Bayesian Analysis of Semiparametric Generalized Linear Mixed Effect Model with Missing Responses

摘要

Semiparametric generalized linear mixed effect models (SPGLMMs) are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariates effects, and random effects to account for the within-subject correlation. In this paper, Bayesian inference of SPGLMMs for longitudinal data with missing outcomes which arise frequently from various scientific areas is considered, and the missingness mechanism is assumed to be missing at random (MAR). The main idea of this article is that the nonparametric function is modeled via a Bayesian formulation of p-spline, while the random effect is assumed to be distributed as a normal distribution. In order to avoid the impropriety, we propose a uniform shrinkage prior for the variance components and the smoothing parameter, then, a Markov Chain Monte Carlo(MCMC) method which combines Gibbs sampler with M-H algorithm as well as Metropolized independence sampler is employed for carry out posterior computation. Finally, a simulation study is used to illustrate the proposed methodologies.