Beta Regression for Modelling Rates and Proportions

Abstract. This paper proposes a regression model where the response is beta distributed using a parameterization of the beta law that is indexed by mean and dispersion pa-rameters. The proposed model is useful for situations where the variable of interest is continuous and restricted to the interval (0, 1) and is related to other variables through a regression structure. The regression parameters of the beta regression model are inter-pretable in terms of the mean of the response and, when the logit link is used, of an odds ratio, unlike the parameters of a linear regression that employs a transformed response. Estimation is performed by maximum likelihood. We provide closed-form expressions for the score function, for Fisher’s information matrix and its inverse. Hypothesis testing is performed using approximations obtained from the asymptotic normality of the max-imum likelihood estimator. Some diagnostic measures are introduced. Finally, practical applications that employ real data are presented and discussed.