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

Abstract

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.

Keywords:

• Equivalence theorem
• Invariant design
• Loewner ordering
• Quadratic subspace

Mathematics Subject Classification:

• Primary 62K05
• Secondary 62J99

Acknowledgment

The authors would like to thank the reviewers for their helpful comments which substantially improved the research presentation.