Recursive Partition in Biostatistics: Stability of Trees and Choice of the Most Stable Classification

Structures found in data by exploratory techniques are notoriously unstable. Suppose that we search for a model within a given family and that we do this on different samples from the same population, D₀, D₁,..., D_B. When only one data set is available, one can think of D as the original data set and the others as bootstrap samples from D₀. Experience shows that one can be practically sure to find different models from different samples. A striking example of this model instability is given by Gong [1], in the context of stepwise logistic regression. The problem can be expected to be even more serious for tree-structured predictors, such as the RECPAM trees [2–4] which are the main concern of this work, since the model is selected out of a family much richer than that of linear regression as usually defined.