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\({\phi_p}\)-optimal designs for a linear log contrast model for experiments with mixtures

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Abstract

A mixture experiment is an experiment in which the k ingredients are nonnegative and subject to the simplex restriction \({\sum_{i=1}^k x_i\,=\,1}\) on the (k − 1)-dimensional probability simplex S k-1. In this work, an essentially complete class of designs under the Kiefer ordering for a linear log contrast model with a mixture experiment is presented. Based on the completeness result, \({\phi_p}\)-optimal designs for all p,−∞ ≤ p ≤ 1 including D- and A-optimal are obtained, where the eigenvalues of the design moment matrix are used. By using the approach presented here, we gain insight on how these \({\phi_p}\)-optimal designs behave.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan, ROC

    Mong-Na Lo Huang

  2. Center for General Education, National Formosa University, Yunlin, 632, Taiwan, ROC

    Miao-Kuan Huang

Authors
  1. Mong-Na Lo Huang
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  2. Miao-Kuan Huang
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Correspondence to Mong-Na Lo Huang.

Additional information

Mong-Na Lo Huang was supported in part by the National Science Council of Taiwan, ROC under grant NSC 93-2118-M-110-001.

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Lo Huang, MN., Huang, MK. \({\phi_p}\)-optimal designs for a linear log contrast model for experiments with mixtures. Metrika 70, 239–256 (2009). https://doi.org/10.1007/s00184-008-0190-7

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  • DOI: https://doi.org/10.1007/s00184-008-0190-7

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