The area under the Receiver operating characteristic (ROC) curve is an aggregate measure of binary classifier performance across all threshold values:
- A classifier that is always right (“perfect classifier”) has area 1.0;
- A random classifier has area 0.5; and
- A classifier that is always wrong has area 0.0.
Is is scale-invariant: the actual prediction values are not taken into consideration. This is helpful if we only care about the final classification, but it is undesirable if we care about the predicted probability (no threshold).
Neither the ROC nor the area under it gives us information about true negatives, and hence about negative predictive value.