GRM Introductory Overview - Mixture Surface Regression
Mixture surface regression designs are identical to factorial regression designs to degree 2 except for the omission of the intercept. Mixtures, as the name implies, add up to a constant value; the sum of the proportions of ingredients in different recipes for some material all must add up 100%. Thus, the proportion of one ingredient in a material is redundant with the remaining ingredients. Mixture surface regression designs deal with this redundancy by omitting the intercept from the design. The design matrix for a mixture surface regression design for 3 continuous predictor variables P, Q, and R would be
Y = b1P + b2Q + b3R +b4P*Q + b5P*R +b6Q*R
These types of designs are commonly employed in applied research (e.g., in industrial experimentation), and a detailed discussion of these types of designs is also presented in the Introductory Overview of the Experimental Design module (see Mixture designs and triangular surfaces).
Between-Subject Designs
Multivariate Designs