Gini Coefficient and AUC in Assessing Predictive Model Performance : Effect of Ranks

Abstract

This paper deals with three traditional measures of concentration: (Corrado) Gini coefficient, adjusted Gini coefficient, and AUC. These metrics are popular methods in assessing the performance of predictive models, like credit scoring models. They are non-parametric variables and therefore only depending on the ranking of events. The three measures are closely related to each other. The adjusted Gini coefficient (Accuracy ratio, AR) is only a transformation of the Corrado Gini coefficient being in a linear relationship with AUC. It also equals to Somers’ D. This paper also introduces the measure E, which is based on a classification of the ranks of events. E produces the same result as AUC, but is simple to calculate and interpret. The features of the metrics are discussed in three numerical examples, one of which deals with credit scoring in a large imbalanced dataset (23.533 active firms and 147 bankrupt firms). Numerical examples are used to illustrate the properties of the metrics, especially at the level of ranks.