Calibration weighting with a blended (probability and nonprobability) sample: Mean and variance estimation when errors can come from both samples

Abstract

We show how calibration weighting can be employed to combine a probability and a nonprobability sample of the same population in a statistically defensible manner. This is done by assuming that the probability of a population element being included in the nonprobability sample can be modeled as a logit function of variables known for all members of both samples. Estimating these probabilities for the members of the nonprobability sample with a calibration equation and treating their inverses as quasi-probability weights is a key to creating composite weights for the blended sample. We use the WTADJX procedure in SUDAAN® to generate those weights and then measure the standard errors of the resulting estimated means and totals as well as assess the potential for bias in those estimates. The appendix contains the SAS-callable code for the SUDAAN procedures used in this paper.