GRM Introductory Overview - Polynomial Regression
Polynomial regression designs are designs which contain main effects and higher-order effects for the continuous predictor variables but do not include interaction effects between predictor variables. For example, the polynomial regression design to degree 2 for three continuous predictor variables P, Q, and R would include the main effects (i.e., the first-order effects) of P, Q, and R and their quadratic (i.e., second-order) effects, but not the 2-way interaction effects or the P by Q by R 3-way interaction effect.
Y = b0 + b1P + b2P2 + b3Q +b4Q2 + b5R + b6R2
Polynomial regression designs do not have to contain all effects up to the same degree for every predictor variable. For example, main, quadratic, and cubic effects could be included in the design for some predictor variables, and effects up the fourth degree could be included in the design for other predictor variables.
Between-Subject Designs
Multivariate designs