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.

Well-being in social interactions: Examining personality-situation dynamics in face-to-face and computer-mediated communication.

“…The two biggest issues were as follows: First, we had used the uncentered binary variables as predictor variables. While this modeling approach is common for binary predictors, it did not allow us to separate within- and between-person effects (Enders & Tofighi, 2007; Yaremych et al, 2021). Second, we had decided to drop the random slopes due to model convergence issues, which could lead to serious model misspecifications (Hamaker & Muthén, 2020).…”

“…The two biggest issues were as follows: First, we had used the uncentered binary variables as predictor variables. While this modeling approach is common for binary predictors, it did not allow us to separate within-and between-person effects (Enders & Tofighi, 2007;Yaremych et al, 2021).…”

Visual Perception of Photographs of Rotated 3D Objects in Goldfish (Carassius auratus)

“…Failure to perform such centering with hierarchically structure data can yield uninterpretable effect estimates and inferences [ 77 ]. For the same reason, contrasts used to test the effects of experimentally manipulated factors were also centered using this scheme [ 78 ]. In addition, change over trials, change over sessions, and an interaction between trial and sessions was modeled to reflect the hierarchical longitudinal sampling design (sometimes referred to as a measurement burst design, [ 79 ]).…”

Catching Up on Multilevel Modeling

“…The insistence on avoiding smushed effects endorsed here continues to gain support (e.g., Antonakis et al, 2019;Bliese et al, 2018;Curran et al, 2012;Hoffman, 2019;Preacher et al, 2016;Wang & Maxwell, 215). It does not matter whether a lower-level predictor is of theoretical interest or is merely a "control" , nor whether it is quantitative or categorical (Yaremych et al, 2021)-it only matters whether it contains systematic higher-level variability.…”