  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.
