Covariance pattern mixture models: Eliminating random effects to improve convergence and performance.

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Growth mixture models (GMMs) are widely used to identify unobserved population heterogeneity through latent classes.
• GMMs frequently encounter convergence issues, necessitating arbitrary model modifications for estimation.
• Within-class random effects often complicate GMMs without addressing core research questions.

Purpose of the Study:

• To introduce and evaluate covariance pattern mixture models (CPMMs) as an alternative to GMMs.
• To demonstrate CPMMs' ability to overcome GMM convergence problems.
• To show CPMMs improve class enumeration and class-specific trajectory estimation.

Main Methods:

• Extension of covariance pattern models to the mixture modeling context, creating CPMMs.
• Theoretical analysis, simulation studies, and an empirical example.
• Comparison of CPMMs with GMMs, including GMMs with cross-class constraints.

Main Results:

• CPMMs demonstrate significantly improved convergence rates compared to GMMs.
• CPMMs lead to more accurate class enumeration and less biased class-specific growth trajectories.
• Even misspecified CPMMs outperform GMMs in terms of computational stability and estimation quality.

Conclusions:

• CPMMs provide a computationally superior and statistically robust alternative to GMMs for analyzing population heterogeneity.
• Researchers should consider CPMMs to avoid convergence issues and improve the reliability of latent class analysis.
• The study provides evidence and tools (Mplus appendix) to facilitate CPMM adoption.