D-Optimally-Constructed Exact Designs under the Variation of Non-D-Optimality Criteria for Varying Regression Polynomials

The behaviour of D-optimal exact designs, constructed using a combinatorial algorithm, is examined under the variations of A-, E- and G-optimality criteria. In particular, the question of whether designs that are optimal with respect to one criterion are also optimal with respect to other criteria is addressed. The Condition Numbers (CN) of the designs as well as the equivalence relations of the criteria are noted. The D-optimal designs under consideration are for low-order bivariate polynomial models. By the rules of the algorithm, not more than 25 percent search on the total available designs is required within a design class since a lot of inferior designs, with respect to the search for optimal design are eliminated. The models, which could be with or without intercept, are defined on design regions which are supported by the points of the circumscribed central composite design. The points are classified into three groups with respect to their distances from the centre of the design region. Results show that D-optimally-constructed designs need not be A-, E- or G-optimum. For the first order models considered, the global best D-optimal exact designs were each, A-, E- and G-optimum. For the bivariate quadratic model considered, the global best D-optimal exact design was not necessarily G-optimum. However, the design was both A- and E-optimum. The prediction capabilities of these designs were graphically evaluated