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

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Factor mixture models (FMMs) are used to identify unobserved subgroups within data.
• The inclusion of covariates can potentially improve the accuracy of these models.
• Understanding how covariates influence FMMs is crucial for accurate subgroup identification.

Purpose of the Study:

• To investigate the impact of covariate inclusion on class enumeration in two-class factor mixture models.
• To compare unconditional and conditional FMMs under various data-generating conditions.
• To evaluate the performance of different statistical criteria for class enumeration.

Main Methods:

• Monte Carlo simulation study.
• Generated data for one-factor, two-class FMMs with varying class separation, sample size, mixing proportion, and covariate effect magnitude.
• Evaluated unconditional and one-step conditional FMMs using information criteria, likelihood-ratio tests, entropy, classification accuracy, and parameter coverage.

Main Results:

• Class separation was the primary driver of model performance; sample size offered secondary benefits.
• Conditional FMMs enhanced classification accuracy when covariates predicted only class membership, especially with stronger covariate effects.
• The advantages of conditional FMMs were less pronounced and more criterion-dependent when covariates also predicted the latent factor.
• Bayesian Information Criterion (BIC) and Consistent Akaike Information Criterion (AICc) proved most stable for class enumeration.

Conclusions:

• Covariate inclusion in FMMs is beneficial for class enumeration, particularly when covariates directly predict class membership.
• The pathway through which a covariate influences the model (i.e., class membership vs. latent factor) critically determines its utility.
• Model selection criteria like BIC and AICc are recommended for robust class enumeration in FMMs.