Date of Award


Document Type

Open Access Dissertation


Health Promotion, Education and Behavior



First Advisor

Bo Cai


Traditional frequentist quantile regression makes few assumptions on the form of the error distribution and thus is able to accommodate non-normal errors. However, inference on the quantile regression models could be challenging for the unknown error distribution, though asymptotic or resampling methods were developed. Bayesian literature on quantile regression with random effects is relatively limited. The quantile regression approach proposed in this dissertation is founded on Bayesian probabilistic modeling for the underlying unknown distributions. By adopting the error density with a nonparametric scale mixture models, we developed Bayesian semiparametric models to make an inference on any quantile of interest and to allow for flexible shapes of the error densities.

In this dissertation, we aimed to develop Bayesian semiparametric quantile regressions for both longitudinal data and clustered interval-censored data. We first proposed a semiparametric quantile mixed effect regression for clustered data, which relaxed normality assumption for both random effects and the error term. We then developed a semiparametric accelerated failure time quantile regression for the clustered interval-censored data. Both of the methods allow for estimates for the subgroup specific parameters and the detection of heterogeneity in the random effects population under nonparametric settings. Markov chain Monte Carlo (MCMC) methods provide computationally feasible implementations of Bayesian inference and learning. However, the speed of convergence can be challenging for highly complex and nonconjugate models. Specifically, Gibbs sampling algorithm that employs the addition of auxiliary parameters was used to speed up posterior sampling in our study. Several variations of the proposed model were considered and compared via the deviance information criterion. The performance of the proposed methods was evaluated by extensive simulation studies, and examples using data from Orthodontic clinics and lymphatic filariasis drug studies were presented as illustration.