Bayesian inference for a class of latent Markov models for categorical longitudinal data

TL;DR

This paper introduces a Bayesian inference method for latent Markov models analyzing longitudinal categorical data, utilizing a reversible jump algorithm for parameter estimation and model selection.

Contribution

It develops a Bayesian approach with Dirichlet-based priors and a reversible jump MCMC algorithm for latent Markov models, including covariate effects.

Findings

Effective inference demonstrated on real datasets

Flexible model selection with reversible jump algorithm

Handles models with and without covariates

Abstract

We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable characteristic. We consider, in particular, the basic latent Markov, which does not account for individual covariates, and its version that includes such covariates in the measurement model. The proposed inferential approach is based on a system of priors formulated on a transformation of the initial and transition probabilities of the latent Markov chain. This system of priors is equivalent to one based on Dirichlet distributions. In order to draw samples from the joint posterior distribution of the parameters and the number of latent states, we implement a reversible jump algorithm which alternates moves of Metropolis-Hastings type with moves of split/combine and birth/death types. The proposed approach is illustrated through two applications based on longitudinal datasets.