Gamma区组效应下Poisson计数数据的最优设计
Optimal Designs for Poisson Count Data with Gamma Block Effects
摘要：
Poisson-Gamma模型是Poisson模型的推广，可用于计数数据建模。我们证明了Poisson-Gamma模型的$D$ -最优性准则等价于Poisson模型的$D$ -最优性和$D_s$ -最优性的组合加权最优性准则。此外，我们确定了具有任意数量协变量的Poisson-Gamma多元回归模型的$D$ -最优设计，得到了Poisson-Gamma和Poisson-Gamma模型的$D_s$ -最优设计作为特例。对于线性最优性准则，如$L$ -和$c$ -最优性，它表明，最优设计的泊松和泊松-伽马模型相吻合。
英文摘要：
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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