Graduate student Sunyoung Ahn (Ph.D. in Computational Science and Engineering) will present a final oral examination (defense) on Tuesday, November 19, from 11:30 am-1:00 pm in MEEM 405 and via virtual meeting. The title of Ahn’s defense is “Bayesian Inference of Longitudinal Binary and Ordinal Data Utilizing Multivariate Probit Models.”
Defense Abstract
This dissertation explores advanced Bayesian inference methods for analyzing longitudinal binary and ordinal data, with a focus on multivariate probit models. In medical and survey research, responses often follow an ordinal structure, presenting unique challenges due to their discrete, ordered nature. Traditional statistical methods, including Linear Mixed Models (LMMs) and Generalized Estimating Equations (GEE), partially address these challenges but face limitations in computational complexity and efficiency, particularly when analyzing high-dimensional longitudinal data. Extensive simulation studies demonstrate the superiority of PX-GS and PX-GSM models over traditional methods in terms of estimation accuracy and convergence speed while real data applications validate the practical effectiveness of these models in handling complex data structure and dependencies. Part 1 focuses on the analysis of multivariate longitudinal ordinal data using LMMs, GEE, and Bayesian methods. It reviews LMMs for capturing individual variability through random effects in repeated measures, as well as GEE, which estimate population-averaged effects without assuming independence between observations. This section compares two frequentist approaches (LMMs and GEE) with three Bayesian sampling algorithms: one for identifiable model (PX-MH) and two for non-identifiable model (PX-GS and PX-GSM) with simulation studies from Add Health data and HRS data. Part 2 expands the Bayesian framework to encompass multivariate binary and ordinal data, concluding with the comparative assessment of estimation performance across the three Bayesian methods. This research provides integrated and comprehensive insights by comparing different approaches to multivariate longitudinal data analysis.