In some applications, the only measurement type available is a pass/fail (binomial) measurement. In this example, two factors are of interest, X1 and X2, which you will vary between -1 and 1. You will construct a nonlinear design for the binomial response and then view it in the context of your proposed nonlinear model.
This model is nonlinear in the unknown parameters β0, β1, and β2. Your goal is to estimate these parameters using an experimental design.
β0 is 0, but might range from -2 to 2
β1 is 5, but might range from 0 to 10
β2 is 5, but might range from 0 to 10
Columns X1 and X2 for the two predictors. The Coding property defined for each of these columns causes the initial factor settings to be -1 and 1.
A column called Logistic Model that contains a formula relating the predictors to the response. To view the formula, click on the plus sign to the right of Logistic Model in the Columns panel. See Formula Relating Predictors to Binomial Probability.
Your initial guesses for the parameters b0, b1, and b2. When you defined these parameters, you were asked to specify a value. You set this value to your initial guess. These values are shown in the formula element panel at the top left of the formula editor window. See Formula Relating Predictors to Binomial Probability.
A column called Variance that contains the formula for the variance of the predicted value based on the assumed logistic model. When you construct your design, this column indicates which design points have comparatively high variances.
Formula Relating Predictors to Binomial Probability
Select Help > Sample Data Library and open Design Experiment/Binomial Optimal
Select DOE > Special Purpose > Nonlinear Design.
Select Y and click Y, Response.
Select Logistic Model and click X, Predictor Formula.
Nonlinear Design Window
Enter the following under Values for the three parameters:
b1: 0 and 10
Nonlinear Design Window with Parameter Values
Click Make Design.
Click Augment Table.
This adds the 14 runs to Binomial Optimal Your design table will be different because the optimization algorithm has a random component.
Augmentation of Binomial Optimal
Now that you have constructed your design, proceed to examine where the design points are located relative to the proposed logistic model. The Variance column gives the prediction variance at each design point, based on the logistic model.
With Binomial Optimal active, select Graph > Graph Builder.
Select X1 and drag it to the X zone.
Select X2 and drag it to the Y zone.
Click Done.
Design Settings
Notice that there are no points at X1 = -1. The only point on a corner of the design region corresponds to X1 = 1 (more precisely, 0.996) and X2 = -1. There are several points in the central part of the design region.
Select Graph > Surface Plot.
Select X1, X2, and Logistic Model and click Columns.
Drag the Marker Size indicator to the right.
Click Done.
Prediction Model with Design Points

Help created on 9/19/2017