Developing Dynamic Tools for Analyzing Irregularly Spaced Longitudinal Affect Data

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The regulation of emotions is an integral part of everyday life. Despite the widespread interest in emotions, very few statistical models exist for formally evaluating the dynamics of emotion regulation. The collaborative work stemming from this project will enhance theoretical and methodological developments in the field of dynamic systems modeling by introducing novel methodologies suited for testing existing theories of emotions. It also will create opportunities for methodologists to refine existing techniques and develop new ones for studying dynamic systems that will benefit other scientific disciplines. The tools developed in this project can be used to examine irregularly spaced survey data frequently observed in the studies of other dynamic processes, such as family dynamics, social networks, and the propagation of diseases. Physicians and other clinical practitioners may benefit from findings concerning how emotions vary over time. To broaden the educational impact of this project, graduate students will be involved in all phases of the project. Statistical tools developed in this study also will be disseminated to a broader research audience through online tutorial, forums, and conference workshops.Empirical studies of human dynamic processes, such as studies of circadian rhythms, emotions, propagation of diseases, and dyadic and family-level interactions, frequently involve irregularly spaced longitudinal survey data. 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 characterizing EMA data. The diverse range of time intervals also leads to computational challenges in determining the appropriate interpolation intervals in fitting differential equation models to empirical data. The study will yield an integrated set of software tools for: (1) fitting and evaluating continuous-time regime-switching models for extracting key phases of emotion processes with homogeneous dynamical structures; (2) conducting Bayesian local influence analysis to assess the sensitivity of the proposed modeling extensions to perturbations to the hypothesized prior, sampling distribution, and data; and (3) determining the most robust interpolation intervals for fitting continuous-time models with regime-switching features under conditions that mirror real-life EMA studies. Simulation studies as well as two existing EMA data sets will be used to test and validate the techniques developed in this study.