D-optimal designs for generalised linear models with variance proportional to the square of the mean

Abstract

SUMMARY Locally D-optimal designs for generalised linear models with a variance proportional to the square of the mean are presented. While the paper limits consideration to the case of power law link functions, it extends previous results by considering an arbitrary number of terms in the linear predictor. Under a condition which involves the parameters in the model, the traditional one-at-a-time factorial design is shown to be optimal. The efficiency of classical factorial designs relative to the optimal design is also considered and we suggest compromise designs which, although not optimal, give efficient alternatives to the optimal design and do not require knowledge of the unknown parameters.