Parsimonious parametrizations of transition matrices of Markov chain and hidden Markov models

We introduce a set of constraints on the multinomial logit (sub)model for the transition probabilities of Markov chain and Hidden Markov models with covariates. These constraints have a straightforward interpretation and make the model more parsimonious with respect to the standard formulation. Estimation based on the maximum likelihood approach is developed under different constraints. The proposal is validated by a series of simulations and illustrated by an application about the evaluation of differences in general self-assessed health according to the available covariates, using longitudinal data from the Health and Retirement Study.