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Statistica Sinica 26 (2016), 385-411
doi:http://dx.doi.org/10.5705/ss.2013.265

OPTIMAL DESIGNS FOR 2k FACTORIAL EXPERIMENTS
WITH BINARY RESPONSE
Jie Yang1, Abhyuday Mandal2 and Dibyen Majumdar1
1University of Illinois at Chicago and 2University of Georgia

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 of locally D-optimal designs. We then develop efficient numerical techniques to search for locally D-optimal designs. Using prior distributions on the parameters, we investigate EW D-optimal designs that maximize the determinant of the expected information matrix. It turns out that these designs can be obtained easily using our algorithm for locally D-optimal designs and are good surrogates for Bayes D-optimal designs. We also investigate the properties of fractional factorial designs and study robustness with respect to the assumed parameter values of locally D-optimal designs.

Key words and phrases: D-optimality, EW D-optimal design, fractional factorial design, full factorial design, generalized linear model, uniform design.

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