c01ed20.doc 07/19/01 4:12 PM 1 Estimating Realized Random Effects in Mixed Models

A common analysis objective is estimation of a realized random effect. The parameter underlying such an effect is usually defined as an average response of a realized unit, such as a cluster mean, domain mean, small area mean, or subject effect. The effects are called random effects since their occurrence is the result of some (actual or assumed) random sampling process. In mixed models, random effects are commonly predicted using best linear unbiased predictors (BLUP). We develop an estimate of a realized random effect under a simple finite population two stage random permutation model using a prediction based approach. The estimate differs from the usual BLUP estimate, but is identical to the commonly used estimate of Scott and Smith (1969) that account for finite population sampling. We show that the es imate, and the MSE of the estimate will be identical with two variance structures, Scott and Smith's and the random permutation variance using a particular re-parameterization of the variance components. The model assumptions correspond to those typically used in survey sampling. The estimator is developed in a balanced setting, and extended to include possible response error. c01ed20.doc 07/19/01 4:12 PM 2 1