PNNL

Abstract

In developing models for mixture experiments, the first step typically involves fitting a complete Scheffé linear mixture (SLM) model using all components varied in the experiment. It next may be desirable to reduce a complete SLM model by (i) eliminating (in a way appropriate for mixture experiments) components that have negligible effects and (ii) combining components that have similar effects. Standard methods for reducing non-mixture linear models, such as t-tests and variable-selection techniques, are not applicable for reducing SLM models. In the mixture experiment literature, a time-consuming, manual iterative approach has been used to reduce SLM models. Automatic and semi-automatic versions of a method for backward reduction of SLM models are proposed to eliminate components (in a way appropriate for mixture experiments) or combine components. The method uses associated partial F-tests to guide the model reduction steps. The method allows for specifying (i) components that must remain in the model, (ii) components that can (or cannot) be combined, and (iii) the stopping criterion. The method is illustrated using examples from the literature.