[R] Odd results from rpart classification tree

Therneau, Terry M., Ph.D. therneau at mayo.edu
Mon May 15 14:43:11 CEST 2017

```You are mixing up two of the steps in rpart.  1: how to find the best candidate split and
2: evaluation of that split.

With the "class" method we use the information or Gini criteria for step 1.  The code
finds a worthwhile candidate split at 0.5 using exactly the calculations you outline.  For
step 2 the criteria is the "decision theory" loss.  In your data the estimated rate is 0
for the left node and 15/45 = .333 for the right node.  As a decision rule both predict
y=0 (since both are < 1/2).  The split predicts 0 on the left and 0 on the right, so does
nothing.

The CART book (Brieman, Freidman, Olshen and Stone) on which rpart is based highlights the
difference between odds-regression (for which the final prediction is a percent, and error
is Gini) and classification.  For the former treat y as continuous.

Terry T.

On 05/15/2017 05:00 AM, r-help-request at r-project.org wrote:
> The following code produces a tree with only a root. However, clearly the tree with a split at x=0.5 is better. rpart doesn't seem to want to produce it.
>
> Running the following produces a tree with only root.
>
> y <- c(rep(0,65),rep(1,15),rep(0,20))
> x <- c(rep(0,70),rep(1,30))
> f <- rpart(y ~ x, method='class', minsplit=1, cp=0.0001, parms=list(split='gini'))
>
> Computing the improvement for a split at x=0.5 manually:
>
> obs_L <- y[x<.5]
> obs_R <- y[x>.5]
> n_L <- sum(x<.5)
> n_R <- sum(x>.5)
> gini <- function(p) {sum(p*(1-p))}
> impurity_root <- gini(prop.table(table(y)))
> impurity_L <- gini(prop.table(table(obs_L)))
> impurity_R <- gini(prop.table(table(obs_R)))
> impurity <- impurity_root * n - (n_L*impurity_L + n_R*impurity_R) # 2.880952
>
> Thus, an improvement of 2.88 should result in a split. It does not.
>
> Why?
>
> Jonathan
>
>

```