Techniques for the analysis of event timings and strengths

Event response data that record the timings of randomly occurred events and the strengths of these events are becoming increasingly important in psychology. Although previous researchers such as Kass et al. and Rathbun et al. have developed techniques to model event timings, and that there are social science literature for modeling event times, few researchers have developed techniques to model the event times as well as the strengths of the events. Thus, the present thesis describes a new model that incorporates the use of functional data analysis to estimate a joint occurrence of event intensity, or the instantaneous rate of occurrence, as well as the strengths of the events. The compound log-likelihood model, which is derived by the sum of the event and the response log-likelihood functions, estimates the intensity function and the smoothed function for the response variable simultaneously. In this thesis, we will discuss the incorporation of covariates into the model, and we will also discuss in detail the positive bounded model, which imposes a constraint to the upper bound of the intensity function, as well as the positive model, where no such constraint is imposed.The model is applied to a set of lupus data that involve the medical histories of 300 lupus sufferers over 20 years to examine the flare intensity and severity of lupus symptoms of each patient. Results of patients 15 and 148 are discussed in this thesis, which reveal that there might be some linear relationship between the patients' intensity rate and the severity of their flares. Finally, the extent to which the maximum likelihood estimation for the model is accurate is tested using simulated data. Results from the simulation show that the model requires a large sample size for a precise estimate