ABSTRACT This study examines the application of information criteria in the selection of multilevel structural equation models (MSEM), analyzing different estimation methods (ULS, GLS, and ML) and statistical criteria (AIC, BIC, BCC, and CAIC). The study defines MSEM and specifies fit functions for different estimation methods. Using Monte Carlo simulations, the analysis evaluates the performance of these criteria in model selection under various data heterogeneity and distribution scenarios. The results demonstrate that the choice of information criterion can significantly influence both variable selection and the interpretation of model results. The study concludes that a comprehensive understanding of the behavior of information criteria can help researchers select and interpret the most appropriate models for hierarchical data, recommending a combined approach tailored to the specific objectives of the analysis.
Resende et al. (2025) studied this question.