Improved likelihood inference in unit gama regressions

Abstract

In this dissertation, we focus on the issue of performing likelihood ratio testing inferences in unit gamma regressions. Our interest lies in testing inferences that are accurate and reliable in small samples. The unit gamma regression model was proposed by Mousa et al. (2016) based on the unit gamma distribution introduced by Grassia (1977). Closed form expressions for the score vector and for Fisher’s information matrix were obtained by Mousa et al. (2016). The model is useful for dealing with doubly limited continuous dependent variables (DLCDV), such as proportions, indices and rates, being an alternative to the beta regression model, which has been widely used in the literature. We derive a small sample adjustment to the likelihood ration ratio test statistic in the class of unit gamma regressions using the approach proposed by Skovgaard (2001). The numerical evidence we present show that the two corrected tests we propose outperform the standard likelihood ratio test in small samples. A real data example is presented.