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Latent time‐varying factors in longitudinal analysis: a linear mixed hidden Markov model for heart rates
Author(s) -
Lagona Francesco,
Jdanov Dmitri,
Shkolnikova Maria
Publication year - 2014
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6220
Subject(s) - expectation–maximization algorithm , covariate , maximization , hidden markov model , random effects model , econometrics , computer science , markov chain , statistics , markov model , likelihood function , mathematics , maximum likelihood , artificial intelligence , mathematical optimization , medicine , meta analysis
Abstract Longitudinal data are often segmented by unobserved time‐varying factors, which introduce latent heterogeneity at the observation level, in addition to heterogeneity across subjects. We account for this latent structure by a linear mixed hidden Markov model. It integrates subject‐specific random effects and Markovian sequences of time‐varying effects in the linear predictor. We propose an expectationŰ‐maximization algorithm for maximum likelihood estimation, based on data augmentation. It reduces to the iterative maximization of the expected value of a complete likelihood function, derived from an augmented dataset with case weights, alternated with weights updating. In a case study of the Survey on Stress Aging and Health in Russia, the model is exploited to estimate the influence of the observed covariates under unobserved time‐varying factors, which affect the cardiovascular activity of each subject during the observation period. Copyright © 2014 John Wiley & Sons, Ltd.