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General mixed Poisson regression models with varying dispersion

机译：离散度变化的一般混合Poisson回归模型

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摘要

A general class of mixed Poisson regression models is introduced. This class is based on a mixing between the Poisson distribution and a distribution belonging to the exponential family. With this, we unified some overdispersed models which have been studied separately, such as negative binomial and Poisson inverse gaussian models. We consider a regression structure for both the mean and dispersion parameters of the mixed Poisson models, thus extending, and in some cases correcting, some previous models considered in the literature. An expectation-maximization (EM) algorithm is proposed for estimation of the parameters and some diagnostic measures, based on the EM algorithm, are considered. We also obtain an explicit expression for the observed information matrix. An empirical illustration is presented in order to show the performance of our class of mixed Poisson models. This paper contains a Supplementary Material.
机译：介绍了混合泊松回归模型的一般类别。此类基于泊松分布与属于指数族的分布之间的混合。这样，我们统一了一些已经分别研究的过度分散模型，例如负二项式模型和泊松逆高斯模型。我们考虑混合泊松模型的均值和离散参数的回归结构，从而扩展了文献中考虑的某些先前模型，并在某些情况下进行了校正。提出了一种期望最大化算法来估计参数，并考虑了基于EM算法的一些诊断措施。我们还为观察到的信息矩阵获得了一个明确的表达式。为了说明我们的混合泊松模型类别的性能，提供了一个经验例证。本文包含补充材料。

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