The COM–Poisson distribution is a two-parameter generalization of the Poisson distribution that can deal with under-, equi- and overdispersed count data. Unfortunately, its location parameter does not correspond to the expectation, which complicates the parameter interpretation. In this article, we propose a straightforward reparametrization of the COM–Poisson distribution based on an approximation to the expectation. Estimation and inference are done using the likelihood paradigm. Simulation studies show that the maximum likelihood estimators are unbiased and consistent for both regression and dispersion parameters. In addition, the nature of the deviance surfaces suggests that these parameters are also orthogonal for most of the parameter space, which is advantageous for interpretation, inference and computational efficiency. Study of the distribution’s properties, through a consideration of dispersion, zero-inflation and heavy tail indexes, together with the results of data analyses show the flexibility over standard approaches. The computational routines and datasets are available in the supplementary material.

中文翻译：

---

COM-Poisson 回归模型的重新参数化及其在实验数据分析中的应用

COM-Poisson 分布是 Poisson 分布的双参数泛化，可以处理分散不足、均匀分布和过度分散的计数数据。不幸的是，它的位置参数不符合预期，这使得参数解释复杂化。在本文中，我们提出了基于期望近似值的 COM-Poisson 分布的直接重新参数化。估计和推理是使用似然范式完成的。模拟研究表明，最大似然估计量对于回归和离散参数都是无偏的和一致的。此外，偏差曲面的性质表明这些参数对于大部分参数空间也是正交的，这有利于解释、推理和计算效率。通过考虑离散、零通胀和重尾指数，以及数据分析的结果，对分布特性的研究显示了标准方法的灵活性。计算例程和数据集可在补充材料中找到。