Bayesian Analysis of Semiparametric Hidden Markov Models With Latent Variables

Abstract

In psychological, social, behavioral, and medical studies, hidden Markov models (HMMs) have been extensively applied to the simultaneous modeling of heterogeneous observation and hidden transition in the analysis of longitudinal data. However, the majority of the existing HMMs are developed in a parametric framework without latent variables. This study considers a novel semiparametric HMM, which comprises a semiparametric latent variable model to investigate the complex interrelationships among latent variables and a nonparametric transition model to examine the linear and nonlinear effects of potential predictors on hidden transition. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the unknown, a Bayesian model comparison statistic, is employed to conduct model comparison. The empirical performance of the proposed methodology is evaluated through simulation studies. An application to a data set derived from the National Longitudinal Survey of Youth is presented.

Keywords:

• Bayesian P-splines
• hidden Markov models
• MCMC methods
• semiparametric models

Acknowledgments

The authors thank the editor and the two reviewers for their valuable comments and suggestions which improved the paper substantially.

Funding

This research was supported by GRF 14601115 and 14303017 from the Research Grant Council of the HKSAR, Direct Grants from the Chinese University of Hong Kong, NSFC 11471277, NSFC from Guangdong Province 2016A030313856, and the high-performance grid computing platform of Sun Yat-sen University.

Additional information

Funding

This research was supported by GRF 14601115 and 14303017 from the Research Grant Council of the HKSAR, Direct Grants from the Chinese University of Hong Kong, NSFC 11471277, NSFC from Guangdong Province 2016A030313856, and the high-performance grid computing platform of Sun Yat-sen University.