Estimation for Volunteer Panel Web Surveys Using Propensity Score Adjustment and Calibration Adjustment

A combination of propensity score and calibration adjustment is shown to reduce bias in volunteer panel Web surveys. In this combination, the design weights are adjusted by propensity scores to correct for selection bias due to nonrandomized sampling. These adjusted weights are then calibrated to control totals for the target population and correct for coverage bias. The final set of weights is comprised of multiple components, and the estimator of a total no longer takes a linear form. Therefore, approximate methods are needed to derive variance estimates. This study compares three variance estimation methods through simulation. The first method resembles what is used in commercial statistical software based on squared residuals. The second approach uses a variance estimator originally derived for the generalized regression estimator. The third method uses jackknife replication. Results indicate bias reduction is crucial for valid variance estimation and favor the replication method over the other approaches.