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Thresholding Nonprobability Units in Combined Data for Efficient Domain

Terrance D Savitsky, Matthew R Williams, Vladislav Beresovsky, and Julie Gershunskaya

Abstract

Quasi-randomization approaches estimate latent participation probabilities for units from a nonprobability / convenience sample. Es-timation of participation probabilities for convenience units allows their combination with units from the randomized survey sample to form a sur-vey weighted domain estimate. One leverages convenience units for domain estimation under the expectation that estimation precision and bias will improve relative to solely using the survey sample; however, convenience sample units that are very different in their covariate support from the survey sample units may inflate estimation bias or variance. This paper de-velops a method to threshold or exclude convenience units to minimize the variance of the resulting survey weighted domain estimator. We compare our thresholding method with other thresholding constructions in a simu-lation study for two classes of datasets based on degree of overlap between survey and convenience samples on covariate support. We reveal that ex-cluding convenience units that each express a low probability of appearing in both reference and convenience samples reduces estimation error.