17 January 2024 | Paolo Giudici, Emanuela Raffinetti
This paper introduces the Rank Graduation Accuracy (RGA) as a unified measure of predictive accuracy that can be applied to both binary and continuous response variables. RGA is shown to be equivalent to the AUROC measure in the binary case and to the Wilcoxon-Mann–Whitney statistic. It evaluates point predictions based on their ranks rather than their actual values, improving robustness. The RGA is derived from the concordance curve, which generalizes the predictive accuracy problem to all ordered variable scales: continuous, ordinal, and binary. The RGA is invariant under positive affine transformations and provides a normalized measure of predictive accuracy. The paper validates the RGA on simulated and real data, showing that it performs well in model selection and comparison. The RGA is particularly useful for evaluating the accuracy of probability forecasts, ordinal ranks, and point predictions. The results demonstrate that RGA is a versatile and robust measure of predictive accuracy that can be applied to a wide range of response variables.This paper introduces the Rank Graduation Accuracy (RGA) as a unified measure of predictive accuracy that can be applied to both binary and continuous response variables. RGA is shown to be equivalent to the AUROC measure in the binary case and to the Wilcoxon-Mann–Whitney statistic. It evaluates point predictions based on their ranks rather than their actual values, improving robustness. The RGA is derived from the concordance curve, which generalizes the predictive accuracy problem to all ordered variable scales: continuous, ordinal, and binary. The RGA is invariant under positive affine transformations and provides a normalized measure of predictive accuracy. The paper validates the RGA on simulated and real data, showing that it performs well in model selection and comparison. The RGA is particularly useful for evaluating the accuracy of probability forecasts, ordinal ranks, and point predictions. The results demonstrate that RGA is a versatile and robust measure of predictive accuracy that can be applied to a wide range of response variables.