Nonresponse weighting is often accompanied by an increase in variance, and the efficacy of weighting adjustments is seen as a bias-variance trade-off. In order to reduce nonresponse bias, the covariate for weighting adjustment must be related to the probability of response and also to the survey outcome. The authors derive an expression that captures both bias and variance components. A detailed analysis of bias and variance is provided in the setting of weighting for an estimate of survey mean based on adjustment of cells. The analysis suggests that the most important feature of variables for inclusion in weighting adjustment is that they are predictive of survey outcomes. In such a case, the weighting can reduce, not increase, sampling variance. A simulation study finds that a simple composite estimator based on the empirical root mean squared error (MSE) yields some gains over the weighted estimator.
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