Multiple bias calibration for valid statistical inference under nonignorable nonresponse

Valid statistical inference is notoriously challenging when the sample is subject to nonresponse bias. We approach this difficult problem by employing multiple candidate models for the propensity score (PS) function combined with empirical likelihood. By incorporating multiple working PS models into the internal bias calibration constraint in the empirical likelihood, the selection bias can be safely eliminated as long as the working PS models contain the true model and their expectations are equal to the true missing rate. The bias calibration constraint for the multiple PS models is called the multiple bias calibration. The study delves into the asymptotic properties of the proposed method and provides a comparative analysis through limited simulation studies against existing methods. To illustrate practical implementation, we present a real data analysis on body fat percentage using the National Health and Nutrition Examination Survey dataset.