How are nominal (ordered) predictors and rank related?
A31. One of the strengths of CART is that, for ordered predictors, the only information CART uses are the rank orders of the data – not the actual value of the data. In other words, if you replace a predictor with its rank order, the CART tree will be unchanged. Thus, CART splits cannot be affected by any transform of the data that preserves order (monotone transform). For instance, AGE, log(AGE), AGE^2, etc., all would yield the same split. If you have a nominal variable with values 1,2,3,4,5, as long as the value “5” properly represents the highest value in the data and “1” represents the lowest value, and so forth, then monotone transforms of the data — transforms that preserve rank ordering — will not alter how the predictor acts in the tree. Of course, if a variable is categorical (discrete, unordered, nominal) then the values are just arbitrary labels. Simply indicating to CART that a predictor is variable is sufficient for proper handling.
