Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients

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 define the Kiefer design ordering. For the second-degree mixture model, we show that the set of weighted centroid designs constitutes a convex complete class for the Kiefer ordering. For four ingredients, the class is minimal complete. Of essential importance for the derivation is a certain moment polytope, which is studied in detail. 1. Introduction. Many practical problems are associated with the investigation of mixture ingredients of m factors, assumed to influence the response only through the proportions in which they are blended together. The definitive text, Cornell (1990), lists numerous examples and provides a thorough discussion of both theory and practice. Early seminal work was done by Scheff´ e (1958, 1963) in which he suggested and analyzed canonical model forms when the regression function for the expected response is apolynomia l of degree one, two, or three.

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