Corrected likelihood ratio test in Beta-Prime regression models
Beta-prime regression models; Likelihood ratio test; Bartlett correction; Skovgaard
adjustment; Bartlett bootstrap correction.
This paper deals with the issue of testing hypotheses in beta-prime regression
models in smallandmoderate-sizedsamples.Wefocusonthelikelihoodratiotest,whichisunreliable
when the sample size is not large enough to guarantee a good approximation between the
exact distribution of the test statistic and the corresponding chi-squared asymptotic
distribution. Bartlett, Skovgaard and Bartlett-bootstrap corrections typically attenuate the size
distortion of the test. Here, we derive a Bartlett correction and a Skovgaard adjustment for the
likelihood ratio test on beta-prime regression models. We numerically compare the usual,
corrected and bootstrapped tests, through simulations. Our results suggest that the corrected
and bootstrapped tests exhibit type I probability error closer to the chosen nominal level The
analytically corrected tests perform with the advantage of not requiring computationally
intensive calculations. We present a real data application to illustrate the usefulness of the
modified tests.