Investigating Sources of Heterogeneity with Three-Step Multilevel Factor Mixture Modeling: Beyond Testing Measurement Invariance in Cross-National Studies

We propose the three-step multilevel factor mixture modeling (ML FMM) to test measurement invariance (MI) across many groups and furthermore to model predictors of latent class membership that possibly induce measurement noninvariance. This Monte Carlo simulation study found that information criteria such as Bayesian Information Criterion tended to select a more complex model when sample size was very large. Thus, the adequacy of three-step ML FMM regarding the correct MI detection was demonstrated with an empirically derived information criterion for large data. However, the number of latent classes was overestimated when intraclass correlation was large. For the test of covariate effects, Type I error was well controlled and power was generally adequate when a correct model was identified at Step 1. Using background variables selected from Trends in International Mathematics and Science Study 2011, the application of three-step ML FMM to a cross-national MI test is demonstrated