# What is the rationale behind ROC curves?

I am not sure how ROC curves work. I see that the X-Axis is the false positive rate while the Y axis is the true positive rate.

1) I don't understand how for a given statistical learning model, you could have the true positive and false positive rate to vary from 0 to 1. Are you changing parameters in the model to make it so?

2) What about true negatives and false negatives? How are these represented in the curve?

Best,

1) Yes, you are supposed to compare "different models" and the curve will help you identify which one is the best for your desired application. So, for instance, if you would like to know how well your system detects "$X$", you should vary a certain threshold value to see how well the system detects $X$ given the different conditions.

You can find more information about it in sources as Wikipedia. You can look specifically in the "ROC space" section where they compare $4$ different models.

2) The True Positive Rate is defined as: $TPR=\frac {TP} {TP+FN}$, the True Negative Rate is defined as: $TNR=\frac{TN} {TN+FP}$, where $TP =$ True Positives, $FN =$ False Negatives, $TN =$ True Negatives, and $FP =$ False Positives.

As you can see, both of them consider the true negatives and the false negatives.

Also, I found this paper quite useful in understanding this better:

Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation. By D.M.W. Powers.

I hope it helps!