title: Hidden Markov latent variable models with multivariate longitudinal data.
abstract: Cocaine addiction is chronic and persistent, and has become a major social and health problem in many countries. Existing studies have shown that cocaine addicts often undergo episodic periods of addiction to, moderate dependence on, or swearing off cocaine. Given its reversible feature, cocaine use can be formulated as a stochastic process that transits from one state to another, while the impacts of various factors, such as treatment received and individuals' psychological problems on cocaine use, may vary across states. This article develops a hidden Markov latent variable model to study multivariate longitudinal data concerning cocaine use from a California Civil Addict Program. The proposed model generalizes conventional latent variable models to allow bidirectional transition between cocaine-addiction states and conventional hidden Markov models to allow latent variables and their dynamic interrelationship. We develop a maximum-likelihood approach, along with a Monte Carlo expectation conditional maximization (MCECM) algorithm, to conduct parameter estimation. The asymptotic properties of the parameter estimates and statistics for testing the heterogeneity of model parameters are investigated. The finite sample performance of the proposed methodology is demonstrated by simulation studies. The application to cocaine use study provides insights into the prevention of cocaine use.
authors.affiliation: Shenzhen Research Institute, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
authors.forename: Xinyuan
authors.initials: X
authors.lastname: Song
authors.affiliation: Department of Applied Mathematics, Nanjing Forestry University, Nanjing, China.
authors.forename: Yemao
authors.initials: Y
authors.lastname: Xia
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, U.S.A.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
mesh_terms: D001699:Biometry / Q000379:methods*; D019970:Cocaine-Related Disorders / Q000473:pathology / Q000517:prevention & control; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D015999:Multivariate Analysis; D013269:Stochastic Processes
keywords: Hidden Markov model; Latent variables; Log-continuation ratio model; MCECM algorithm; Multivariate longitudinal data