Improving convergence in growth mixture models without covariance structure constraints.

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.