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. Yang, Mandal and Majumdar (2011) considered this problem for $2^2$ factorial experiments. In this paper, we generalize the results for $2^k$ designs and explore in new directions. 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 initial parameter values of locally D-optimal designs. Using prior distribution on the parameters, we investigate EW D-optimal designs, that are designs which 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 Bayesian D-optimal designs, as well as quite robust.