Bayesian analysis of non-homogeneous Markov chains: Application to mental health data. Statistics in Medecine

In this paper we present a formal treatment of nonhomogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the nonhomogeneity of transition patterns. In so doing, we introduce a logistic regression setup for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study