GLM Introductory Overview - Nested ANOVA Designs

Nested designs are similar to fractional factorial designs in that all possible combinations of the levels of the categorical predictor variables are not represented in the design. In nested designs, however, the omitted effects are lower-order effects. Nested effects are effects in which the nested variables never appear as main effects. Suppose that for 2 variables A and B with 3 and 2 levels, respectively, the design includes the main effect for A and the effect of B nested within the levels of A. The X matrix for this design using the overparameterized model is

Note: if the sigma-restricted coding were used, there would be only 2 columns in the X matrix for the B nested within A effect instead of the 6 columns in the X matrix for this effect when the overparameterized model coding is used (i.e., columns X4 through X9). The sigma-restricted coding method is overly-restrictive for nested designs, so only the overparameterized model is used to represent nested designs.

Between-subject designs

Within-subject (repeated measures) designs

Multivariate designs