Robust fitting of hidden Markov regression models under a longitudinal setting

Abstract

We propose a robust estimation procedure for the analysis of longitudinal data including a hidden process to account for unobserved heterogeneity between subjects in a dynamic fashion. We show how to perform estimation by an expectation–maximization-type algorithm in the hidden Markov regression literature. We show that the proposed robust approaches work comparably to the maximum-likelihood estimator when there are no outliers and the error is normal and outperform it when there are outliers or the error is heavy tailed. A real data application is used to illustrate our proposal. We also provide details on a simple criterion to choose the number of hidden states.

Keywords:

• hidden Markov models
• longitudinal data
• robust estimation
• EM algorithm

Acknowledgements

I am grateful to Weixin Yao for his insightful comments and suggestions. I thank an anonymous referee for the precise review of my article and the very useful comments.