Jie Yang, Abhyuday Mandal and Dibyen Majumdar (2012). Optimal designs for two-level factorial experiments with binary response. Vol. 22, No. 2, 885-907.

Statistica Sinica 22 (2012), 885-907

doi:http://dx.doi.org/10.5705/ss.2010.080

OPTIMAL DESIGNS FOR TWO-LEVEL FACTORIAL

EXPERIMENTS WITH BINARY RESPONSE

Jie Yang $^{1}$ , Abhyuday Mandal $^{2}$ and Dibyen Majumdar $^{1}$

University of Illinois at Chicago and University of Georgia

Abstract: We consider the problem of obtaining locally D-optimal designs for factorial experiments with qualitative factors at two levels each and with binary response. For the $2^{2}$ factorial experiment with main-effects model, we obtain optimal designs analytically in special cases and demonstrate how to obtain a solution in the general case using cylindrical algebraic decomposition. The optimal designs are shown to be robust to the choice of the assumed values of the prior, and when there is no basis to make an informed choice of the assumed values we recommend the use of the uniform design that assigns equal number of observations to each of the four points. For the general $2^{k}$ case we show that the uniform design has a maximin property.

Key words and phrases: Cylindrical algebraic decomposition, D-optimality, information matrix, full factorial design, generalized linear model, uniform design.