Statistica Sinica 19 (2009), 721-730

D-OPTIMAL DESIGNS FOR POISSON REGRESSION

MODELS

K. G. Russell$^1$, D. C. Woods$^2$, S. M. Lewis$^2$ and J. A. Eccleston$^3$

$^1$University of Wollongong, $^2$University of Southampton and

$^3$University of Queensland

Abstract: We consider the problem of finding an optimal design under a Poisson regression model with a log link, any number of independent variables, and an additive linear predictor. Local D-optimality of a class of designs is established through use of a canonical form of the problem and a general equivalence theorem. The results are applied in conjunction with clustering techniques to obtain a fast method of finding designs that are robust to wide ranges of model parameter values. The methods are illustrated through examples.

Key words and phrases: Clustering, locally optimal design, log-linear models, robust design.