Mixed Effects Location-Scale Models: Methodological and Substantive Considerations

When the assumption of variance homogeneity is violated in multilevel analysis, standard procedure is to estimate robust standard errors. However, this approach acknowledges the violation, it does not fix it. Fitting a model to data with variance heterogeneity can be seen as model misspecification. In addition to methodological considerations, variance heterogeneity may be of substantive interest in research contexts such as teacher ratings of student performance. Examining variance heterogeneity in assigned ratings can provide insight into rater effects. The mixed effects location-scale model (MELSM) can be used to model random variation in within-rater behavior in addition to random variation in rater severity. This study uses a simulation study and an analytical data set to demonstrate the utility of the MELSM.