  We consider an experiment with two qualitative factors at 2 levels each and a
binary response, that follows a generalized linear model. In Mandal, Yang and
Majumdar (2010) we obtained basic results and characterizations of locally
D-optimal designs for special cases. As locally optimal designs depend on the
assumed parameter values, a critical issue is the sensitivity of the design to
misspecification of these values. In this paper we study the sensitivity
theoretically and by simulation, and show that the optimal designs are quite
robust. We use the method of cylindrical algebraic decomposition to obtain
locally D-optimal designs in the general case.
