# How to make a ROC curve for multiple parameters/thresholds

I have a prediction model that performs a binary classification. The model takes 3 independent predictor parameters variables that can only be integers. I have calculated true positive rates (TPR) and false positive rates for each combination of three predictors. Each dot in the figure below represents TPR (y-axis) vs FPR (x-axis) of each combination.

Since there are more than 1 parameter, I can not apply a conventional ROC curve, however is there a way to represent success of a model with multiple parameters? Or would it still be reasonable to construct ROC for best and worst case scenarios, such as the figure below?

• I think you need to edit this to clarify. What do you mean by an integer parameter? Do you mean predictor variables which can only take on integer values? What do the dots represent? Why are there different numbers of dots in each column, or is that just overprinting? – mdewey Jan 30 '18 at 13:10
• It is not overprinting, they are just happened as a consequence of multiple predictor parameters. I edited the rest as you suggested, I hope it is clearer. – odoluca Jan 30 '18 at 13:17
• Im also confused as to how you drew your curve. An roc curve is parameterized by varying the classification threshold in your model. Is this what you did? Why does the x axis stop short of 1? – Matthew Drury Jan 30 '18 at 16:48
• I only drew lines over best tpr vs fpr scores. :D I drew it in paint. it stop short of 1 cuz I didnt bother drawing anymore. – odoluca Jan 30 '18 at 21:25

The main problem with using multiple variables in the way you suggest is that it's undefined: let's say you have two variables, so your ROC would use 2 thresholds T_A and T_B. If at some threshold combination (e.g. T_A = 1 and T_B = 1) an observation is positive according to T_A but negative according to T_B, what is the prediction? Combine using logical AND? Logical OR? Round the average?