Correcting Selection Bias in a Non-Probability Two-Phase Payment Survey

We develop statistical inferences for a non-probability two-phase survey sample when relevant auxiliary information is available from a probability survey sample. To reduce selection bias and gain efficiency, both selection probabilities of Phase 1 and Phase 2 are estimated, and two-phase calibration is implemented. We discuss both analytical plug-in and pseudo-population bootstrap variance estimation methods that account for the effects of using estimated selection probabilities and calibrated weights. The proposed method is assessed by simulation studies and used to analyze a non-probability two phase payment survey.