Nonlinear Superpopulation Model Inference for Non‐Probability Samples With Nonignorable Missingness

ABSTRACT In the era of big data and increasing survey costs, non‐probability samples become increasingly popular in sampling surveys but may be subject to selection biases with unknown inclusion probabilities. In addition to selection bias, non‐probability samples may also suffer from missingness in practice, even nonignorable nonresponse with unknown response probabilities. Superpopulation model methods have been discussed for reducing selection biases from non‐probability samples, but not for dealing with nonignorable missingness for non‐probability samples yet. In this paper, we propose a nonlinear superpopulation model inference approach for non‐probability samples with nonignorable missingness. We develop rigorous procedures for estimating the response probabilities for units in the non‐probability sample and the nonlinear superpopulation model parameters, and construct the finite population mean estimator based on the nonlinear superpopulation model, response probabilities, and inclusion probabilities. Asymptotic properties of the proposed estimators and variance estimation are also discussed under the proposed framework. In a simulation study, we compare the proposed method with some existing methods. The real data analysis results using the National Health Interview Survey data illustrate the good performance of the proposed method.