A comparison of some estimation methods for latent Markov models with covariates

We compare dierent estimation methods for latent Markov models with covariates. These models represent a powerful tool for the analysis of longitudinal categorical data when the interest is to represent the evolution of a latent characteristic of a sample of units over time. In applications to complex data, with a large number of observed response variables and latent states, estimation of these models may present some critical aspects. These are mainly due to the presence of many local maxima of the model log-likelihood and to the slowness to converge of the Expectation-Maximization algorithm, which is typically used for parameter estimation. In such a context, alternative methods which allow us to overcome the drawbacks of the full maximum likelihood approach, with an advantage also in terms of computational cost, are of interest. In particular, we focus on estimation methods which may be seen as modied versions of the three-step approach for the latent class model with covariates. The behavior of these alternative approaches is investigated by means of a Monte Carlo simulation study on the basis of a wide set of model specications.