Bayesian analysis of hidden Markov structural equation models with an unknown number of hidden states

Abstract

Hidden Markov models (HMMs) are widely used to analyze heterogeneous longitudinal data owing to their capability to model dynamic heterogeneity. Early advancements in HMMs have mainly assumed that the number of hidden states is fixed and predetermined based on the knowledge of the subjects or a certain criterion. However, as a limitation, this approach determines the number of hidden states on a pairwise basis, which becomes increasingly tedious when the state space is enlarged. Moreover, criterion-based statistics tend to select complex models with overestimated numbers of components in mixture modeling. A full Bayesian approach is developed to analyze hidden Markov structural equation models with an unknown number of hidden states. An efficient and hybrid algorithm that combines the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm, the forward filtering and backward sampling scheme, and the Metropolis-Hastings algorithm is proposed to simultaneously select the number of hidden states and perform parameter estimation. The simulation study shows the satisfactory performance of the proposed method. Two real datasets collected from the UCLA Drug Abuse Research Center and National Longitudinal Survey of Youth are analyzed.