Varying-coefficient hidden Markov models with zero-effect regions

Abstract

In psychological, social, behavioral, and medical studies, hidden Markov models (HMMs) have been extensively applied to the simultaneous modeling of longitudinal observations and the underlying dynamic transition process. However, the existing HMMs mainly focus on constant-coefficient HMMs. This study considers a varying-coefficient HMM, which enables simultaneous investigation of the dynamic covariate effects and between-state transitions. Moreover, a soft-thresholding operator is introduced to detect zero-effect regions of the coefficient functions. A full Bayesian approach with a hybird Markov chain Monte Carlo algorithm that combines B-spline approximation and penalization technique is developed for statistical inference. The empirical performance of the propose method is evaluated through simulation studies. An application to a study on the Alzheimer's Disease Neuroimaging Initiative dataset is presented.