Designs for Generalized Linear Models With Several Variables and Model Uncertainty

Abstract

Standard factorial designs sometimes may 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 that uses a criterion allowing 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.

KEY WORDS :

• Binary response
• D-optimality
• Logistic regression
• Robust design
• Simulation