Data Analysis and Related Applications, Volume 1

13A New Non-monotonic Link Function for Beta Regressions

Beta regression is used to analyze data whose value is within the range (0,1), such as rates, proportions or percentages, and therefore is useful for analyzing the variables that affect them (Ferrari and Cribari-Neto 2004; Simas et al. 2010). This method is based on the beta distribution or its re-parametrizations, proposed by Ferrari and Cribari-Neto (2004) and Cribari-Neto and Souza (2012), to obtain a regression structure on the mean that is easier to analyze and interpret. For the regression for binary data, the literature has debated the problem of incorrect link functions and therefore proposed new links, such as gev (generalized extreme value), while, for the mean of the beta regression, the traditional link functions for binary regressions were used, i.e. logit, probit and complementary log–log. In this chapter, a new inverse link function is proposed for the mean parameter of a beta regression, which has as its particular cases inverse logit, representing a traditional symmetric inverse link function, and gev, proposed for binary data due to its asymmetry. The new inverse link function proposed in this chapter has the advantage that it can also be non-monotonic, unlike those proposed until now. The parameters are estimated maximizing the likelihood function, using a modified version of the genetic algorithm, therefore giving greater importance to traditional link functions than the others. This method is compared ...