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Name: Gloria Gheno

Talk Title: A new link function for frequentist beta regression

Abstract: The beta regression is used to analyze variables which affect variables whose value is included in the unit interval. For the regressions with binary data, the literature has debated the problem of incorrect link functions and therefore new links have been proposed, such as gev (Generalized extreme value). For the mean of the beta regression, instead, the traditional link functions used for binary regressions, i.e. logit, probit and complementary log-log, are used. In my previous work I proposed a new non-monotone function for the beta regression in the Bayesian context. In this paper I propose, instead, a different link function for the mean parameter of a beta regression but in frequentist domain, a modification which also requires the creation of an algorithm created by me ad hoc for parameter estimation. Both link functions have as their particular cases the logit function, representing a traditional symmetric link function, and the gev function, proposed for binary data due to its asymmetry. These two link functions, proposed by me, have the advantage that they can also be non-monotone, unlike those until now present in the literature. In this work the parameters are estimated maximizing the likelihood function, using a version, which I modified, of the genetic algorithm so as to give greater relevance to the traditional link functions than the others. The algorithm divides the dataset into training sets and test sets to evaluate the model and choose the best one. I compare my method with those already present in the literature, in which the researcher decides a priori the link function, using simulated data, in order to establish which of the 2 methods is closest to the true values. My method is better because it is able to correctly determine the link function with which the data are simulated and to estimate the parameters with less error. Its use increases the understanding of the relationships among variables.

This talk is a contributed talk at EVA 2021.