Finite mixture varying coefficient models for analyzing longitudinal heterogenous data.

This paper aims to develop a mixture model to study heterogeneous longitudinal data on the treatment effect of heroin use from a California Civil Addict Program. Each component of the mixture is characterized by a varying coefficient mixed effect model. We use the Bayesian P-splines approach to approximate the varying coefficient functions. We develop Markov chain Monte Carlo algorithms to estimate the smooth functions, unknown parameters, and latent variables in the model. We use modified deviance information criterion to determine the number of components in the mixture. A simulation study demonstrates that the modified deviance information criterion selects the correct number of components and the estimation of unknown quantities is accurate. We apply the proposed model to the heroin treatment study. Furthermore, we identify heterogeneous longitudinal patterns.