Optimal Designs for 2^k Factorial Experiments with Binary Response

We consider the problem of obtaining locally D-optimal designs for factorial experiments with binary response and $k$ qualitative factors at two levels each. We obtain a characterization for a design to be locally D-optimal. Based on this characterization, we develop efficient numerical techniques to search for locally D-optimal designs. We also investigate the properties of fractional factorial designs and study the robustness with respect to the assumed parameter values of locally D-optimal designs. Using prior distributions on the parameters, we investigate EW D-optimal designs, which are designs that maximize the determinant of the expected information matrix. It turns out that these designs are much easier to find and still highly efficient compared to Bayes D-optimal designs, as well as quite robust.