“Optimal” Estimation of Correlated Response Variance under Additive Models

原文摘要

Additive models are often employed to measure the impact of response errors on the accuracy of survey estimates. An important feature of these models is that the correlated errors from specified error sources, such as interviewers and coders, contribute additive components, called correlated response variance (CRV) components, to the total variance of a survey estimator. As a result of these correlated components, the usual estimators of variance of a mean or a total are negatively biased, thus overstating the reliability of estimates. The underestimation, however, can be reduced or eliminated if estimates of CRV components are available. Further, the estimated CRV components can be employed as measures of quality of the particular operation(s) under investigation, for example, interviewer performance. The method of minimum norm quadratic unbiased estimation, due to C. R. Rao, is applied to obtain “optimal” estimators of CRV from interviewer variance experiments involving both interpenetrated and noninterpenetrated interviewer assignments (interpenetration means random assignment of sample units within an enumeration area to two or more interviewers). A computationally convenient expression for the minimum norm quadratic unbiased (MINQU) estimators is derived. Efficiency of the MINQU estimator relative to the analysis of variance estimators of Fellegi, the composite estimator of Biemer and Stokes, and the MINQU estimator from interpenetrated data alone is evaluated in the balanced case of equal error variances and equal work loads across enumeration areas.

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