D- and A-Optimal Designs - Model Tab
Select the Model tab of the D- and A-Optimal Designs dialog box to access options to specify the model that you want to fit to the data (after you have completed the experiment). Statistica selects points from the candidate list to optimize the chosen criterion given the current model, that is, given the current design matrix (see also the Introductory Overview).
Use the Experimental Design module to construct optimal designs for standard response surfaces, where the model includes an intercept (or grand mean), and for mixtures where the models (in their standard canonical form) do not include an intercept. To learn more about these different models refer to the to the information on central composite designs and mixture designs in the Introductory Overview.
y = b0 + b1*x1 +...+ bk*xk + b12*x1*x2 + b13*x1*x3 +...+ bk-1,k*xk-1*xk + b11*x12 +...+ bkk *xk2
where b0 is the intercept, b1 is the coefficient for the main effect for factor 1 (b2 for factor 2, and bk for factor k), b12 (bjk) is the coefficient for the interaction effect for factors 1 and 2, and b11 (bkk) is the coefficient for the quadratic effect.
Linear main effects
Lin./quad. main effects
Linear main eff. + 2-ways
Lin/quad main eff. + 2-ways
Linear.
y = b1*x1 + b2*x2 + b3*x3
Quadratic.
y = b1*x1 + b2*x2 + b3*x3 +b12*x1*x2 +b13*x1*x3 + b23*x2*x3
Special cubic.
y = b1*x1 + b2*x2 + b3*x3 +b12*x1*x2 +b13*x1*x3 + b23*x2*x3 +b123*x1*x2*x3
Full cubic.
y = b1*x1 + b2*x2 + b3*x3 +b12*x1*x2 +b13*x1*x3 + b23*x2*x3 + d12*x1*x2*(x1-x2) + d13*x1*x3*(x1-x3) + d23*x2*x3*(x2-x3) + b123*x1*x2*x3
(Note that the dij's are also parameters of the model.)
Notes: Recoding of factor effects. By default, Statistica optimizes the design (i.e., compute X'X, where X stands for the design matrix) after recoding the factor settings found in the list of candidate points. This recoding can be turned off on the Options tab. Specifically, if you select a Response surface (with intercept) model (see above), the design matrix is computed from the factor settings recoded to the ±1 range (e.g., the smallest value for each factor is recoded to -1, the largest value is recoded to +1). If you select a Mixture (no intercept) model (see above), the design matrix is computed from factor settings transformed to pseudo-components (see also Introductory Overview):
x'i = (xi-Li)/(Total-L)
Here, x'i stands for the i'th pseudo-component, xi stands for the original component value, Li stands for the lower constraint (limit) for the ith component, L stands for the sum of all lower constraints (limits) for all components in the design, and Total stands for the mixture total. For additional discussion of these transformations, refer also to the results dialogs of Analysis of a Central Composite (Response Surface) Experiment and Analysis of a Mixture Experiment.