c01ed20.doc 3/19/01 6:51 AM 1 Estimating Realized Random Effects in Mixed Models

A common analysis objective is estimation of realized random effects. Parameters underlying these effects are usually defined as cluster means, domain means, small area means, or subject effects. The effects are called random effects since their occurrence is the result of some random sampling process. In mixed models, random effects are commonly predicted using best linear unbiased predictors (BLUP). But what is really being estimated? We illustrate that although realized random effects appear to be eliminated from the usual exchangeable random variables, a full representation of the population allows the effects to be defined. Accounting for the finite population sizes in a balanced two stage random permutation framework, we use methods that parallel the typical superpopulation model survey sampling approach to develop estimators of realized random effects. The estimates incorporate finite population correction factors inherent in the finite population. The framework is non-parameteric, frequency based, and does not require additional assumptions that usually accompany superpopulations. Although the new estimators are proposed for a balanced setting, the direction for extensions to unbalanced settings, and response error are given. c01ed20.doc 3/19/01 6:51 AM 2 1