A Component Slope Linear Model for Mixture Experiments

Abstract

The Scheffé linear model and the Cox linear model are two first-order model forms commonly used for analyzing mixture experiment data. In a fitted Scheffé linear model, the coefficient for a mixture component is the predicted response at that pure component (i.e., single-component mixture). In a fitted Cox linear model, the coefficient for a mixture component is the predicted difference in response at that pure component and at a pre-specified reference mixture. An alternative first-order model for mixture experiments, the component slope linear mixture (CSLM) model, is proposed in this article. In a fitted CSLM model, the coefficient for a mixture component is the predicted slope of the linear response surface along the Cox effect direction for that component (where the direction is determined by a pre-specified reference mixture). The CSLM model and methods for fitting it are presented. The advantages and disadvantages of the CSLM model, Scheffé linear model, and Cox linear model are discussed. The three models are illustrated and interpreted for an example involving the liquidus temperature of spinel crystals in simulated nuclear waste glass.