Selecting model terms
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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 the Terms subdialog box, you can choose a linear, quadratic, special cubic, full cubic model, 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].

This model type    fits these terms    and models this type of blending

linear
(first-order)

linear

additive

quadratic
(second-order)

linear and quadratic

additive
nonlinear synergistic binary
or
additive
nonlinear antagonistic binary

special cubic
(third-order)

linear, quadratic,
and special cubic

additive
nonlinear synergistic ternary
nonlinear antagonistic ternary

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,
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,
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 above models as long as the lower bound for any component is not zero and you choose to analyze the design in proportions. Inverse terms allow you to 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 taste. An extreme change in the acceptance of lemonade occurs when the proportion of sweetener goes to zero. That is, the taste becomes unacceptably sour.

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

Y = b1A + b2B + b3C + b12AB + b13AC + b23BC