In this paper, case-deletion diagnostics in beta regression models are proposed. The diagnostics are based on the distance between the distributions of the maximum likelihood estimates of the model parameters resulting from the entire sample and after removing a sample case. Two metrics between probability distributions are considered: the Frèchet distance (Frèchet in Comptes Rendus hebdomadaires des seances de l’Academie des Sciences de Paris 244:689–692, 1957), and the Rao distance (Rao in Indian J Stat Ser A 9:246–291, 1949). Moreover, a jackknife-after-bootstrap transformation of the diagnostics is also proposed to make clear the decision about cases to be considered as influential. Artificial and real examples are included to illustrate the usefulness of the diagnostics and to compare them to others in the literature.

中文翻译：

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Beta回归模型中分布之间的距离的影响度量

本文提出了β回归模型中的病例删除诊断方法。诊断是基于整个样本和移除样本后的模型参数的最大似然估计分布之间的距离。考虑了概率分布之间的两个指标：Frèchet距离（Frèchet距离，巴黎科学研究院计算机科学系244：689-692，1957年）和Rao距离（印度J Stat Ser A 9中的Rao： 246–291，1949年）。此外，还提出了诊断程序的“折刀后引导”转换，以明确有关被认为具有影响力的案例的决定。包含了人工的和真实的示例，以说明诊断的有效性并将其与文献中的其他示例进行比较。