Covariate Inclusion and Class Enumeration in Factor Mixture Modeling: A Monte Carlo Simulation Study

This Monte Carlo study examined how covariate inclusion affects class enumeration in one-factor, two-class factor mixture models (FMMs). Data were generated under two scenarios: a continuous covariate predicted latent class membership only, or predicted both latent class membership and the latent factor. Conditions varied by class separation, sample size, mixing proportion, and covariate-effect magnitude. Unconditional and one-step conditional FMMs were evaluated using information criteria, likelihood-ratio-based tests, entropy, classification accuracy, and parameter coverage. Results showed that class separation was the strongest determinant of performance, with sample size providing secondary benefits. When the covariate predicted class membership only, conditional FMMs generally improved classification accuracy and became more competitive for class enumeration as the covariate effect increased. When the covariate also predicted the latent factor, these advantages weakened and became more criterion-dependent. Across conditions, the Bayesian information criterion and consistent Akaike's information criterion were the most stable enumeration criteria, whereas entropy and likelihood-ratio-based tests were less reliable. The findings indicate that the value of covariate inclusion in FMM depends on the pathway through which the covariate affects the population model.