Ridge analysis of mixture response surfaces

✍ Scribed by Norman R. Draper; Friedrich Pukelsheim

• Book ID: 104303280
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 158 KB
• Volume: 48
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00195-9

✦ Synopsis

Previous applications of ridge analysis to second-order response surfaces based on mixture ingredients (x1; x2; : : : ; xq) which sum to 1 have required transforming from the origin (0; 0; : : : ; 0), which is not in the mixture space, to a point inside the space, most often the centroid (1=q; 1=q; : : : ; 1=q). We show that this transformation is not necessary for tracking the maximum ŷ and the minimum ŷ paths. In addition, we show that the application of ridge analysis is somewhat simpliÿed if the Sche à e model form is replaced by the K (Kronecker) model form, an alternative, homogeneous model given elsewhere.