Bootstrap Bartlett correction in inflated beta regression

TL;DR

This paper introduces a bootstrap Bartlett correction for likelihood ratio tests in inflated beta regression models, improving inference accuracy in small samples through a simple Monte Carlo method.

Contribution

It proposes a novel bootstrap Bartlett correction for likelihood ratio tests in inflated beta regression, enhancing small-sample inference reliability.

Findings

Corrected test shows better size accuracy in simulations

Improved power compared to uncorrected tests

Application to real data demonstrates practical usefulness

Abstract

The inflated beta regression model aims to enable the modeling of responses in the intervals $(0,1]$, $[0,1)$ or $[0,1]$. In this model, hypothesis testing is often performed based on the likelihood ratio statistic. The critical values are obtained from asymptotic approximations, which may lead to distortions of size in small samples. In this sense, this paper proposes the bootstrap Bartlett correction to the statistic of likelihood ratio in the inflated beta regression model. The proposed adjustment only requires a simple Monte Carlo simulation. Through extensive Monte Carlo simulations the finite sample performance (size and power) of the proposed corrected test is compared to the usual likelihood ratio test and the Skovgaard adjustment already proposed in the literature. The numerical results evidence that inference based on the proposed correction is much more reliable than that based on the usual likelihood ratio statistics and the Skovgaard adjustment. At the end of the work, an application to real data is also presented.