What is variable importance?
A30. CART automatically produces a predictor ranking (also known as variable importance) based on the contribution predictors make to the construction of the tree. Predictor rankings are strictly relative to a specific tree; change the tree and you might get very different rankings. Importance is determined by playing a role in the tree, either as a main splitter or as a surrogate. CART users have the option of fine tuning the variable importance algorithm. Variable importance for a particular predictor is the sum across all nodes in the tree of the improvement scores that the predictor has when it acts as a primary or a surrogate (but not as a competitor) splitter. Specifically, for node i, if the predictor appears as the primary splitter, then it has a contribution toward the importance of: importance_contribution_node_i = improvement If instead, the predictor appears as the nth surrogate instead of as the primary predictor, the expression is: importance_contribution_node_i = (p ^ n)
