Hierarchical Bayesian Analysis of Repeated Binary Data with Missing Covariates

Missing covariates are a common problem in many biomedical and environmental studies. In this chapter, we develop a hierarchical Bayesian method for analyzing data with repeated binary responses over time and time-dependent missing covariates. The fitted model consists of two parts: a generalized linear mixed probit regression model for the repeated binary responses and a joint model to incorporate information from different sources for time-dependent missing covariates. A Gibbs sampling algorithm is developed for carrying out posterior computation. The importance of the covariates is assessed via the deviance information criterion. We revisit the real plant dataset considered by Huang et al. (2008) and use it to illustrate the proposed methodology. The results from the proposed methods are compared with those in Huang et al. (2008). Similar top models and estimates of model parameters are obtained by both methods.