A Bayesian approach to detect time-specific group differences between nonlinear temporal curves

Researchers from many fields have found it difficult to fit statistical models that can incorporate multiple random effects, account for the correlated nature of the data, and simultaneously fit and compare multiple groups. In this dissertation, we have taken a Bayesian hierarchical modeling approach for this multivariate non-linear longitudinal data problem. Within this framework, we develop both parametric and nonparametric approaches in simultaneously modeling multiple longitudinal curves. Finally, we put forth comparison techniques to allow for a between group comparison of group curves under the Bayesian framework. The work is motivated from the visual world paradigm which is a tool that is widely used in the field of psycholinguistics to help investigate how people listen and understand words and sentences. Proportions of fixations to several different objects are recorded for a number of subjects, over a specific time period. Within this dissertation is the model development, demonstrations of the ability of the model via simulation, and answers to scientific research questions from visual world paradigm data.