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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 unobservablecharacteristic. We consider, in particular, the basic latent Markov, which doesnot account for individual covariates, and its version that includes suchcovariates in the measurement model. The proposed inferential approach is basedon a system of priors formulated on a transformation of the initial andtransition probabilities of the latent Markov chain. This system of priors isequivalent to one based on Dirichlet distributions. In order to draw samplesfrom the joint posterior distribution of the parameters and the number oflatent states, we implement a reversible jump algorithm which alternates movesof Metropolis-Hastings type with moves of split/combine and birth/death types.The proposed approach is illustrated through two applications based onlongitudinal datasets.

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