Mixture Poisson point process

Abstract

The times of repeated behavioral events can be viewed as a realization of a temporal point process. Rathbun, Shi man, and Gwaltney (2007) used a Poisson process (Cox 1972) for modeling 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 fi nite mixture model estimation, we will further extend models to handle data arising from a heterogeneous population. In Chapter 2, we present a fi nite mixture model for Poisson point processes, classifying subjects into clusters sharing identical responses to time-varying covariates within clusters. In Chapter 3, a mixture mixed-effect model is presented which accommodates variation among subjects within clusters with respect to their responses to the time-varying covariates. In Chapter 4, we discuss some issues we encountered in the research and point out potential topics for future research. All the approaches in this dissertation are illustrated using data from an ecological momentary assessment of smoking.