Improved likelihood ratio tests in beta-prime regression models

{Bartlett correction factor and a Skovgaard adjustment for the likelihood ratio test in beta-prime regression models are derived and compared numerically using Monte Carlo simulations.} We address the problem of testing hypotheses in beta-prime regression models when the sample size is small or moderate. We focus on the likelihood ratio test, which can suffer from size distortion when the sample size is not large enough to ensure a good approximation between the exact distribution of the likelihood ratio statistic and its reference asymptotic chi-square distribution in this class of regression models. To overcome this shortcoming, we derive the Bartlett correction factor and a Skovgaard adjustment for the likelihood ratio test statistic. We numerically compare the (usual and modified) likelihood ratio tests and bootstrap-based tests using Monte Carlo simulation experiments. The numerical results reveal that the corrected tests and the bootstrap tests exhibit a type I error probability closer to the true nominal level without loss of power. Finally, we present an application to a real data set for illustrative purposes.