Methods for Combining Probability and Nonprobability Samples Under Unknown Overlaps

Abstract

Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size. Estimation of a population quantity derived from a convenience sample will typically result in bias since the distribution of variables of interest in the convenience sample is different from the population. A recent set of approaches estimates conditional (on sampling design predictors) inclusion probabilities for convenience sample units by specifying reference sample-weighted pseudo likelihoods. This paper introduces a novel approach that derives the propensity score for the observed sample as a function of conditional inclusion probabilities for the reference and convenience samples