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 Scheffe´ and Cox parameterizations of the linear mixture model are commonly used for analyzing mixture experiment data. With the Scheffe´ 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 prespecified reference composition. The component-slope, Scheffe´, and Cox parameterizations of the linear mixture model are compared and their advantages and disadvantages are discussed