The model terms that are available depend on the type of mixture design. You can fit a model to a simple mixture design (components only), a mixture-process variable design (components and process variables), or a mixture-amounts design (components and amounts).

The order of the model you choose determines which terms are fit and whether or not you can model linear or curvilinear aspects of the response surface.

In linear, quadratic, special cubic, full cubic, special quartic, or full quartic model. Or, you can fit a model that is a subset of these terms. The following table summarizes these models. For a discussion of the various blending effects you can model, see [1].

, you can choose aModel type | Terms | Type of blending |
---|---|---|

linear (first-order) |
linear |
additive |

quadratic (second-order) |
linear and quadratic |
additive nonlinear synergistic binary
additive nonlinear antagonistic binary |

special cubic (third-order) |
linear, quadratic, and special cubic |
additive nonlinear synergistic binary nonlinear antagonistic binary |

full cubic (third-order) |
linear, quadratic, special cubic, and full cubic |
additive nonlinear synergistic binary nonlinear antagonistic binary nonlinear synergistic ternary nonlinear antagonistic ternary |

special quartic (fourth-order) |
linear, quadratic, special cubic, full cubic, and special quartic |
additive nonlinear synergistic binary nonlinear antagonistic binary nonlinear synergistic ternary nonlinear antagonistic ternary nonlinear synergistic quaternary nonlinear antagonistic quaternary |

full quartic (fourth-order) |
linear, quadratic, special cubic, full cubic, special quartic, and full quartic |
additive nonlinear synergistic binary nonlinear antagonistic binary nonlinear synergistic ternary nonlinear antagonistic ternary nonlinear synergistic quaternary nonlinear antagonistic quaternary |

You can fit inverse terms with any of the previous models if the lower bound for any component is not zero and you choose to analyze the design in proportions. Inverse terms lets you model extreme changes in the response as the proportion of one or more components nears its boundary. Suppose you are formulating lemonade and you are interested in the acceptance rating for flavor. An extreme change in the acceptance of lemonade occurs when the proportion of sweetener goes to zero. That is, the flavor becomes too sour.

Analyze Mixture Design fits a model without a constant term. For example, a quadratic in three components is as follows:

Y = b_{1}A + b_{2}B + b_{3}C + b_{12}AB + b_{13}AC + b_{23}BC

To open Analyze Mixture Design, choose .

[1] J.A. Cornell (2002). *Experiments With Mixtures: Designs, Models, and the Analysis of Mixture Data*, Third Edition, John Wiley & Sons.