Commonly employed weighting methods to address nonresponse generally lead to reduced precision, spurring trade-offs between bias and variance. Corrections for measurement error are rare and left to methodological case studies. Unit nonresponse, item nonresponse, and measurement error can be addressed through multiple imputation, making use of frame data, paradata, and survey data with varying levels of missingness. Compared to weighting nonresponse adjustment as typically implemented, multiple imputation offers the potential for lower variances and total survey error (MSE), and doing so for multiple sources of error.
This approach was applied to data from a study that includes a rich sampling frame, paradata, and replicate measures less prone to measurement error. The two error sources seemed to be orthogonal in these data. Imputation was used to provide estimates of each source of bias, finding that measurement error bias was almost three times larger than nonresponse bias. Although the same conclusion was reached through weighting, multiple imputation yielded substantially lower variance estimates and estimates of MSE. Standard errors were 3.6 times smaller and MSE was 3.4 to 16.0 times smaller under multiple imputation. Moreover, variances were also substantially lower than in the complete case analysis. Further research is needed, yet this approach has theoretical and practical advantages over current practice, such as reducing costs and respondent burden resulting from the need to collect fewer data to meet precision objectives, by making more frugal use of auxiliary information.
