Investigating an Alternative for Estimation from a Nonprobability Sample: Matching plus Calibration

Matching a nonprobability sample to a probability sample is one strategy both for selecting the nonprobability units and for weighting them. This approach has been employed in the past to select subsamples of persons from a large panel of volunteers. One method of weighting, introduced here, is to assign a unit in the nonprobability sample the weight from its matched case in the probability sample. The properties of resulting estimators depend on whether the probability sample weights are inverses of selection probabilities or are calibrated. In addition, imperfect matching can cause estimates from the matched sample to be biased so that its weights need to be adjusted, especially when the size of the volunteer panel is small. Calibration weighting combined with matching is one approach to correct bias and reduce variances. We explore the theoretical properties of the matched and matched, calibrated estimators with respect to a quasirandomization distribution that is assumed to describe how units in the nonprobability sample are observed, a superpopulation model for analysis variables collected in the nonprobability sample, and the randomization distribution for the probability sample. Numerical studies using simulated and real data from the 2015 US Behavioral Risk Factor Surveillance Survey are conducted to examine the performance of the alternative estimators.