INVESTIGATION OF ALTERNATIVE CALIBRATION ESTIMATORS IN THE PRESENCE OF NONRESPONSE
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Calibration weighting is widely used to decrease variance, reduce nonresponse bias, and improve the face validity of survey estimates. In the purely sampling context, Deville and Särndal (1992) demonstrate that many alternative forms of calibration weighting are asymptotically equivalent, so for variance estimation purposes, the generalized regression (GREG) estimator can be used to approximate some general calibration estimators with no closed-form solutions such as raking. It is unclear whether this conclusion holds when nonresponse exists and single-step calibration weighting is used to reduce nonresponse bias (i.e., calibration is applied to the basic sampling weights directly without a separate nonresponse adjustment step). In this dissertation, we first examine whether alternative calibration estimators may perform differently in the presence of nonresponse. More specifically, properties of three widely used calibration estimations, the GREG with only main effect covariates (GREG_Main), poststratification, and raking, are evaluated. In practice, the choice between poststratification and raking are often based on sample sizes and availability of external data. Also, the raking variance is often approximated by a linear substitute containing residuals from a GREG_Main model. Our theoretical development and simulation work demonstrate that with nonresponse, poststratification, GREG_Main, and raking may perform differently and survey practitioners should examine both the outcome model and the response pattern when choosing between these estimators. Then we propose a distance measure that can be estimated for raking or GREG_Main from a given sample. Our analytical work shows that the distance measure follows a Chi-square probability distribution when raking or GREG_Main is unbiased. A large distance measure is a warning sign of potential bias and poor confidence interval coverage for some variables in a survey due to omitting a significant interaction term in the calibration process. Finally, we examine several alternative variance estimators for raking with nonresponse. Our simulation results show that when raking is model-biased, none of the linearization variance estimators under evaluation is unbiased. In contrast, the jackknife replication method performs well in variance estimation, although the confidence interval may still be centered in the wrong place if the point estimate is inaccurate.