| Recent developments in many scientific fields have produced large number of huge collections of functional data. A typical goal of collecting such data is to group the individual records into appropriate clusters. Existing methods for grouping or clustering functional data, however, are not flexible enough when the curves are irregularly sampled and also, they are not adapted for the efficient use of information on covariates. This dissertation focuses on developing a method of classifying functional data based on a mixture random effects model, which can be applied to sparsely and irregularly sampled data collected over time. Individual latent trajectories, giving rise to the observed functional data, are modeled in terms of a functional basis and random effects that account for variation in the individual trajectories. The proposed hierarchical model provides a flexible and efficient framework for studying the effects of covariates on classification and for identifying group-specific covariate effects on changes in outcome over time. A relabeling algorithm, based on some appropriate loss function, is developed for solving the non-identifiability problem in parametric inference by adapting the method of Stephens (2000b). A Bayesian procedure is developed to estimate the number of groups/clusters by simulating the joint posterior distribution of the unknown number of groups and the model parameters associated with this group number. We assess the performance of the proposed method based on a deviance information criterion (DIC) and a Bayesian estimation procedure using reversible jump Markov chain Monte Carlo (RJMCMC) sampler for selecting the number of clusters. The results from the simulation studies are very satisfactory and suggest promising applications of our method in both classifying functional data and estimating parameters of interest. |
