Kiefer ordering of simplex designs for first- and second-degree mixture models

For mixture models on the simplex, we discuss the improvement of a given design in terms of increasing symmetry as well as obtaining a larger moment matrix under the Loewner ordering. The two criteria together constitute the Kiefer design ordering. The latter can be discussed either in the usual Scheffe model algebra, or in Kronecker product algebra which better reflects the symmetries of the simplex experimental region. For the first-degree mixture model, we show that the vertex points design is the unique optimal design under the Kiefer ordering. For the second-degree mixture models with two or three ingredients, complete class results relative to the Kiefer ordering are derived. A brief overview of related literature completes the paper. (C) 1999 Elsevier Science B.V. All rights reserved.