Adjusting for Selection Bias in Nonprobability Samples by Empirical Likelihood Approach

Large amount of data are today available, that are easier and faster to collect than survey data, bringing new challenges. One of them is the nonprobability nature of these big data that may not represent the target population properly and hence result in highly biased estimators. In this article two approaches for dealing with selection bias when the selection process is nonignorable are discussed. The first one, based on the empirical likelihood, does not require parametric specification of the population model but the probability of being in the nonprobability sample needed to be modeled. Auxiliary information known for the population or estimable from a probability sample can be incorporated as calibration constraints, thus enhancing the precision of the estimators. The second one is a mixed approach based on mass imputation and propensity score adjustment requiring that the big data membership is known throughout a probability sample. Finally, two simulation experiments and an application to income data are performed to evaluate the performance of the proposed estimators in terms of robustness and efficiency.