D-optimal design for a quadratic log contrast model for experiments with mixtures |
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Authors: | Ling-Yau Chan |
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Institution: | Department of Industrial and Manufacturing Systems Engineering , University of Hong Kong , Pokfulam Road, Hong Kong |
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Abstract: | A practical method is suggested for solving complicated D-optimal design problems analytically. Using this method the author has solved the problem for a quadratic log contrast model for experiments with mixtures introduced by J. Aitchison and J. Bacon-Shone. It is found that for a symmetric subspace of the finite dimensional simplex, the vertices and the centroid of this subspace are the only possible support points for a D-optimal design. The weights that must be assigned to these support points contain irrational numbers and are constrained by a system of three simultaneous linear equations, except for the special cases of 1- and 2-dimensional simplexes where the situation is much simpler. Numerical values for the solution are given up to the 19-dimensional simplex |
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Keywords: | D-optimality experiments with mixtures log contrast models finite dimensional simplex |
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