In random forests, on the other hand, a tree model is fit to every bootstrap sample only once. Then the predictor variables are permuted in an attempt to mimic their absence in the prediction. This approach can be considered in the framework of classical permutation test procedures (Strobl, Boulesteix, Kneib, Augustin, and Zeileis 2008) and is feasible for large problems, but lacks the sound statistical background available for the approach of Azen et al. (2001). Another difference is that random forest variable importances reflect the effect of a variable in complex interactions as outlined above, while the approach of Azen et al. (2001) reflects the main effects – at least as long as interactions are not explicitly included in the candidate models.
