Three-step estimation of latent Markov models with covariates

TL;DR

This paper introduces a modified three-step estimation method for latent Markov models with covariates, improving efficiency and stability over traditional EM-based maximum likelihood estimation, especially with many response variables.

Contribution

The paper develops a consistent three-step estimation approach for latent Markov models with covariates, suitable for large response variable sets and complex data structures.

Findings

The proposed method is consistent as the number of response variables increases.

Simulation results show improved performance over full likelihood methods.

Application to elderly health data demonstrates practical utility.

Abstract

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.