Bayesian analysis for mixture of latent variable hidden Markov models with multivariate longitudinal data

Latent variable hidden Markov models (LVHMMs) are important statistical methods in exploring the possible heterogeneity of data and explaining the pattern of subjects moving from one group to another over time. Classic subject- and/or time-homogeneous assumptions on transition matrices in transition model as well as the emission distribution in the observed process may be inappropriate to interpret heterogeneity at the subject level. For this end, a general extension of LVHMM is proposed to address the heterogeneity of multivariate longitudinal data both at the subject level and the occasion level. The main modeling strategy is that the observed time sequences are first grouped into different clusters, and then within each cluster the observed sequences are formulated via latent variable hidden Markov model. The local heterogeneity at the occasion level is characterized by the distribution related to the latent states, while the global heterogeneity at the subject level is identified with the finite mixture model. Compared to the existing methods, an appeal underlying the proposal is its capacity of accommodating non-homogeneous patterns of state sequences and emission distributions across the subjects simultaneously. As a result, the proposal provides a comprehensive framework for exploring various kinds of relevance among the multivariate longitudinal data. Within the Bayesian paradigm, Markov Chains Monte Carlo (MCMC) method is used to implement posterior analysis. Gibbs sampler is used to draw observations from the related full conditionals and posterior inferences are carried out based on these simulated observations. Empirical results including simulation studies and a real example are used to illustrate the proposed methodology.