PARAMETER ESTIMATION FOR LATENT MIXTURE MODELS WITH APPLICATIONS TO PSYCHIATRY

by Ren, Lulu

Longitudinal and repeated measurement data commonly arise in many scientific research areas. Traditional methods have focused on estimating single mean response as a function of a time related variable and other covariates in a homogeneous population. However, in many situations the homogeneity assumption may not be appropriate. Latent mixture models combine latent class modeling and conventional mixture modeling. They accommodate the population heterogeneity by modeling each subpopulation with a mixing component. In this paper, we developed a hybrid Markov Chain Monte Carlo algorithm to estimate the parameters of the latent mixture model. We show through simulation studies that MCMC algorithm is superior than the EM algorithm when missing value percentage is large. As an extension of latent mixture models, we also propose the use of cubic splines as a curve fitting technique instead of classic polynomial fitting. We show that this method gives better fits to the data, and our MCMC algorithm estimates the model efficiently. We apply the cubic spline technique to a data set which was collected in a study of alcoholism. Our MCMC algorithm shows several different P300 amplitude trajectory patterns among children and adolescents. Other topics that are covered in this thesis include the identifiability of the latent mixture model and the use of such model to predict a binary outcome. We propose a bivariate version of the latent mixture model, where two courses of longitudinal responses can be modeled at the same time. Computational aspects of such models remain to be completed in the future.