Doubly robust estimation for non-probability samples with heterogeneity

With the development of network technology and the rise of big data, non-probability sampling has wider applications in practice. However, it brings a challenge to make inference from non-probability samples since the inclusion probabilities of non-probability samples are unknown. The propensity score approach, superpopulation model approach, doubly robust estimation are three main methods to infer the population from non-probability samples. However, the first two methods are sensitive to the misspecified models. Thus, they cannot generate desirable performances when deal with heterogeneous non-probability samples. In this paper, a doubly robust estimation method for non-probability samples with heterogeneous data is proposed. A heterogeneous superpopulation model is fitted based on a heterogeneous non-probability sample and used to construct a doubly robust estimator for the population mean. Specifically, the inverse estimated inclusion probabilities of the non-probability sample are added into the estimating equation as weights in model parameter estimation. The simulation results confirm that the proposed method outperforms the other contrastive methods in terms of bias, standard deviation and mean square error. Its application is illustrated with the Pew Research Center dataset and the Behavioral Risk Factor Surveillance System dataset, which is consistent with the simulation results.