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 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.Comment: 17 pages, 2 figures, 3 table

Improved heteroskedasticity likelihood ratio tests in symmetric nonlinear regression models

“…Alternatively, the decision rule can be written based on the bootstrap p-value given by p * = #{L R b boot ≥ L R}/B. Recent works have developed inference based on these tests, see for example Bayer and Cribari-Neto (2013), Cribari-Neto and Queiroz (2014), and Loose et al (2016). An advantage of using the bootstrap Bartlett correction instead of the usual bootstrap technique is its computational efficiency.…”