Comparação de funções de ligação em modelos de regressão para respostas binárias com dados desbalanceados

Abstract

This work aims to compare different link functions applied to Generalized Linear Models (GLMs) for binary response variables, especially in contexts with unbalanced data. Traditional link functions, such as Logit, Probit, and Cloglog, as well as generalized extensions based on Power and Reverse Power functions, were evaluated. The interest in conducting this study arises from the claims in the literature that asymmetric links tend to exhibit superior predictive performance compared to symmetric functions in scenarios with strong imbalance. Accordingly, this work sought to systematically investigate whether such an advantage is indeed observed in practice. To this end, Monte Carlo simulation studies and applications to various real datasets were conducted, allowing observation in practice of how these functions behave under different degrees of imbalance. The analyses allowed us to evaluate, in various contexts, whether the flexibility introduced by the additional parameters of these links results in relevant gains in performance or stability. In general, the results showed that the different link functions, both traditional and generalized, presented very similar Area Under the ROC Curve (AUC) values in both simulations and practical applications, maintaining similar performance patterns even when faced with changes in the degree of imbalance, the distribution of covariates,or the number of predictors.