The Implications of Ignoring the Uncertainty in Control Totals for Generalized Regression Estimators

• Activity Number: 625
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Jill Dever*+ and Richard Valliant
• Companies: RTI International and University of Maryland
• Keywords: survey-estimated control totals ; weight calibration ; generalized regression estimator (GREG) ; simulation ; mean square error (MSE)

Abstract

Calibration estimators borrow strength from auxiliary information to improve the efficiency of survey estimates over other forms such as a simple Horvitz-Thompson estimator. Improvements to the mean square error (MSE) are directly linked to the association of the study outcome and the auxiliary data. Generalized regression estimators, or GREGs, are particularly flexible because they can be used to calibrate survey weights to a variety of auxiliary control totals, and to produce a variety of estimators depending on the specified form of the linear model. However, it is rare to find control totals that are generated from the target population and therefore known without error, and also strongly related to the outcomes of interest. Many researchers instead turn to control totals estimated from other surveys, assuming a negligible impact on MSE. We add to our previous research on estimated-control calibration by developing the bias and variance estimators for a GREG total, accounting for the uncertainty in the control totals. Theoretical and empirical comparisons are made to traditional GREG estimators to demonstrate the implications for ignoring this uncertainty.