A-OPTIMAL DESIGNS FOR AN ADDITIVE QUADRATIC MIXTURE MODEL

Quadratic models are widely used in the analysis of experiments involving mixtures. This paper gives A-optimal designs for an additive quadratic mixture model for q ≥ 3 mixture components. It is proved that in these A-optimal designs, vertices of the simplex S q�1 are support points, and other support points shift gradually from barycentres of depth 1 to barycentres of depth 3 as q increases. A-optimal designs with minimal support are also discussed. be expressed as y = η(x )+ e(x), where η(x) is the expected response and e(x) is the error at x. We assume that for independent observations, the errors e(x) are statistically independent and have mean zero and the same variance. The following quadratic mixture model for η(x) was first studied by Darroch and Waller (1985) for the case q =3 : η DW2 (x )= � 1≤i≤q αixi + �

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