Thresholding nonprobability units in combined data for efficient domain estimation

Quasi-randomization approaches estimate latent participation probabilities for units from a nonprobability / convenience sample. Estimation of participation probabilities for convenience units allows their combination with units from the randomized survey sample to form a survey-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 develops 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 simulation study for two classes of datasets based on the degree of overlap between survey and convenience samples on covariate support. We reveal that excluding convenience units that each express a low probability of appearing in both reference and convenience samples reduces estimation error.