Bayesian Semiparametric Modeling of Response Mechanism for Nonignorable Missing Data

TL;DR

This paper introduces a Bayesian semiparametric approach for handling nonignorable missing data, combining flexible response models with efficient computation, demonstrated through simulations and real data analysis.

Contribution

It proposes a novel Bayesian semiparametric framework with penalized splines and radial basis functions for modeling nonresponse mechanisms in missing data problems.

Findings

Effective in simulation studies

Handles nonignorable missing data robustly

Demonstrated on longitudinal data

Abstract

Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To avoid the misspecification, we propose semiparametric Bayesian estimation in which an outcome model is parametric, but the response model is semiparametric in that we do not assume any parametric form for the nonresponse variable. We adopt penalized spline methods to estimate the unknown function. We also consider a fully nonparametric approach to modeling the response mechanism by using radial basis function methods. Using Polya-gamma data augmentation, we developed an efficient posterior computation algorithm via Gibbs sampling in which most full conditional distributions can be obtained in familiar forms. The performance of the proposed method is demonstrated in simulation studies and an application to longitudinal data.