Specifying Location-Scale Models for Heterogeneous Variances as Multilevel SEMs

Standard multilevel models focus on variables that predict the mean while the within-group variability is largely treated as a nuisance. Recent work has shown the advantage of including predictors for both the mean (the location submodel) and the variability (the scale submodel) within a single model. Constrained versions of the model can be fit in standard mixed effect model software, but the most general version with random effects in each of the location and scale submodels has been noted for being difficult to fit and estimate in software. However, the latest release of Mplus includes new capabilities that facilitate fitting the general version of the model as a multilevel structural equation model (SEM). This article introduces the general form of the model that includes location and scale random effects (called the location-scale model) and notes how it can be envisioned as a multilevel SEM. We provide a tutorial with example analyses and Mplus code for the model with two-level cross-sectional data and three-level repeated measures data and discuss how such a model has potential to extend recent developments in organizational science.