Correcting Selection Bias in Big Data by Pseudo-Weighting.

This article focuses on extending the pseudo-weight estimation method originally proposed by Elliott and Valliant (EV) to correct selection bias in nonprobability samples by leveraging a two-sample setup involving both probability and nonprobability samples drawn from the same population. The extension relaxes the original assumption that the two samples do not overlap, allowing for large sampling fractions and potential overlap between samples, which are common in administrative and Big Data contexts. The authors propose new estimators for inclusion probabilities that account for possible dependency between the samples and introduce pseudo population bootstrap algorithms for variance estimation applicable to a wide range of sampling designs and propensity models. A simulation study based on Dutch vehicle registration data demonstrates that the proposed methods outperform existing approaches in bias and root mean square error, particularly when accounting for sample dependency, and provide reliable variance estimates. Limitations include assumptions about sample quality, availability of design variables or unique identifiers, and challenges in identifying overlapping units, with suggestions for practical alternatives and further improvements discussed.