Evaluating Class Enumeration Criteria in Factor Mixture Models: A Monte Carlo Study Across Model Complexity

Selecting the number of latent classes is a critical challenge in factor mixture modeling, particularly as model complexity increases and class separation weakens. This Monte Carlo study evaluated the performance of information criteria, likelihood ratio tests, entropy-based classification rules, classification accuracy, and parameter recovery across varying factor dimensionality, indicator density, class separation, sample size, and class proportions. Results showed that conservative criteria, particularly BIC and CAIC under moderate-to-large separation, provided the most stable recovery of the true two-class solution, whereas AIC, likelihood ratio tests, entropy, and ICL-BIC were more sensitive to weak separation, class imbalance, and model dimensionality. Parameter recovery was most strongly affected by class separation and sample size, with measurement-design effects most evident for factor mean recovery. Supplementary shape-difference analyses showed that the classification advantage of higher-dimensional models was preserved when class differences reflected profile shape rather than level differences alone. Overall, findings support a triangulated approach to class enumeration that integrates conservative information criteria, classification quality, parameter recovery, and measurement-design considerations.