Bessel regression and bbreg package to analyse bounded data

• Published in: Australian & New Zealand journal of statistics 2021-12, Vol.63 (4), p.685-706
• Main Authors: Barreto‐Souza, Wagner, Mayrink, Vinícius D., Simas, Alexandre B.
• Format: Article
• Language: English
• Subjects: Adequacy; Algorithms; beta regression; Dirichlet problem; Empirical analysis; expectation–maximisation algorithm; Gaussian process; Inference; misspecification; model selection; normalised inverse‐Gaussian distribution; Regression models
• ISSN: 1369-1473; 1467-842X
• DOI: 10.1111/anzs.12354

Summary 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.