Superpopulation model inference for non-probability samples under informative sampling

Abstract

Non-probability samples have been extensively applied in many various fields in recent years. However, it is difficult to infer the population from non-probability samples since selection probabilities of non-probability samples is unknown. Superpopulation modeling has been recently explored to make inference from non-probability samples. However, the existing superpopulation model approaches rely mostly on the noninformative sampling assumption. When sampling is informative, the sample distribution differs from the population distribution. Ignoring this point may result in biased estimation. In this paper, taking into account the informative sampling scheme, a superpopulation model approach for non-probability samples is proposed. Exponential model, logistic model and probit model are established to explain the informative sampling mechanism, respectively. The sample likelihood is derived to estimate the superpopulation model parameters for non-probability samples under various informative sampling models. The population mean estimator can be obtained based on the fitted superpopulation model from non-probability samples under different informative sampling approaches. The theoretical properties of the proposed estimator are established. Simulation results illustrate the performance of our proposed method for different informative sampling models and sample sizes. Also, the proposed method is applied to the data from the National Health and Nutrition Examination Survey.