Optimal Designs for 2^k Factorial Experiments with Binary Response

2011/09/25 by Yang, Jie, Mandal, Abhyuday, Majumdar, Dibyen · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1109.5320

Abstract

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.

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