Bootstrap Bartlett correction in inflated beta regression

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 article 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.

KEYWORDS:

• Bootstrap Bartlett correction
• Improvements in small samples
• Inflated beta regression
• Likelihood ratio test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F40
• 62F03
• 62Jxx

Acknowledgments

The authors thank two referees for comments and suggestions.

Funding

The authors acknowledge the financial support received by CAPES, FAPERGS, and CNPq, Brazil.