General Regression Estimation Adjusted for Undercoverage and Estimated Control Totals

Survey weight calibration, such as raking and poststratification, incorporates auxiliary information to reduce undercoverage bias and to increase the efficiency of survey estimates. The control totals used in the standard calibration techniques are assumed to be population values. Often, however, these controls are estimated from other surveys. Many researchers apply standard calibration variance formulas to situations where the control totals are estimated, thus assuming any additional sampling variance associated with these controls is negligible. The findings presented in this article add to the body of research on estimated-control (EC) calibration, which suggests that these control totals are useful for bias reduction and the variation in the control total estimates is not always ignorable. Using theory, we evaluate bias and variance for an EC-calibrated general regression estimator of a population mean, calculated as the ratio of two estimated totals, for stratified, multistage designs. Simulation studies provide the empirical justification for the theory where effects on the variance from different levels of precision in the estimated controls are shown. Our research suggests that (i) calibration to design-unbiased estimated controls can reduce bias; (ii) standard variance estimators can seriously underestimate the theoretical variance; and (iii) two newly developed EC-calibration variance estimators—one linearization and one replication—can mitigate the negative bias.