D s -Optimal Designs for Quadratic Log Contrast Model for Experiments with Mixtures |
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Authors: | Miao-Kuan Huang Mong-Na Lo Huang |
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Institution: | 1. Center for General Education , National Formosa University , Taiwan, ROC huangmk@math.nsysu.edu.tw;3. Department of Applied Mathematics , National Sun Yat-sen University , Taiwan, ROC |
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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
Aitchison , J. ,
Bacon-Shone , J. ( 1984 ). Log contrast models for experiments with mixtures . Biometrika 71 : 323 – 330 .Crossref], Web of Science ®] , Google Scholar]) is investigated, where the experimental domain is restricted further as in Chan (1992
Chan , L. Y. ( 1992 ). D-Optimal design for a quadratic log contrast model for experiments with mixtures . Commun. Statist. Theor. Meth. 21 ( 10 ): 2909 – 2930 .Taylor & Francis Online], Web of Science ®] , Google Scholar]). 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
Aitchison , J. ,
Bacon-Shone , J. ( 1984 ). Log contrast models for experiments with mixtures . Biometrika 71 : 323 – 330 .Crossref], Web of Science ®] , Google Scholar]) are also discussed. |
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Keywords: | Equivalence theorem Invariant design Loewner ordering Quadratic subspace |
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