Bayesian Sparse Propensity Score Estimation for Unit Nonresponse

TL;DR

This paper introduces a Bayesian sparse propensity score estimation method using Spike-and-Slab priors to efficiently handle high-dimensional auxiliary variables in nonresponse adjustment, avoiding model misspecification and improving estimation consistency.

Contribution

It proposes a novel Bayesian approach that simultaneously performs variable selection and estimation for propensity scores without outcome model assumptions.

Findings

Method is computationally efficient and theoretically sound.

Simulation studies show improved estimation accuracy.

Application to real data demonstrates practical utility.

Abstract

Nonresponse weighting adjustment using propensity score is a popular method for handling unit nonresponse. However, including all available auxiliary variables into the propensity model can lead to inefficient and inconsistent estimation, especially with high-dimensional covariates. In this paper, a new Bayesian method using the Spike-and-Slab prior is proposed for sparse propensity score estimation. The proposed method is not based on any model assumption on the outcome variable and is computationally efficient. Instead of doing model selection and parameter estimation separately as in many frequentist methods, the proposed method simultaneously selects the sparse response probability model and provides consistent parameter estimation. Some asymptotic properties of the proposed method are presented. The efficiency of this sparse propensity score estimator is further improved by incorporating related auxiliary variables from the full sample. The finite-sample performance of the proposed method is investigated in two limited simulation studies, including a partially simulated real data example from the Korean Labor and Income Panel Survey.