Improved testing inferences for beta regressions with parametric mean link function

Abstract

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.