Locally D- and A-Optimal Design Framework for Poisson Regression with Square Root Link function

Abstract

The majority of the research articles on optimum experimental designs for generalized linear models focus on Poisson regression models with log-link function. In the generalized linear model (GLM) configuration, the information matrix depends on the unknown parameters of the model. In such a case, an experimenter must take the strategy of identifying local optimum designs i.e. first guessing the best value for the parameters and then calculating the optimal designs. In this article, we examine locally D- and A-optimal designs for a Poisson regression model using square root link function. The Equivalence theorem validates the necessary and sufficient conditions of this optimality criterion.