Three step estimation of latent Markov models

Latent Markov models represent a powerful tool for the analysis of longitudinal categorical data. In the presence of many response variables for each time occasion and with individual covariates, full maximum likelihood estimation of these models may present some critical aspects. Moreover, the simultaneous estimation of the parameters of the measurement model and the latent process may not be easily interpreted by applied researchers. We propose an alternative three-step approach to estimate these models, which is based on a preliminary clustering of sample units on the basis of the time-specific responses only. This method is particularly useful to overcome the drawbacks of the full likelihood approach, with an advantage both in terms of interpretability of the estimation process and in terms of computing time.