Investigating the Impact of Covariate Inclusion on Sample Size Requirements of Factor Mixture Modeling: A Monte Carlo Simulation Study

ABSTRACT

Factor mixture modeling (FMM) has been increasingly used in behavioral and social sciences to capture underlying population heterogeneity. This Monte Carlo simulation study investigated a common issue in applications of FMM, sample size requirements, particularly taking into account the impact of covariate inclusion. Results indicated that it was critical to include a proper covariate into FMM for accurate class enumeration and the required sample size became smaller with larger covariate effect. Overall, the statistical power for detecting factor mean difference was adequate but positive bias was observed in some conditions. The required minimum sample sizes were suggested for applied researchers.

KEYWORDS:

• Factor mixture modeling
• sample size
• covariate
• model selection

Disclosure statement

We have no conflicts of interests to disclose.

Notes

¹ Note that in addition to the covariate effect on the latent class variable, covariate effects on other FMM parameters (e.g., factor, item) might be present (Lee & Beretvas, 2014; G. H. Lubke & Muthén, 2005; Wang et al., 2020). However, these additional covariate effects are beyond the scope of the study.

² Inadmissible solutions were defined as the presence of negative item residual variances or factor variances, factor correlations greater than one, or a zero latent class proportion.