Methods for combining probability and nonprobability samples under unknown overlaps

Terrance D. Savitsky; Matthew R. Williams; Julie Gershunskaya; Vladislav Beresovsky

doi:https://doi.org/10.59170/stattrans-2023-061

Methods for combining probability and nonprobability samples under unknown overlaps

Terrance D. Savitsky 1Office of Survey Methods Research, U.S. Bureau of Labor Statistics, USA. ORCID:https://orcid.org/0000-0003-1843-3106 , Matthew R. Williams RTI International, USA ORCID:https://orcid.org/0000-0001-8894-1240 , Julie Gershunskaya OEUS Statistical Methods Division, U.S. Bureau of Labor Statistics, USA ORCID:https://orcid.org/0000-0002-0096-186X , Vladislav Beresovsky Office of Survey Methods Research, U.S. Bureau of Labor Statistics, USA ORCID:https://orcid.org/0009-0002-8375-5195 Statistics in Transition new series, vol. 24, 2023, 5, pages: 1-34 Published online: 7 December 2023 https://doi.org/10.59170/stattrans-2023-061 Citation: Savitsky, T. D., Williams, M. R., Gershunskaya, J., Beresovsky, V., 2023. Methods for combining probability and nonprobability samples under unknown overlaps. Statistics in Transition new series, 24(5), pp. 1-34. https://doi.org/10.59170/stattrans-2023-061

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ABSTRACT

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated 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 distribution. A recent set of approaches estimates 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 inclusion probabilities for the reference and convenience samples as our main result. Our approach allows specification of a likelihood directly for the observed sample as opposed to the approximate or pseudo likelihood. We construct a Bayesian hierarchical formulation that simultaneously estimates sample propensity scores and the convenience sample inclusion probabilities. We use a Monte Carlo simulation study to compare our likelihood based results with the pseudo likelihood based approaches considered in the literature.

KEYWORDS

Survey sampling, Nonprobability sampling, Data combining, Inclusion probabilities, Exact sample likelihood, Bayesian hierarchical modeling.

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