outliers, heavy-tailed distributions, MCEM algorithm, Gibbs sampler, path sampling, Bayesian information criterion. ,

Summary 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 paper 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.

robust Bayesian methods, normal/independent distributions, nonlinear structural equation models with covariates, model comparison,

Recently, structural equation models (SEMs) have been applied for analyzing interrelationships among observed and latent variables in biological and medical research. Latent variables in these models are typically assumed to have a normal distribution. This article considers a Bayesian semparametric SEM with covariates, and mixed continuous and unordered categorical variables, in which the explanatory latent variables in the structural equation are modeled via an appropriate truncated Dirichlet process with a stick-breaking procedure. Results obtained from a simulation study and an analysis of a real medical data set are presented to illustrate the methodology.

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