Centering Categorical Covariates in Cross-Classified Random Effects Models

• In Event: Innovations for Complexity in Models and Design: Inference, Estimation, Classification, and Longitudinal Issues

Abstract

This study examines centering strategies for categorical covariates in cross-classified random effects models (CCREM), which model individuals nested within multiple, non-nested clusters. While centering has been widely studied for continuous predictors, limited research addresses categorical covariates, especially under endogeneity and unequal distributions across clusters. Using Monte Carlo simulations, we evaluated grand-mean, cluster-mean, and cell-mean centering, along with fixed-effect and hybrid models for binary variables. Results show that cell-mean centering and hybrid models with fixed neighborhood effects produce more accurate within-cluster estimates and standard errors under endogeneity. For between-cluster effects, bias patterns vary depending on which clustering dimension violates exogeneity. Findings offer practical guidance for modeling categorical predictors in multilevel and cross-classified contexts.

Author

• Young Ri Lee, Seoul National University