Propensity Score Estimation Using Density Ratio Model under Item Nonresponse

Missing data is frequently encountered in practice. Propensity score estimation is a popular tool for handling such missingness. The propensity score is often developed using the model for the response probability, which can be subject to model misspecification. In this paper, we consider an alternative approach of estimating the inverse of the propensity scores using the density ratio function. By partitioning the sample into two groups based on the response status of the elements, we can apply the density ratio function estimation method and obtain the inverse propensity scores for nonresponse adjustment. Density ratio estimation can be obtained by applying the so-called maximum entropy method, which uses the Kullback-Leibler divergence measure under calibration constraints. By including the covariates for the outcome regression models only into the density ratio model, we can achieve efficient propensity score estimation. We further extend the proposed approach to the multivariate missing case. Some limited simulation studies are presented to compare with the existing methods.