Nonconvergence, Covariance Constraints, and Class Enumeration in Growth Mixture Models

Growth mixture models (GMMs) are a popular method to identify latent classes of growth trajectories. One shortcoming of GMMs is nonconvergence, which often leads researchers to apply covariance equality constraints to simplify estimation. This approach is criticized because it introduces a dubious homoskedasticity assumption across classes. Alternative methods have been proposed to reduce nonconvergence without imposing covariance equality constraints, and though studies have shown that these methods perform well when the correct number of classes is known, research has not examined whether they can accurately identify the number of classes. Given that selecting the number of classes tends to be the most difficult aspect of GMMs, more information about class enumeration performance is crucial to assess the potential utility of these methods. We conduct an extensive simulation based on model characteristics from studies in the PTSD literature to explore class enumeration and classification accuracy of methods for improving nonconvergence. Despite its popularity, results showed that typical approach of applying covariance equality constraints performs quite poorly and is not recommended. However, we recommended covariance pattern GMMs because they (a) had the highest convergence rates, (b) were most likely to identify the correct number of classes, and (c) had the highest classification accuracy in many conditions, even with modest sample sizes. An analysis of empirical PTSD data is provided to show that the typical 4-Class solution found in many empirical PTSD studies may be an artefact of the covariance equality constraint method that has permeated this literature.