We consider the problem of obtaining D-optimal designs for factorial
experiments with a binary response and k qualitative factors each at two
levels. 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. 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 can be obtained very easily using our algorithm for locally
D-optimal designs and are very good surrogates for Bayes 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.Comment: 41 pages, 3 figures, 8 table
