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The predicted response for each observation in a partition model is a value between 0 and 1. To use the predicted response to classify observations as positive or negative, a cut point is used. For example, if the cut point is 0.5, an observation with a predicted response at or above 0.5 would be classified as positive, and an observation below 0.5 as negative. There are trade offs in classification as the cut point is varied.
The sensitivity is the proportion of true positives or the percent of positive observations with a predicted response greater than the cut point.
The specificity is the proportion of true negatives or the proportion of negative observations with a predicted response less than the cut point.
The ROC curve plots sensitivity against 1 - specificity. A partition model with n splits has n+1 predicted values. The ROC curve for the partition model has n+1 line segments.
Figure 5.17 ROC Curves for a Three Level Response

Help created on 3/19/2020