Using Auxiliary Information in Probability Survey Data to Improve Pseudo-Weighting in Nonprobability Samples: A Copula Model Approach

Abstract While probability sampling has been considered the gold standard of survey methods, nonprobability sampling is increasingly popular due to its convenience and low cost. However, nonprobability samples can lead to biased estimates due to the unknown nature of the underlying selection mechanism. In this article, we propose parametric and semiparametric approaches to integrate probability and nonprobability samples using common ancillary variables observed in both samples. In the parametric approach, the joint distribution of ancillary variables is assumed to follow the latent Gaussian copula model, which is flexible to accommodate both categorical and continuous variables. In contrast, the semiparametric approach requires no assumptions about the distribution of ancillary variables. In addition, logistic regression is used to model the mechanism by which population units enter the nonprobability sample. The unknown parameters in the copula model are estimated through the pseudo maximum likelihood approach. The logistic regression model is estimated by maximizing the sample likelihood constructed from the nonprobability sample. The proposed method is evaluated in the context of estimating the population mean. Our simulation results show that the proposed method is able to correct the selection bias in the nonprobability sample by consistently estimating the underlying inclusion mechanism. By incorporating additional information in the nonprobability sample, the combined method can estimate the population mean more efficiently than using the probability sample alone. A real-data application is provided to illustrate the practical use of the proposed method.