Métodos de categorização de variáveis preditoras em modelos de regressão para variáveis binárias

Abstract

Regression models for binary response variables are very common in several areas of knowledge. The most used model in these situations is the logistic regression model, which assumes that the logit of the probability of a certain event is a linear function of the predictors variables. When this assumption is not reasonable, it is common to make some changes in the model, such as: transformation of predictor variables and/or add quadratic or cubic terms to the model. The problem with this approach is that it hinders parameter interpretation, and in some areas it is fundamental to interpret the parameters. Thus, a common approach is to categorize the quantitative covariates. This work aims to propose two new classes of categorization methods for continuous variables in binary regression models. The first class of methods is univariate and seeks to maximize the association between the response variable and the categorized covariate using measures of association for qualitative variables. The second class of methods is multivariate and incorporates the predictor variables correlation structure through the joint categorization of all covariates. To evaluate the performance, we applied the proposed methods and four existing categorization methods in 3 credit scoring databases and in two simulated cenarios. The results in the real databases suggest that the proposed univariate class of categorization methods performs better than the existing methods when we compare the predictive power of the logistic regression model. The results in the simulated databases suggest that both proposed classes perform better than the existing methods. Regarding computational performance, the multivariate method is inferior and the univariate method is superior to the existing methods.