ROC Curve

The Receiver Operating Characteristic (ROC) curve is a graphical plot that illustrates the diagnostic ability of a binary classifier (e.g. Logistic Regression) as its discrimination threshold is varied. At each threshold, predictions form a Confusion Matrix from which the curve’s two axes are derived.

Components

• X-axis: False Positive Rate (FPR) = FP / (FP + TN)
• Y-axis: True Positive Rate (TPR) = TP / (TP + FN) (also called Recall or Sensitivity)

AUC (Area Under the Curve)

AUC summarizes the curve as one of the standard classification metrics:

• AUC = 1.0: Perfect classifier
• AUC = 0.5: Random classifier (diagonal line)
• AUC < 0.5: Worse than random

Interpretation

• The closer the curve follows the left-hand border and then the top border of the ROC space, the more accurate the test
• The closer the curve comes to the 45-degree diagonal, the less accurate the test

Advantages

• Threshold-independent evaluation
• Useful for imbalanced datasets (compare with Average Precision for very skewed data)
• Allows comparison of different models