GLM Introductory Overview - Factorial Regression
Factorial regression designs are similar to factorial ANOVA designs, in which combinations of the levels of the factors are represented in the design. In factorial regression designs, however, there may be many more such possible combinations of distinct levels for the continuous predictor variables than there are cases in the data set. To simplify matters, full-factorial regression designs are defined as designs in which all possible products of the continuous predictor variables are represented in the design. For example, the full-factorial regression design for two continuous predictor variables P and Q would include the main effects (i.e., the first-order effects) of P and Q and their 2-way P by Q interaction effect, which is represented by the product of P and Q scores for each case. The regression equation would be:
Y = b0 + b1P + b2Q + b3P*Q
Factorial regression designs can also be fractional, that is, higher-order effects can be omitted from the design. A fractional factorial design to degree 2 for 3 continuous predictor variables P, Q, and R would include the main effects and all 2-way interactions between the predictor variables:
Y = b0 + b1P + b2Q + b3X3 + b4P*Q + b5P*R + b6Q*R
Between-subject designs
Within-subject (repeated measures) designs
Multivariate designs