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 maynot represent the target population properly and hence result in highly biased estimators. Inthis article two approaches for dealing with selection bias when the selection process isnonignorable are discussed. The first one, based on the empirical likelihood, does not requireparametric specification of the population model but the probability of being in thenonprobability sample needed to be modeled. Auxiliary information known for the populationor estimable from a probability sample can be incorporated as calibration constraints, thusenhancing the precision of the estimators. The second one is a mixed approach based on massimputation and propensity score adjustment requiring that the big data membership is knownthroughout a probability sample. Finally, two simulation experiments and an application toincome data are performed to evaluate the performance of the proposed estimators in terms ofrobustness and efficiency.