Evaluation of the Design Effect for Optimizing the Model Discrimination Strength to Detect Non-Zero Interactions in Factorial Experiments
It is important for a design to be able to discriminate between all pairwise model comparisons when searching for non-zero interactions. If a design does not have this capability, finding non-zero interactions may not be possible. We propose a procedure at analyzing the model discrimination strength when searching for non-zero interactions by understanding the pairwise differenced error sum of squares for a given design. This is done by calculating eigenvalues and eigenvectors of differenced projection matrices which are completely dependent on the design and not the observed values for the response variable. Using this procedure, we have compared two balanced designs and two Placket-Burman (1946) designs which both have n=12 runs, m=5 factors each with 2 levels, and searching over (5¦2)=10 two-factor interaction effects. Additionally, ridge regression and LASSO were used for a model selection approach which both use tuning parameters to calculate the model parameter estimates. All three model selection approaches were used on all four example designs to compare the performance when searching for non-zero interactions.