Corrected likelihood ratio test statistics for a class of beta regressions with parametric 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 these parameters that index the model 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 master’s thesis, we introduce the linear and nonlinear beta regression models with parametric mean link function, and derive two modified likelihood ratio test statistics for performing improved testing inferences in that class of models. We also obtain a score test statistic that can be used to test, in the same class of models, whether the true link function is logit. 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.