Unmodeled DIF in Latent Class Analysis: Consequences for Class Enumeration

This paper builds upon previous research to investigate the effects of misspecified covariate relations in latent class analysis (LCA) using a Monte Carlo simulation. A key issue in latent class enumeration arises when direct effects (DEs) between covariates and indicators are unmodeled, potentially altering latent class enumeration and the measurement model. Previous research recommends that latent class enumeration be completed before incorporating auxiliary (covariates or distal outcome) variables. Whether these recommendations hold in complex conditions remains unclear, particularly when differential item functioning (DIF) is present but unaccounted for. This paper builds on prior work by examining enumeration in more complex modeling conditions, including varying LCA measurement models (i.e., different numbers of classes and indicators), sample sizes, class proportions, DE magnitudes, class separation, and multiple covariates. Specifically, this study evaluates whether unconditional enumeration remains a reliable approach in these complex settings and identifies which model selection criteria perform consistently well across conditions. Consistent with previous research, the results indicate that the Bayesian Information Criterion (BIC) consistently identifies the number of classes regardless of misspecification, followed by the Consistent Akaike’s Information Criteria (CAIC). However, they are less accurate with smaller sample sizes. Increasing sample size improves enumeration accuracy, but diminishing effects occur with large sample sizes on misspecified models. These findings have important implications for the current recommended approach when incorporating auxiliary variables in mixture models and lay the foundation for continued work on the importance of detecting DEs in LCA.