Slack-variable models versus Scheffé's mixture models

Abstract

Slack-variable models are compared against Scheffé's polynomial model for mixture experiments. The notion of model equivalence and the use of various diagnostic measures provide effective tools in making such comparisons, particularly when the experimental region is highly constrained. It is demonstrated that the choice of the best fitting model, through variable selection, depends on which mixture component is selected as a slack variable, and on the size of the fitted model. In addition, the equivalence of two well-known representations of a complete mixture model is shown to be valid. Two numerical examples are presented.

Keywords:

• Collinearity
• column space
• condition number
• constrained mixture region
• mixture components
• model equivalence
• L-pseudocomponents
• variable selection
• variance-decomposition proportions
• variance inflation factors
• well-formulated model