Mixed location scale hidden Markov model for the analysis of intensive longitudinal data
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Mixed location scale hidden Markov model for the analysis of intensive longitudinal data Xiaolei Lin1 · Robin Mermelstein2 · Donald Hedeker3 Received: 24 March 2020 / Revised: 26 July 2020 / Accepted: 5 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Intensive longitudinal data · Mixed effect models · Latent class classification
1 Introduction Hidden Markov models (HMMs) are an ubiquitous tool for modeling time dependent data. They are used to represent the probability distributions over sequences of observations and include two stochastic processes: an underlying hidden (latent) process that is assumed to follow a Markov chain, and an observed process that are modeled as independent distributions conditional on the hidden process. The hidden process is specified by an initial * Xiaolei Lin [email protected] 1
Fudan University, Shanghai, China
2
University of Illinois at Chicago, Chicago, USA
3
University of Chicago, Chicago, USA
13
Vol.:(0123456789)
Health Services and Outcomes Research Methodology
probability distribution over discrete states and a transition probability matrix that represents the probability of moving from one state to another. As with first-order Markov chain, the hidden process assumes that the probability of a particular state depends on its history only through the previous state. The observed process is specified by the emission probabilities or conditional probabilities, representing the likelihood of an observation being generated from a specific state. It assumes that the observations depend on their history only through their current state instead o
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