Exact D-Optimal Designs for Linear Log Contrast Models

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Mong-Na Lo Huang*+ and Miao-Kuan Huang and Baisuo Jin
• Companies: National Sun Yat-sen University and National Formosa University and University of Science and Technology of China
• Keywords: Efficient designs ; Hadamard matrix

Abstract

In this work, exact D-optimal designs for linear log contrast models with mixture experiment are investigated. In the mixture experiment considered, it is assumed the measured response depends only on the proportions of the ingredients present in the mixture. Aitchison and Bacon-Shone (1984) suggested the log contrast models for mixture experiments and the design space was restricted further by Chan (1992). In this talk, firstly a new method for constructing efficient designs is presented by using the properties of Hadamard matrix. Through the new method, A-, D- and E- optimal designs for a linear log contrast model with minimal number of observations are constructed. Later exact D-optimal designs are discussed and it will be shown for k=3, 4 there is an exact D-optimal design supported as evenly as possible at the supports of the approximate D-optimal designs.