Nonresponse weighting is a common method for handling unit nonresponse in surveys. A widespread view is that the weighting method is aimed at reducing nonresponse bias, at the expense of an increase in variance. Hence, the efficacy of weighting adjustments becomes a bias-variance trade-off. This note suggests that this view is an oversimplification -- nonresponse weighting can in fact lead to a reduction in variance as well as bias. A covariate for a weighting adjustment must have two characteristics to reduce nonresponse bias - it needs to be related to the probability of response, and it needs to be related to the survey outcome. If the latter is true, then weighting can reduce, not increase, sampling variance. A detailed analysis of bias and variance is provided in the setting of weighting for an estimate of a survey mean based on adjustment cells. The analysis suggests that the most important feature of variables for inclusion in weighting adjustments is that they are predictive of survey outcomes; prediction of the propensity to respond is a secondary, though useful, goal. Empirical estimates of root mean squared error for assessing when weighting is effective are proposed and evaluated in a simulation study.
Design of Experiments and Sample Surveys
Little, Rod and Vartivarian, Sonya L., "Does Weighting for Nonresponse Increase the Variance of Survey Means?" (April 2004). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 35.