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Nonresponse weighting adjustment using the response propensity score is apopular tool for handling unit nonresponse. Statistical inference after thenonresponse weighting adjustment is complicated because the effect ofestimating the propensity model parameter needs to be incorporated. In thispaper, we propose an approximate Bayesian approach to handle unit nonresponsewith parametric model assumptions on the response probability, but withoutmodel assumptions for the outcome variable. The proposed Bayesian method iscalibrated to the frequentist inference in that the credible region obtainedfrom the posterior distribution asymptotically matches to the frequentistconfidence interval obtained from the Taylor linearization method. Unlike thefrequentist approach, however, the proposed method does not involve Taylorlinearization. The proposed method can be extended to handle over-identifiedcases in which there are more estimating equations than the parameters.Besides, the proposed method can also be modified to handle nonignorablenonresponse. Results from two simulation studies confirm the validity of theproposed methods, which are then applied to data from a Korean longitudinalsurvey.

An approximate Bayesian inference on propensity score estimation under unit nonresponse