Combining non-probability and probability survey samples through mass imputation

Analysis of non-probability survey samples requires auxiliary information at the population level. Such information may also be obtained from an existing probability survey sample from the same finite population. Mass imputation has been used in practice for combining non-probability and probability survey samples and making inferences on the parameters of interest using the information collected only in the non-probability sample for the study variables. Under the assumption that the conditional mean function from the non-probability sample can be transported to the probability sample, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies. We also address important practical issues of the method through the analysis of a real-world non-probability survey sample collected by the Pew Research Centre