Stephen Rathbun, Saul Shiffman, and Chad Gwaltney
Rathbun, Shiffman & Gwaltney introduce point process models for event history data. A point process is a stochastic mechanism for generating the times of repeated events on a clock or calendar. This is in contrast to the typically applied survival models, which focus on the durations of time between successive events. A series of increasingly complex point process models are illustrated on electronically recorded records of the times at which cigarettes are lit. Poisson point process models are used to describe how smoking rate varies with day of the week and time of day. A modulated Poisson process model is used to describe the effects of time-varying covariates on smoking rates. Possible extensions of the above models are described, but not illustrated on the smoking data. These include a semiparametric model that takes the diurnal patterns of smoking into account when modeling the effects of time-varying covariates, a Cox point process for modeling random subject effects, and multivariate point processes for multiple types of events. Although point process modeling is illustrated using behavioral data, point processes have potential applications in all types of event history data, for example, the timings of riots, ethnic confrontations, and labor protests, or the times at which firms are founded or go bankrupt.