Estimation of measurement bias using a model prediction approach

Abstract

Methods for estimating response bias in surveys require "unbiased" remeasurements for at least a subsample of observations. The usual estimator of response bias is the difference between the mean of the original observations and the mean of the unbiased observations. In this article, we explore a number of alternative estimators of response bias derived from a model prediction approach. The assumed sampling design is a stratified two-phase design implementing simple random sampling in each phase. We assume that the characteristic, y, is observed for each unit selected in phase 1 while the true value of the characteristic, µ, is obtained for each unit in the subsample selected at phase 2. We further assume that an auxiliary variable x is known for each unit in the phase 1 sample and that the population total of x is known. A number of models relating y, µ and x are assumed which yield alternative estimators of E(y - µ), the response bias. The estimators are evaluated using a bootstrap procedure for estimating variance, bias, and mean squared error. Our bootstrap procedure is an extension of the Bickel-Freedman single phase method to the case of a stratified two-phase design. As an illustration, the methodology is applied to data from the National Agricultural Statistics Service reinterview program. For these data, we show that the usual difference estimator is outperformed by the model-assisted estimator suggested by Särndal, Swensson and Wretman (1991), thus indicating that improvements over the traditional estimator are possible using the model prediction approach.