Classification trees are known to be unstable with respect to training data. Recently I have read an article on stability of classification trees by Briand et al. (2009). They propose a quantitative similarity measure between two trees. The method is interesting and it inspired me to prepare a simple test data based example showing instability of classification trees.

I compare stability of logistic regression and classification tree on Participation data set from Ecdat package. The method works as follows:

1. Divide the data into training and test data set;
2. Generate a random subset of training data and build logistic regression and classification tree using them;
3. Apply the models on test data to obtain predicted probabilities;
4. Repeat steps 2 and 3 many times;
5. For each observation in test data set calculate standard deviation of obtained predictions for both classes of models;
6. For both models plot kernel density estimator of standard deviation distribution in test data set.

The code performing the above steps is as follows:


And here is the generated comparison. As it can be clearly seen logistic regression gives much more stable predictions in comparison to classification tree.