On the formation of weighting class adjustments for unit nonresponse in sample surveys.

Abstract

Response rates are declining in many sample surveys. Nonresponse is a serious problem because of the potential bias and loss of efficiency due to missing information. Unit nonresponse occurs when entire interviews are missing due to noncontact or participant refusal. Weighting is the standard method of unit nonresponse adjustment, where responding units are weighted inversely proportional to the probability of selection and response. This thesis considers three important problems in unit nonresponse weighting. First, we examine when weighting for nonresponse improves estimates of population means. A widespread view is that nonresponse weights aim at reducing nonresponse bias, at the expense of an increase in variance, resulting in a bias-variance trade-off. We present a detailed analysis of the bias and variance that suggests that this view is an oversimplification---nonresponse weighting can in fact lead to a reduction in variance as well as bias. The analysis suggests that predictiveness of the survey outcome is the most important feature of covariates for inclusion in weighting adjustments; prediction of the propensity to respond is a secondary, if useful, goal. In the second problem, the role of the sampling weights in the definition of the nonresponse weight is considered. Two approaches to incorporating the sampling weight information are: (a) to compute a nonresponse weight that is the inverse of the sample-weighted response rate and (b) to compute a nonresponse weight that is the inverse of the unweighted response rate within adjustment cells from a classification of both survey and design variables. Approach (a) is the more common approach in current surveys. Simulations are conducted to demonstrate that approach (b) is superior. The third problem examines a coarsening method for reducing the number of adjustment cells. Simulations indicate improved efficiency and robustness of weighting adjustments based on the joint classification by the response propensity and the predictive mean. Predictive mean stratification has the disadvantage that it leads to a different set of weights for each key outcome. This research suggests basing the predictive mean dimension on a single canonical variate; simulations show that efficiency is somewhat comparable to predictive stratification alone.