International Business and Information School, Shanghai University of International Business and Economics; Mathematics and Sciences College, Shanghai Normal University

The paper investigates the problem of
optimal balanced designs in general linear regression models with
mixed effects. The interest lies in estimating fixed effects, random
effects and prediction of the future observation of an individual,
respectively. By using the de la Garaz phenomenon and Loewner order
domination, the dimension of determining the optimal designs are
reduced. The optimal designs are derived by using analytical or
numerical methods, and their optimalities are verified through the
general equivalence theorems.