I have a problem related to classifying results and performing an ROC analysis or something analagous. Here is my situation:

I have data from subjects that I use to calculate a "laterality index" for each individual. This number can range from -1 to 1. It is possible for each subject to be left-sided, right-sided or bilateral. Typically a cutoff is specified, such that if the absolute value of the laterality index is less than that number, the subject is bilateral, otherwise positive is left, negative is right. E.g. cutoff of 0.15 means a subject with an index less than -0.15 is right-sided, -0.15 to 0.15 is bilateral, and greater than 0.15 is left-sided.

I would like to perform something similar to an ROC analysis to show how varying the cutoff of what is considered left, right, or bilateral affects test characteristics.

I was thinking of true/false positives/negatives in terms of each subject having 2 sides that can be classified correctly or incorrectly. So a left-sided person, given a classification of left-sided counts for one TP and one TN. A bilateral person classified as left-sided would count for one TP and one FN (since the classifier called their right-side negative, when it should not have). The problem with this scheme is that there is no way to make a bilateral person count for 2 FNs, so there is no cutoff value that gives a TPR and FPR of 0.

Sorry if this was confusing, but if I'm approaching this completely incorrectly, I would love some help from experts!