Credit scoring optimization using the area under the curve

Anne Kraus and Helmut Küchenhoff

Abstract

ABSTRACT

In consumer credit scoring, the area under the receiver operating characteristic curve (AUC) is one of the most commonly used measures for evaluating predictive performance. In our analysis, we aim to explore different methods for optimizing the scoring problem in order to maximize the AUC. Not only are the existing methods pertaining to the use of the AUC to measure prediction accuracy evaluated, but the AUC is introduced as an objective function to optimize prediction accuracy directly. For the AUC approach, the coefficients are estimated by calculating the AUC measure using the Wilcoxon-Mann-Whitney and Nelder-Mead algorithms. In a simulation study, we compare our new method to the logit model using different measures for predictive performance. The simulation study indicates the superiority of the AUC approach in cases where the logistic model assumption fails. From machine learning we explore boosting methods by additionally using the AUC as a loss function. Our evaluation of German retail credit data includes different performance measures and shows superior results in terms of the prediction accuracy of the boosting algorithms as well as the AUC approach compared with the most widely used logistic regression model.