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Methods for combining probability and nonprobability samples under unknown overlaps

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Savitsky T. D., Williams M. R., Gershunskaya J., Beresovsky V.

Statistics in Transition new series

2023

vol. 24

issue 5

1-34

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.

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1 Statistics in Transition new series

1 Beresovsky V.

1 Gershunskaya J.

1 Savitsky T. D.

1 Williams M. R.

1 2023

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Methods for combining probability and nonprobability samples under unknown overlaps