  We propose a modified version of the three-step estimation method for the
latent class model with covariates, which may be used to estimate latent Markov
models for longitudinal data. The three-step estimation approach we propose is
based on a preliminary clustering of sample units on the basis of the time
specific responses only. This approach represents an useful estimation tool
when a large number of response variables are observed at each time occasion.
In such a context, full maximum likelihood estimation, which is typically based
on the Expectation-Maximization algorithm, may have some drawbacks, essentially
due to the presence of many local maxima of the model likelihood. Moreover, the
EM algorithm may be particularly slow to converge, and may become unstable with
complex LM models. We prove the consistency of the proposed three-step
estimator when the number of response variables tends to infinity. We also show
the results of a simulation study aimed at evaluating the performance of the
proposed alternative approach with respect to the full likelihood method. We
finally illustrate an application to a real dataset on the health status of
elderly people hosted in Italian nursing homes.
