Random effects in point processes: adding flexibility to Ecological Momentary Assessment analysis

Models based upon the research done by Rathbun, Shiffman, and Gwaltney (2007) and Waagepetersen (2008) are developed for modeling repeated behavioral events impacted by time-varying covariates. Using forms similar to Poisson-Gamma Hierarchical Generalized Linear Models and Generalized Linear Mixed Models, two modulated Poisson process with random effects are introduced to allow for inter-subject variability. The first allows for random baseline event rates across subjects, and the second is a mixed-effect model with normally distributed random components. Estimation of the parameters for each model is discussed in the case that the covariates are only known at certain random event and non-event assessment times. Integral estimation methods developed by Rathbun et al. (2007) and Waagepetsersen (2008) are utilized to calculate computationally efficient estimating functions. Prediction of the subject-level effects is also discussed. The approaches are illustrated using data from an Ecological Momentary Assessment of smoking.