Slack-Variable Models Versus Component-Proportion Models For Mixture Experiments: Literature Review, Evaluations, And Recommendations

A mixture experiment (ME) combines components in various proportions and observes the values of one or more responses for each mixture. The proportions of theqcomponents in each mixture must sum to 1.0. Two statistical approaches for modeling MEs have been discussed in the literature. The slack-variable (SV) approach uses proportions of all but one (q - 1) of the components varied in a mixture (the SV). The component-proportion (CP) approach uses the relative proportions of allqcomponents varied in a mixture. Several articles have claimed advantages and recommended the SV modeling approach over the CP modeling approach. In contrast, a 2009 article recommended the CP modeling approach for several reasons. Our article reviews the literature, evaluates the literature justifications for using the SV modeling approach, and uses literature examples to compare the CP and SV modeling approaches. Recommendations regarding when to use the CP and SV modeling approaches are provided.