Modelo de regressão beta para diferença de proporções: teoria e aplicações

Abstract

In this work is related a study about a beta regression, in order to model rates or proportions that vary in the interval (−1,1).The probability distribution studied is a particular case of the truncated beta distribution, which assumes values in the interval (a,1), (a < 1), or even the general formula of the beta distribuition in the interval (a,b), where −∞ < a < b < ∞. The beta distribution in the interval (−1,1) was called, in the present work, as modular beta distribution, in which parameterizations were made as a function of the mean and precision, and, therefore, regression structures were assigned to these new parameters. In addition, new link functions were proposed and the parameter estimation was performed using the maximum likelihood method. A simulation study was carried out to verify the performance of the maximum likelihood estimators considering three different types of link functions for the mean. Furthermore, the modular beta regression model was applied to two real data sets referring to the US presidential election in 2016 and the difference between the voting percentages of former president Lula in the 2002 and 2006 elections.