Latent Markov models with discrete separate cluster random effects on initial and transition probabilities

In this paper, a multilevel latent Markov model is proposed where through discrete random effects a two-way classification of sample unit clusters is obtained. Such random effects are defined as two discrete random variables, one of which affecting the initial probabilities and the other one affecting the transition probabilities of the Markovian latent process. We apply the model to data on health status of elderly patients clustered in nursing homes. The two-dimensional criterion used for classifying nursing homes highlights a plausible pattern, which can be useful for their management.