Bessel regression model: Robustness to analyze bounded data

TL;DR

This paper introduces the bessel regression model based on the univariate N-IG distribution as a robust alternative to beta regression for analyzing bounded data, with demonstrated advantages through simulations and real data applications.

Contribution

It proposes a novel bessel regression model using the univariate N-IG distribution, including estimation, inference, and model discrimination procedures, addressing robustness issues.

Findings

Bessel regression shows robustness under model misspecification.

The EM algorithm effectively estimates model parameters.

The discrimination procedure reliably compares bessel and beta regressions.

Abstract

Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data and there is no strong and similar competitor having its main features. A class of normalized inverse-Gaussian (N-IG) process was introduced in the literature, being explored in the Bayesian context as a powerful alternative to the Dirichlet process. Until this moment, no attention has been paid for 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 a robust alternative to the beta model. This robustness is illustrated through simulated and real data applications. The estimation of the parameters is done through an Expectation-Maximization 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. Monte Carlo simulation results are presented to verify the finite-sample behavior of the EM-based estimators and the discrimination procedure. Further, the performances of the regressions are evaluated under misspecification, which is a critical point showing the robustness of the proposed model. Finally, three empirical illustrations are explored to confront results from bessel and beta regressions.