Bayesian Adaptive Lasso for Regression Models with Nonignorable Missing Responses

Abstract

The main purpose of this article is to develop a Bayesian adaptive lasso procedure for analyzing linear regression models with nonignorable missing responses, in which the missingness mechanism is specified by a logistic regression model. A sampling procedure combining the Gibbs sampler and Metropolis-Hastings algorithm is employed to obtain the Bayesian estimates of the regression coefficients, shrinkage coefficients, missingness mechanism models parameters, and their standard errors. We extend the partial posterior predictive $p$ value for goodness-of-fit statistic to investigate the plausibility of the posited model. Finally, several simulation studies and the air pollution data example are undertaken to demonstrate the newly developed methodologies.