Optimality Criteria for Models with Random Effects

In the context of linear models, an optimality criterion is developed for models that include random effects. Traditional information-based criteria are premised on all model effects being regarded as fixed. When treatments and/or nuisance parameters are assumed to be random effects, an appropriate optimality criterion can be developed under the same conditions. This paper introduces such a criterion, and this criterion also allows for the inclusion of fixed and/or random nuisance parameters in the model and for the presence of a general covariance structure. Also, a general formula is presented for which all previously published optimality criteria are special cases.