Date of Award
2026
Document Type
Campus Access Dissertation
Degree Name
Doctor of Philosophy in Statistics (PhD)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
Xiao Zhang
Committee Member 1
Kui Zhang
Committee Member 2
Qiuying Sha
Committee Member 3
Hairong Wei
Abstract
Longitudinal binary and ordinal outcomes are common in medicine, epidemiology, and the social sciences, where repeated measurements are often subject to missing responses arising from nonresponse, missed visits, or dropout. Bayesian multivariate probit models provide a flexible framework for jointly modeling correlated discrete outcomes, but inference under identifiable formulations is computationally challenging because of constraints on the latent correlation structure. This dissertation develops efficient Bayesian methods for analyzing incomplete longitudinal binary and ordinal data using parameter-expanded multivariate probit models.
This dissertation considers three parameter-expanded Markov chain Monte Carlo (MCMC) algorithms: parameter-expanded Metropolis--Hastings (PX--MH), parameter-expanded Gibbs sampling (PX--GS), and parameter-expanded Gibbs sampling with marginalization (PX--GSM). The algorithms are extended within a unified multivariate probit framework to handle missing completely at random (MCAR) and missing at random (MAR) mechanisms through Bayesian data augmentation, jointly estimating regression coefficients, and correlation parameters for both longitudinal binary and ordinal data, with cut-point parameters estimated only for ordinal outcomes.
Extensive simulation studies compare the computational efficiency and inferential performance of the three algorithms under varying sample sizes and missingness settings. The methods are further illustrated using applications to health insurance coverage and life satisfaction data from the Panel Study of Income Dynamics.
Across both binary and ordinal outcomes, the proposed methods provide reliable parameter estimation while substantially improving posterior mixing and convergence relative to the identifiable formulation. The Gibbs sampling approaches consistently outperform the parameter-expanded Metropolis--Hastings algorithm in estimating correlation parameters, with PX--GS providing the best overall balance of computational efficiency and estimation accuracy for binary outcomes and PX--GSM demonstrating superior performance for ordinal outcomes. These results establish parameter-expanded multivariate probit models as efficient and practical tools for Bayesian analysis of incomplete longitudinal discrete data.
Recommended Citation
Acheampong, Stephen Kofi, "Bayesian Analysis for Longitudinal Binary and Ordinal Data with Missing Values Using Multivariate Probit Model", Campus Access Dissertation, Michigan Technological University, 2026.
https://digitalcommons.mtu.edu/etdr/2151