Construction of Optimal and Efficient Designs of Experiments for Individualized Prediction in Hierarchical Models

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The object of the present project is hierarchical random coefficient regression models as well as generalized linear and nonlinear mixed models. Such models were initially introduced in biosciences for plant and animal breeding and are nowadays utilized in an increasing number of fields in statistical applications. The aim of the project is to develop analytical approaches for the determination of optimal designs for the problem of prediction in these models. The most available analytical results for experimental designs have the form of an optimality condition in the sense of an equivalence theorem. Only for some particular cases the solutions are given explicitly. Methods for the computation of optimal designs are a substantial part of this project.Analytical approaches for the determination of optimal designs are often successfully based on the concept of approximate designs. Although approximate designs are not directly realizable, optimal or at least efficient exact designs can be determined using suitable rounding algorithms, in which approximate designs may then serve as a benchmark for the efficiency of the obtained exact designs. Within this project the construction and characterization of optimal designs will be investigated in detail under realistic experimental restrictions caused by overall experimental conditions (balanced longitudinal, cross sectional, sparse, multi-factor or randomized block designs). It has to be noted that the so obtained optimal designs are only locally optimal in the sense that they depend on the dispersion matrix of the random effects. If the dispersion matrix is unknown, this problem will be attacked by using so-called robust design criteria, which show a low sensitivity with respect to the dispersion parameters. In the final part of the project the results obtained for linear random coefficient regression models will be extended to more complicated (generalized linear and nonlinear mixed) models.