Bartlett corrections in beta regression models

TL;DR

This paper develops Bartlett corrections for likelihood ratio tests in beta regression models, improving small-sample inference accuracy for proportions and rates, and demonstrates their effectiveness through simulations and an empirical example.

Contribution

It introduces Bartlett and bootstrap Bartlett corrections for beta regression likelihood ratio tests, enhancing small-sample performance over existing methods.

Findings

Corrected tests outperform standard likelihood ratio tests in simulations.

Numerical results favor Bartlett-corrected tests over Skovgaard's adjustment.

Empirical application illustrates practical benefits of the corrections.

Abstract

We consider the issue of performing accurate small-sample testing inference in beta regression models, which are useful for modeling continuous variates that assume values in $(0,1)$, such as rates and proportions. We derive the Bartlett correction to the likelihood ratio test statistic and also consider a bootstrap Bartlett correction. Using Monte Carlo simulations we compare the finite sample performances of the two corrected tests to that of the standard likelihood ratio test and also to its variant that employs Skovgaard's adjustment; the latter is already available in the literature. The numerical evidence favors the corrected tests we propose. We also present an empirical application.