Optimal designs for prediction of random effects in two-groups models with multivariate response

In this work an analytical solution is proposed for optimal designs for the prediction of individual random effects and the group difference in two-groups models with multivariate response. The solution is given by optimality conditions for approximate designs. In particular two-groups models with the same regression function for both groups, Bayesian optimal designs are optimal for the prediction of the group difference. The results are illustrated by examples of linear and bi-linear regression.