“Optimal” Estimation of Correlated Response Variance under Additive Models
Abstract 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...