Irregularly spaced longitudinal data have become increasingly prevalent in empirical studies. In the study of human emotions, researchers often adopt ecological momentary assessment (EMA) procedures to obtain responses at random or event-contingent time intervals. Such designs facilitate the collection of data that reflect an individual's ongoing emotional states “in the moment." Common approaches based on ordinary and stochastic differential equations can be used to accommodate the irregular time intervals observed in such data, but they are not directly suited for handling the noisy, high-dimensional nature and diverse time scales of EMA affect data. Determining the appropriate interpolation intervals for fitting differential equation models to empirical data can be particularly challenging. The proposed project seeks to (1) develop and test the performance of a multiresolution Bayesian procedure for fitting stochastic differential equation (SDE) models of human emotions, (2) extend the models and estimation procedures to accommodate regime-switching processes, namely, processes that are characterized by phases with homogeneous dynamical structures, and (3) conduct Bayesian local influence analysis to assess the sensitivity of the proposed modeling procedures. This project is supported by funding from the National Science Foundation.
