Kulvanich PhD Candidate, Statistics Wed, 03/06/2013 - 3:00pm 201, BS Miller Hall, Health Sciences Campus The times of repeated behavioral events can be viewed as a realization of a temporal point process. Rathbun, Shiffman, and Gwaltney (2007) used a Poisson process (Cox 1972) for modelling repeated behavioral events impacted by time-varying covariates. Taking an inspiration from the techniques of Generalized Linear Mixed Models, and the EM algorithm (Dempster et al. 1977) for finite mixture model estimation, we will further extend their models to handel data arising from a heterogeneous population. In Chapter 2 of this dissertation, we present the implementation of the finite mixture model for the Point process model to describe variation among subjects with respect to the effects of time-covariates from which clusters of subjects showing similar patterns. In Chapter 3, a Mixture mixed-effect model, that also allows for inter-subject variability is proposed. In Chapter 4, we discuss some issues we encountered in the research and point out the potential topics for future research. All the approaches in this dissertation are illustrated using data from an Ecological Momentary Assessment of smoking.