R-squared Measures for Multilevel Mixture Models with Random Effects

Multilevel regression mixtures involving both discrete latent classes and continuous random effects are an increasingly popular approach for accommodating nested data structures. However, their application has outpaced the development of effect size measures to aid model interpretation. In response, we provide a general framework of R-squared measures for multilevel regression mixtures with random effects as well as either classes only at level-1 (L1MIX), or classes only at level-2 (L2MIX), or classes at both levels (L1L2MIX). This work extends and unites a previous suite of R-squared measures for multilevel mixtures with latent classes but no random effects (Rights & Sterba, 2018) and a suite of R-squared measures for multilevel models with random effects but no latent classes (Rights & Sterba, 2019).The general framework provided here includes total and class-specific measures that each allow the researcher to distinguish among distinct sources of explained variance in the fitted model. We provide software for implementing these measures and provide two illustrative empirical examples.