Ranking-based evaluation of regression models

We suggest the use of ranking-based evaluation measures for regression models, as a complement to the commonly used residual-based evaluation. We argue that in some cases, such as the case study we present, ranking can be the main underlying goal in building a regression model, and ranking performance is the correct evaluation metric. However, even when ranking is not the contextually correct performance metric, the measures we explore still have significant advantages: They are robust against extreme outliers in the evaluation set; and they are interpretable. The two measures we consider correspond closely to non-parametric correlation coefficients commonly used in data analysis (Spearman\´s p and Kendall\´s r); and they both have interesting graphical representations, which, similarly to ROC curves, offer useful "partial" model performance views, in addition to a one-number summary in the area under the curve. We illustrate our methods on a case study of evaluating IT wallet size estimation models for IBM\´s customers.