Beta regressions are widely used for modeling random variables that assume values in the standard unit interval, (0, 1), such as rates, proportions, and income concentration indices. Parameter estimation is typically performed via maximum likelihood, and hypothesis testing inferences on the model parameters are commonly performed using the likelihood ratio test. Such a test, however, may deliver inaccurate inferences when the sample size is small. It is thus important to develop alternative testing procedures that are more accurate when the sample contains only few observations. In this paper, we consider the beta regression model with parametric mean link function and derive two modified likelihood ratio test statistics for that class of models. We provide simulation evidence that shows that the new tests usually outperform the standard likelihood ratio test in samples of small to moderate sizes. We also present and discuss two empirical applications.

Beta回归广泛用于建模随机变量，这些随机变量采用标准单位区间（0，1）中的值，例如比率，比例和收入集中度指数。通常通过最大似然来执行参数估计，通常使用似然比检验来执行对模型参数的假设检验推断。但是，当样本量较小时，此类测试可能无法提供准确的推断。因此，重要的是要开发出替代的测试程序，当样品仅包含少量观察值时，这些测试程序应更加准确。在本文中，我们考虑具有参数均值链接函数的beta回归模型，并为该类模型得出两个修改的似然比检验统计量。我们提供的模拟证据表明，在中小规模样本中，新测试通常优于标准似然比测试。我们还将介绍和讨论两个经验应用。