Mixed location scale hidden Markov model for the analysis of intensive longitudinal data

Abstract

Hidden Markov models (HMM) presents an attractive analytical framework for capturing the state-switching process for auto-correlated data. These models have been extended to longitudinal data setting where simultaneous multiple processes are observed by including subject specific random effects. However, application of HMMs for intensive longitudinal data, where each subject gets measured intensively over relatively short period of time, has not been widely studied. In this paper, we extend the mixed hidden Markov model and allow subject heterogeneity with respect to the mean and within subject variance by including subject random effects in both perspectives. We focus on the application of this model to intensive longitudinal studies in psychological and behavioral research where individual’s latent states and state-switching process are of interest. Models are estimated using forward–backward algorithm via Bayesian sampling approach. Advantages over regular HMM and mixed HMM that only accounts for the subjects’ mean heterogeneity are illustrated through a series of simulation studies. Finally, models are applied to an adolescent mood study data set and results show that the proposed mixed location scale HMM achieves better model fit and more interpretative mood state identification in terms of state specific covariate effects compared to regular HMM and mixed HMM.