Optimal Designs for Poisson Count Data with Gamma Block Effects
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The Poisson-Gamma model is a generalization of the Poisson model, which can be used for modelling count data. We show that the D-optimality criterion for the Poisson-Gamma model is equivalent to a combined weighted optimality criterion of D-optimality and D_s-optimality for the Poisson model. Moreover, we determine the D-optimal designs for the Poisson-Gamma model for multiple regression with an arbitrary number of covariates, obtaining the D_s-optimal designs for the Poisson and Poisson-Gamma model as a special case. For linear optimality criteria like L- and c-optimality it is shown that the optimal designs in the Poisson and Poisson-Gamma model coincide.
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