Designs for Generalized Linear Models With Several Variables and Model Uncertainty

Standard factorial designs may sometimes be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments which uses a criterion that allows for uncertainty in the link function, the linear predictor or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications and their advantages over factorial and central composite designs are demonstrated.