I'm interested in assessing model performance on data with an ordinal categorical dependent variable. For my use case, the ideal metric would:
1) Not assume equal intervals between classes or that recoding to a continuous scale is appropriate
2) Be scale independent
3) Give preference to models that rank the outcomes accurately, with higher penalties for mis-ranking classes with a larger degree of difference (e.g., Excellent > Poor > Good is better than Excellent > Very Poor > Good)
4) Accept continuous predictions and be indifferent to their distributions
For example, suppose we have the following test set, where "response" is 5-category ordinal response and "pred1", "pred2", and "pred3" are predictions:
id response pred1 pred2 pred3 1 Excellent 1.00 150 10 2 Good .80 39 9 3 Good .85 12 5 4 Fair .40 11 4 5 Poor .39 10 3 6 Very Poor .20 3 2 . . . . . . . . . .
For my purposes, the ideal metric would score all three predictions as equally accurate since all three perfectly rank the response.
What are my options and the benefits/drawbacks to each? Bonus points for references to R packages or functions. Thanks!