Estimation of a Population Total Under Nonresponse Using Follow-up

In this article, we propose methods to minimize bias due to unit nonresponse. We consider a two-phase sampling design where the second phase is a probability subsample of nonrespondents from the first phase. In this context, we propose three weighting procedures to estimate the total when not all units in the subsample respond. The weighting is based on the response homogeneity group (RHG) model. Given the RHG model, theoretical results on bias and variance estimation are obtained for all estimators. In a simulation study, we evaluate the empirical properties of the three estimators as well as of estimators based on two commonly used procedures to handle unit nonresponse in single-phase sampling design. These two procedures include: (i) nonresponse calibration weighting, also known as the one-step approach, and (ii) nonresponse probability weighting followed by calibration, also known as the two-step approach. Our results indicate that when there is significant deviation from the assumed RHG model, the nonresponse follow-up estimators perform better in terms of bias and coverage.