Simultaneous Decision on the Number of Latent Clusters and Classes for Multilevel Latent Class Models

The Multilevel Latent Class Model (MLCM) proposed by Vermunt (2003) has been shown to be an excellent framework for analyzing nested data with assumed discrete latent constructs. The nonparametric version of MLCM assumes 2 levels of discrete latent components to describe the dependency observed in data. Model selection is an important step in any statistical modeling. The task of model selection for MLCM amounts to the decision on the number of discrete latent components at both higher and lower levels and is more challenging than standard Latent Class Models. In this article, simulation studies were conducted to systematically examine the effects of sample sizes, clusters/classes distinctness, and the number of latent clusters and classes on the performance of various information criteria in recovering the true latent structure. Results of the simulation studies are summarized and presented. The final section presents the remarks and recommendations about the simultaneous decision regarding the number of latent classes and clusters when applying MLCMs to analyze empirical data.