The
specificity of a model is the true negative rate. To
derive the
false positive rate, subtract the specificity from 1. The false positive rate, labeled
1
– Specificity, is the X axis of the ROC chart.
The
sensitivity of a model is the true positive rate. This is the Y axis of the ROC chart. Therefore,
the ROC chart plots how the true positive rate changes as the false positive rate
changes.
A good ROC chart has a very steep initial slope and levels off quickly. That is, for
each misclassification of an observation, significantly more observations are correctly
classified. For a perfect model, one with no
false positives and no
false negatives, the ROC chart would start at (0,0), continue vertically to (0,1), and then horizontally
to (1,1). In this instance, the model would correctly classify every observation before
a single misclassification could occur.
The ROC chart includes two lines to help you interpret the ROC chart. The first line
is a
baseline model that has a slope of 1. This line mimics a model that correctly classifies observations
at the same rate it incorrectly classifies them. An ideal ROC chart maximizes the
distance between the baseline model and the ROC chart. A model that classifies more
observations incorrectly than correctly would fall below the baseline model. The second
line is a vertical line at the false positive rate where the difference between the
Kolmogorov-Smirnov values for the ROC chart and
baseline models is maximized.