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It is widely believed that the prediction accuracy of decision tree models isinvariant under any strictly monotone transformation of the individualpredictor variables. However, this statement may be false when predicting newobservations with values that were not seen in the training-set and are closeto the location of the split point of a tree rule. The sensitivity of theprediction error to the split point interpolation is high when the split pointof the tree is estimated based on very few observations, reaching 9%misclassification error when only 10 observations are used for constructing asplit, and shrinking to 1% when relying on 100 observations. This studycompares the performance of alternative methods for split point interpolationand concludes that the best choice is taking the mid-point between the twoclosest points to the split point of the tree. Furthermore, if the (continuous)distribution of the predictor variable is known, then using its probabilityintegral for transforming the variable ("quantile transformation") will reducethe model's interpolation error by up to about a half on average. Accordingly,this study provides guidelines for both developers and users of decision treemodels (including bagging and random forest).

Splitting matters: how monotone transformation of predictor variables may improve the predictions of decision tree models