A note comparing component-slope, Scheffé and Cox parameterizations of the linear mixture experiment model
A mixture experiment involves combining two or more components in various proportions and collecting data on one or more responses. A linear mixture model may adequately represent the relationship between a response and mixture component proportions and be useful in screening the mixture
components. The Scheffé and Cox parameterizations of the linear mixture model are commonly used for analyzing mixture experiment data. With the Scheffé parameterization, the fitted coefficient for a component is the predicted response at that pure component (i.e. single-component
mixture). With the Cox parameterization, the fitted coefficient for a mixture component is the predicted difference in response at that pure component and at a pre-specified reference composition. This article presents a new component-slope parameterization, in which the fitted coefficient
for a mixture component is the predicted slope of the linear response surface along the direction determined by that pure component and at a pre-specified reference composition. The component-slope, Scheffé, and Cox parameterizations of the linear mixture model are compared and their
advantages and disadvantages are discussed.
Keywords: Cox linear mixture model; Mixture component effects; Scheffé; component-slope linear mixture model; linear mixture model
Document Type: Research Article
Affiliations: Statistical Sciences, Pacific Northwest National Laboratory, Richland, Washington, USA
Publication date: 01 May 2006
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