Three-step estimation of latent Markov models with covariates

Abstract

A three-step approach is proposed to estimate latent Markov (LM) models for longitudinal data with and without covariates. The approach is based on a preliminary clustering of sample units on the basis of time-specific responses only, and is particularly useful 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, this algorithm may be particularly slow to converge, and may become unstable with complex LM models. The properties of the proposed estimator are illustrated theoretically and by a simulation study in which this estimator is compared with the full likelihood estimator. How reliable standard errors for the three-step parameter estimates are obtained is also shown. The approach is applied to the analysis of a dataset about the health status of elderly people resident in certain Italian nursing homes.