Bayesian Estimation of Marginal Quantiles with Missing Data in a Multivariate Regression Framework

In this article, we propose and study a class of multivariate regression models that account for ignorable missing data in skewed, potentially heavy-tailed response vectors with positive components. It can be used to estimate the marginal quantiles of the response vectors based on a set of covariates, while considering the potential association among the components of the response vectors. We adopt an MCMC Bayesian approach to perform the posterior analysis via a monotone data augmentation algorithm for data imputation. The satisfactory performance of the posterior distributions and the handling of missing data in quantile estimation are verified through simulation studies. The procedures are illustrated using real children's anthropometric data.