Using calibration weighting to adjust for nonignorable unit nonresponse
When calibration weighting is be used to adjust for unit nonresponse in a sample survey, the response/nonresponse mechanism is often assumed to be a function of a set of covariates, which we call “model variables.” These model variables usually also serve as the benchmark variables in the calibration equation. In principle, however, the model variables do not have to coincide with the benchmark variables. Since the model-variable values need only be known for the respondents, this allows the treatment of what is usually considered nonignorable nonresponse in the prediction approach to survey sampling. One can invoke either a quasi-randomization or prediction approach to justify calibration weighting as a means for adjusting for nonresponse. Both frameworks rely on unverifiable model assumptions, and both require large samples to produce nearly unbiased estimators even when those assumptions hold. We will explore these issues theoretically using a joint framework and with an empirical study.