Defining R-squared measures for mixed-effects location scale models

Abstract

Ecological momentary assessment and other modern data collection technologies facilitate research on both within-subject and between-subject variability of health outcomes and behaviors. For such intensively measured longitudinal data, Hedeker et al extended the usual two-level mixed-effects model to a two-level mixed-effects location scale (MELS) model to accommodate covariates' influence as well as random subject effects on both mean (location) and variability (scale) of the outcome. However, there is a lack of existing standardized effect size measures for the MELS model. To fill this gap, our study extends Rights and Sterba's framework of (Formula presented.) measures for multilevel models, which is based on model-implied variances, to MELS models. Our proposed framework applies to two different specifications of the random location effects, namely, through covariate-influenced random intercepts and through random intercepts combined with random slopes of observation-level covariates. We also provide an R function, R2MELS, that outputs summary tables and visualization for values of our (Formula presented.) measures. This framework is validated through a simulation study, and data from a health behaviors study and a depression study are used as examples to demonstrate this framework. These (Formula presented.) measures can help researchers provide greater interpretation of their findings using MELS models.