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Three approaches to estimation from nonprobability samples are quasi-randomization, superpopulation modeling, and doubly robust estimation. In the first, the sample is treated as if it were obtained via a probability mechanism, but unlike in probability sampling, that mechanism is unknown. Pseudo selection probabilities of being in the sample are estimated by using the sample in combination with some external data set that covers the desired population. In the superpopulation approach, observed values of analysis variables are treated as if they had been generated by some model. The model is estimated from the sample and, along with external population control data, is used to project the sample to the population. The specific techniques are the same or similar to ones commonly employed for estimation from probability samples and include binary regression, regression trees, and calibration. When quasi-randomization and superpopulation modeling are combined, this is referred to as doubly robust estimation. This article reviews some of the estimation options and compares them in a series of simulation studies.

Comparing Alternatives for Estimation from Nonprobability Samples