Adjusted R2 - type measures for beta regression model

Abstract

R² measure, which named coefficient of determination, is usually used as tools for evaluation the predictive power of the regression models. However, this measure, which is based on deviance for generalized linear models, is sensitive to the small samples. Therefore, it is necessary to adjust R² measure according to the number of covariates. Beta regression model has received much attention in several science fields in modeling proportions or rates data. In this paper, several adjusted R² measures are proposed in beta regression models. The performance of the proposed measures is evaluated through simulation and real data application. Results demonstrate the superiority of the proposed measures compared to others.