Invited Talk: Jason Rights | Quantitative

Title: Advances in R-squared measures for quantifying explained variance in multilevel models

Abstract:
Multilevel models (MLMs) are commonly used by psychologists to accommodate nested data (e.g., students nested within schools or patients nested within clinicians). Psychologists interested in reporting effect size measures for MLMs often mention the need for R-squared measures of explained variance for MLMs. In this talk, I first provide an integrative framework of MLM R-squared measures that subsumes existing measures, clarifies equivalencies among existing measures, and fills gaps for new measures that answer key substantive questions. To resolve prior difficulties researchers have faced when reconciling alternative MLM R-squared definitions, I provide a unifying approach to interpreting, visualizing, and choosing among measures. I then extend my MLM R-squared framework to the contexts of (a) model comparison among multiple MLMs, (b) MLMs with three or more levels (e.g., patients nested within clinician nested within hospital), and (c) multilevel mixture models (that involve, e.g., latent classes of patients and/or latent classes of clinicians). I implement these methodological developments in freely available statistical software, provide illustrative empirical examples, make recommendations for practice, and discuss my future research directions. The ultimate goal is for these developments to aid researchers in considering effect size and conveying practical significance for multilevel models.