Database Reference
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type="l" )
axis(side=4)
mtext(side=4, line=3, "False positive rate")
text(0.18,0.18,"FPR")
text(0.58,0.58,"TPR")
Figure 6.16
The effect of the threshold value in the churn example
For a threshold value of 0, every item is classified as a positive outcome. Thus, the
TPR value is 1. However, all the negatives are also classified as a positive, and the
FPR value is also 1. As the threshold value increases, more and more negative class
labels are assigned. Thus, the FPR and TPR values decrease. When the threshold
reaches 1, no positive labels are assigned, and the FPR and TPR values are both 0.
For the purposes of a classifier, a commonly used threshold value is 0.5. A positive
label is assigned for any probability of 0.5 or greater. Otherwise, a negative label is
assigned. As the following R code illustrates, in the analysis of the Churn dataset,
the 0.5 threshold corresponds to a TPR value of 0.56 and a FPR value of 0.08.
i <- which(round(alpha,2) == .5)
paste("Threshold=" , (alpha[i]) , " TPR=" , tpr[i] , "
FPR=" , fpr[i])
[1] "Threshold= 0.5004 TPR= 0.5571 FPR= 0.0793"
Thus, 56% of customers who will churn are properly classified with the
Churn
label, and 8% of the customers who will remain as customers are improperly
labeled as
Churn
. If identifying only 56% of the churners is not acceptable, then
the threshold could be lowered. For example, suppose it was decided to classify
with a
Churn
label any customer with a probability of churning greater than 0.15.
