When would you use an I-optimal design over a D-optimal design?

Question

We were discussing in DOE designs that it was best for model development to us d-optimal designs to identify your design space. The common alternative would be an i-optimal design. When would it be advantageous to do i-optimal design?

Answer 1

D-optimality is related to the covariance matrix of the parameter estimates, so if you wanted to identify which factors aren't significant (factor screening experiment) it's a natural choice. I-optimality minimizes the average prediction variance of your model over a region of measurement parameters, so it is more naturally applied when you know the form of the model and want "good" prediction over your design space. For this reason, I-optimality finds more use in a response surface optimization context.

In reality, the prediction variance and the parameter estimate covariance are related. There's an interesting equivalence theorem (for designs as measures) between minimizing the maximum prediction variance (G-optimality) and D-optimality due to Kiefer and Wolfowitz.