Providing double protection for unit nonresponse with a nonlinear calibration routine

Abstract

There are at least two reasons to calibrate survey weights: force estimators to be unbiased under a prediction model and adjust for the bias caused by unit nonresponse. Although a prediction-model justification is possible, Lundströrm and Särndal (1999) argued that a unit's weight adjustment under calibration estimates the inverse of the unit's response probability. The functional form of the response model in their linear calibration adjustment is awkward and unlikely. We describe a nonlinear calibration procedure available in SUDAAN that includes a logistic response model, generalized raking, and bounds the weight adjustments limiting their inflationary impact on mean squared errors. Using this procedure provides double protection against nonresponse bias. If the linear prediction model or implied unit response model holds, the resulting estimator is asymptotically unbiased.