Optimal Designs for Balanced Linear Mixed-Effects Regression Models

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.