Ds-Optimal Designs for Quadratic Log Contrast Model for Experiments with Mixtures

The approximate D-s-optimal design for discriminating between linear and quadratic log contrast models for experiments with mixtures suggested by Aitchison and Bacon-Shone (1984) is investigated, where the experimental domain is restricted further as in Chan (1992). It is found that for a symmetric subspace of the finite dimensional simplex, there is a D-s-optimal design with the nice structure that puts a weight 1/2(k-1) on the centroid of this subspace and the remaining weight is uniformly distributed on the vertices of the experimental domain. Finally, the D-s-efficiency of the D-optimal design for quadratic model and the design given by Aitchison and Bacon-Shone (1984) are also discussed.