15. R-Squareds as Standardized Effect Sizes for Mixed-Effects Location Scale Models

Ecological momentary assessment and other modern data collection technologies facilitate research on both within-person and between-person variability of people's health outcomes and behaviors. For such intensively measured longitudinal data, regular mixed-effects models were extended to mixed-effects location scale (MELS) models to accommodate random subject effects on both mean and variability of the outcome. However, standardized effect sizes for the MELS model are lacking. To address this gap, we extend an existing framework of R-squared measures for regular mixed-effects models, which are based on model-implied variances, to MELS models. Our proposed framework applies to two specifications of the random location effects: random intercepts with covariate-influenced variances and random intercepts combined with random slopes of observation-level covariates. We also provide an R package, R2MELS, that generates summary tables and visualization for values of our R-squared measures. We validated our framework through a simulation study. These R-squared measures can help researchers who are using MELS models interpret their findings more effectively.

mixed-effects location scale model

R-squared

standardized effect size

EMA