Automated Method for Reducing Scheffé Linear Mixture Experiment Models

TLDR: 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.

Abstract: In developing models for mixture experiments, the first step typically involves fitting a complete Scheffe 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 th...