Abstract Multilevel modeling (MLM) is frequently used in the social sciences when data are nested or clustered (e.g., students nested within classrooms; clients nested within therapists). Centering is an important topic in MLM because it can be conducted in different ways, each of which yields slightly different parameter estimates that also must be interpreted differently. However, work regarding centering has focused almost exclusively on continuous predictors. Little attention has been paid to categorical predictors, whether and how they should be centered, and how their resulting coefficients should be interpreted. This is problematic, because categorical predictors and covariates are ubiquitous across all fields wherein MLM is used. Thus, the goals of this report are 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 present an overview of popular centering options and provide best-practice recommendations for centering and interpretation of binary and multicategorical predictors. We provide a detailed demonstration of our conclusions with an empirical example from the education literature. In addition, we discuss the practical implications of our work at length; topics include multicategorical covariates, interaction terms with categorical focal predictors, and multilevel latent variable models.

Automated summary

The topic of centering in multilevel modeling has been extensively studied for continuous predictors but not for categorical predictors. This tutorial aims to clarify the importance of centering categorical predictors in multilevel modeling and provides guidance on the interpretation of resulting coefficients. The article also discusses the practical implications of the findings in various applications.