D-Optimal Designs for Exponential and Poisson Regression Models

Abstract

In the present study, the class of nonlinear models, with intrinsically linearly related mean response and input variables, were explored for the generation of locally D-optimal designs. It has been found that these models have the advantage of design construction in transformed or coded design space with suitable transformation in initial parameter guesses. Exponential and Poisson regression models with two continuous input variables were investigated. For the construction of D-optimal designs, the modified version of Fedorov algorithm was used that require a suitable candidate set representing the design space along with the initial parameter guesses. The efficient method of constructing the candidate sets with respect to each model is proposed. The optimality of generated designs was validated using general equivalence theorem.