A comparison of methods for specifying optimal random effects structures

Abstract

Using Monte Carlo simulations, this study compared the performance of various approaches to the specification of random effects structures in linear mixed effects models (LMMs), including the minimal approach, the maximal approach, the forward search, the backward search, and the all-possible structures approach. The results showed that if the predictor of interest is at the within-cluster level or involves a cross-level interaction, the maximal approach, the best-path forward search, and the best-path backward search are all desirable methods. If the predictor of interest is at the cluster level, it is not essential to specify random slopes of Level-1 predictors. In addition, it is important to specify random slopes of within-cluster control variables, as they can increase the statistical power for testing the main within-cluster variables, especially when the sample size is small and the variance of the random slope of the control variable is large.