What does the Gini coefficient measure in binary prediction?

The Gini coefficient in the context of binary prediction is indeed a measure derived from the ROC (Receiver Operating Characteristic) curve. More specifically, it is calculated as twice the area under the ROC curve minus one, which can also be expressed as 2 × (ROC index - 0.5). This relationship means that a Gini coefficient provides a summary measure of a model's ability to discriminate between positive and negative classes; a higher Gini coefficient indicates better model performance.

In terms of interpretation, the Gini coefficient reflects how much better the model is at predicting the outcome compared to random guessing. Since the ROC index measures the true positive rate against the false positive rate, the Gini coefficient effectively captures this discrimination power by transforming the index into a more interpretable scale.

Other options, such as identifying expected revenues and costs, measuring prediction error, or determining model complexity, do not accurately describe the Gini coefficient. While those aspects are indeed important in model evaluation and development, they do not relate to the specific function of the Gini coefficient in assessing classification performance.