Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data without a strong competitor having the same main features. A class of normalised inverse-Gaussian (N-IG) process was introduced in the literature and has been explored in the Bayesian context as a powerful alternative to the Dirichlet process. Until this moment, no attention has been paid to the univariate N-IG distribution in the classical inference. In this paper, we propose the bessel regression based on the univariate N-IG distribution, which is an alternative to the beta model. The estimation of the parameters is done through an expectation–maximisation (EM) algorithm and the paper discusses how to perform inference. A useful and practical discrimination procedure is proposed for model selection between bessel and beta regressions. A new R package called bbreg is developed for fitting both bessel and beta regression models based on the EM-algorithm and further providing graphical tools for model adequacy and model selection as well. Proper documentation for this package is available. The performances of the models are evaluated under misspecification in a simulation study. An empirical illustration is explored to confront results from bessel and beta regressions by using the new R package bbreg.

中文翻译：

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贝塞尔回归和 bbreg 包分析有界数据

Beta 回归已被统计学家和从业者广泛用于对有界连续数据进行建模，而没有强大的竞争对手具有相同的主要特征。文献中介绍了一类归一化反高斯 (N-IG) 过程，并已在贝叶斯环境中作为 Dirichlet 过程的有力替代方案进行了探索。到目前为止，还没有注意到经典推理中的单变量 N-IG 分布。在本文中，我们提出了基于单变量 N-IG 分布的贝塞尔回归，它是 beta 模型的替代方案。参数的估计是通过期望最大化（EM）算法完成的，本文讨论了如何进行推理。为贝塞尔和贝塔回归之间的模型选择提出了一种有用且实用的判别程序。名为bbreg的R包是为基于 EM 算法拟合贝塞尔和贝塔回归模型而开发的，并进一步为模型充分性和模型选择提供图形工具。该软件包的适当文档可用。在模拟研究中，模型的性能是在错误指定的情况下进行评估的。通过使用新的R包bbreg，探索了一个经验说明来面对贝塞尔和贝塔回归的结果。