Optimal Designs for Poisson Count Data with Gamma Block Effects

Marius Schmidt; Rainer Schwabe

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arXiv · 1808.05412

Optimal Designs for Poisson Count Data with Gamma Block Effects

Marius Schmidt·Rainer Schwabe

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Abstract

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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Marius Schmidt, Rainer Schwabe. 2018-08-16. Optimal Designs for Poisson Count Data with Gamma Block Effects. https://arxiv.org/abs/1808.05412

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