Improved Sampling Weight Calibration by Generalized Raking with Optimal Unbiased Modification

Traditional methods for sampling weight adjustment involve weighting class adjustment for nonresponse bias reduction, followed by post-stratification (raking-ratio or regression) adjustment for coverage bias reduction, and then trimming (or winsorization) of extreme weights for variance reduction followed by final post-stratification to meet desired control totals and for further variance reduction. Using calibration methods (or generalized raking), the nonresponse weight adjustment can be considerably simplified and improved by relying on external control totals for nonresponse predictors (or auxiliary variables) instead of frame level information for the full sample, resulting typically in a rich set of auxiliary variables. Moreover, this allows in general for a simplification of the process by eliminating the post-stratification step after the nonresponse bias adjustment as long as the set of auxiliary variables used is deemed adequate for post-stratification. However, in calibration methods, there is no built-in mechanism for ensuring variance reduction although generally it does lead to variance reduction. Besides, the nature of the commonly used method of weight trimming before final post-stratification is ad hoc and likely to introduce bias although it is expected to reduce variance. We propose modeling to smooth extreme weights instead of trimming, and introduce new (super) stratum-specific scale parameters in the calibration (or generalized raking) model to capture possibly varying design characteristics by strata or super-strata. The new calibration model with extra parameters maintains approximate unbiasedness of calibration estimators for which the new parameters are estimated outside the calibration equations by minimizing the generalized variance of key study variables or alternatively the unequal weighting effect for simplicity. Using a hypothetical calibration problem based on the 2011 National Immunization Survey (NIS) public use file data, an illustrative example of the proposed method is presented.