Bayesian Identification and Estimation of Growth Mixture Models

Abstract This article addresses problematic behaviors of Markov chain Monte Carlo (MCMC) methods for finite mixture models due to what we call degenerate nonidentifiability. We discuss the reasons for these behaviors, propose diagnostics to detect them, and show through simulations that using more informative priors than the vague defaults can mitigate the problems in growth mixture models (GMMs). Our motivating example is an application of GMMs to data from the National Longitudinal Survey of Youth (NLSY) to examine heterogeneity in the development of reading skills in children aged 6–14. We also suggest ways of describing and visualizing within-class heterogeneity in GMMs, provide a literature review of likelihood identification and Bayesian identification, propose a viable definition of Bayesian identification for latent variable models based on the marginal likelihood (integrated over the latent variables), and give a brief didactic description of Hamiltonian Monte Carlo (HMC) as implemented in Stan .