Nonconvergence, covariance constraints, and class enumeration in growth mixture models

Area of Science:

• Statistics
• Psychometrics
• Longitudinal Data Analysis

Background:

• Growth Mixture Models (GMMs) are widely used for identifying latent classes of growth trajectories.
• Nonconvergence is a common issue in GMMs, often addressed by imposing covariance equality constraints, which may be an invalid assumption.
• Previous research on alternative GMM specifications robust to nonconvergence has not evaluated their performance in class enumeration when the number of classes is unknown.

Purpose of the Study:

• To investigate the class enumeration and classification accuracy of GMM specifications robust to nonconvergence.
• To compare the performance of covariance pattern GMMs against the typical approach using covariance equality constraints.

Main Methods:

• Conducted an extensive simulation study.
• Evaluated GMMs with and without covariance equality constraints.
• Assessed convergence rates, class enumeration accuracy, and classification accuracy across various conditions.

Main Results:

• The typical approach of applying covariance equality constraints resulted in poor performance.
• Covariance pattern GMMs demonstrated superior performance with higher convergence rates.
• Covariance pattern GMMs were more likely to identify the correct number of classes and showed higher classification accuracy, even with smaller sample sizes.

Conclusions:

• Covariance pattern GMMs are recommended as a more robust alternative to standard GMMs with covariance equality constraints.
• The common finding of a four-class solution in posttraumatic stress disorder (PTSD) literature may be an artifact of the covariance equality constraint method.