Saturday, August 18, 2012

Experimental Design Criteria

I used the AlgDesign package in R to generate some optimal designs for a 6th order 2D response surface. There is still clustering near the boundaries (as shown in this post) with the I optimal design, but there are a few more points "in the middle" of the parameter space.

There are many choices of cost function for optimal experimental design. I-optimal designs attempt to minimize the variance of predictions over some region, while D-optimal designs attempt to minimize the variance of parameter estimates. The D-optimal designs tend to be the more commonly used approach, but for some applications (e.g. response surface modeling) the I-optimal design will give some improvement. Wheeler notes that the designs tend to look pretty similar (and we see that with this example). Often doing the D-optimal design will be "good enough." On a more political/social note, getting some more points into those white spaces in the middle of the parameter space has a tendency to make clients/customers/bosses feel a little better about the approach if they are not that familiar with designed experiments.

I'm not quite sure if I'm using the "space" parameter of optMonteCarlo correctly, but it seems to work.

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