I am building new features for a binary classifier. The new features fall into two categories: categorical and ordinal. An example of the first feature would be the colours
red, blue, green and one of the second would be integer counts
1, 2, 3, ....
For the ordinal variables I can roughly get an idea at how good each feature is by computing the area under the roc (AUROC) curve. If the AUROC is close to 1, it means that there is a good threshold value for the new feature such that it can discern well between true and false positives.
I would like to have a similar measure for the categorical features. For example, I know in each category what the rate of 1's is. However, it is hard to compare this rate across many category levels. Would be keen to hear your suggestions on what to do.
One thought I had was to fit a logistic regression with the categorical variable as the only predictor, and then calculate the AUROC for the predicted probabilities under this regression.