Experimental Design - Note on Unbalanced Designs and Singular Effects Matrices

Note: the information here is relevant for analyses of Experiments with two-Level factors, Screening experiments, Experiments with three-level factors, Experiments with two- and three-level factors, and Central composite (response surface) experiments. Additionally, the comments on Singular Effects Matrices also apply to Mixture experiments.
Unbalanced Designs
The Experimental Design module estimates the parameters for the respective model (see the options in the Include in model group box) via least-squares multiple regression, using the so-called sweeping algorithm (e.g., see Dempster, 1969). Therefore, the design does not need to be balanced to estimate the parameters; however, if it is unbalanced then the parameter estimates are not independent of each other (see Singular effects matrices below, option Corr. matrix and option Effects estimates).
Singular Effects Matrices
When analyzing results, the Experimental Design module uses the generalized inverse of the design matrix when estimating effects. Completely confounded effects are pooled into the error term. (See also Unbalanced Designs, above).