Identification of Latent Classes in Mixture Models: A Monte Carlo Simulation Study
Factor mixture modeling is an increasingly popular method used in applied research settings that combines latent class models and common factor models. The method is often used to detect the presence of heterogeneous populations (i.e., latent classes) that differ on one or more population parameters of a factor model in a sample that lacks a priori information regarding population membership.
Researchers have faced many challenges when using the factor mixture modeling method. The present study employs a Monte Carlo approach to compare the performance of factor mixture modeling with three other tenable methods: Q-Factor Analysis, Marcoulides and Drezner Model, and McDonald Eigen Analysis, in detecting latent classes in a sample. Data were simulated by manipulating six design factors: sample size, number of classes, mixing proportion, class separation, distributional characteristics, and complexity of within-class factor structures. The performance of each method was assessed by determining the proportion of replications for which each method detected the correct number of latent classes (i.e., populations) and Cohen's h effect size for each manipulated design factor.
Overall, the factor mixture model performed best. In particular, the sample size, number of classes, and distributional characteristic of the latent variable significantly impacted the ability of factor mixture model to detect the correct number of classes. The McDonald Eigen Analysis performed second best, overall. The method was only significantly influenced by the number of classes. The other design conditions had a small or negligent influence on the performance. Q-Factor Analysis was influenced most by the complexity of the within-class factor structure and the number of classes. Finally, Marcoulides and Drezner Model was most influenced by the sample size and the number of classes.
From the results, it can be concluded that under certain design conditions, less parameterized and less complex methods perform just as well as factor mixture modeling in detecting latent classes. Researchers can be guided in determining the best method to use based on the characteristics of their data.