Bayesian analysis of longitudinal data via empirical likelihood

Abstract

Longitudinal data consists of repeated observations that are typically correlated, which makes the likelihood-based inference challenging. This limits the use of Bayesian methods for longitudinal data in many general situations. To address this issue, empirical likelihood is used to develop a fully Bayesian method for analyzing longitudinal data based on a set of moment equations parallel to the form of generalized estimating equations. It is demonstrated in the context of two popular priors for Bayesian inference and regularization, the Laplace prior and the horseshoe prior. The proposed Bayesian shrinkage method performs well in both estimation accuracy and variable selection, while also providing a full quantification of uncertainty. The method is illustrated using a yeast cell-cycle microarray time course gene expression data set.