After a split is conducted, the observations in the learning sample are divided into the different nodes defined by the respective splitting variable and cutpoint, and in each node splitting continues recursively until some stop condition is reached. Common stop criteria are: split until (a) all leaf nodes are pure (i.e. contain only observations of one class) (b) a given threshold for the minimum number of observations left in a node is reached or (c) a given threshold for the minimum change in the impurity measure is not succeeded any more by any variable. Recent classification tree algorithms also provide statistical stopping criteria that incorporate the distribution of the splitting criterion (Hothorn, Hornik, and Zeileis 2006), while early algorithms relied on pruning the complete tree to avoid overfitting.
