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 22 factorial experiments. In this paper, we generalize the results for 2k 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 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.

TR Number: 
Jie Yang, Abhyuday Mandal and Dibyen Majumdar
Key Words: 
Generalized linear model, full factorial design, fractional factorial design, D-optimality, uniform design, EW D-optimal design.

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