Thanks Terry!

I managed to figure that out shortly after posting (as is the way!) Adding an additional covariate that splits below one of the x branches but not the other and means the class proportion to go over 0.5 means the x split is retained.

However, I now have another conundrum, this time with rpart in anova mode...

library(rpart)

test_split <- function(offset) {

y <- c(rep(0,10),rep(0.5,2)) + offset

x <- c(rep(0,10),rep(1,2))

if (is.null(rpart(y ~ x, minsplit=1, cp=0, xval=0)$splits)) 0 else 1

}

sum(replicate(1000, test_split(0))) # 1000, i.e. always splits

sum(replicate(1000, test_split(0.5))) # 2-12, i.e. splits only sometimes...

Adding a constant to y and getting different trees is a bit strange, particularly stochastically.

Will see if I can track down a copy of the CART book.

Jonathan

________________________________________

From: Therneau, Terry M., Ph.D. [

[hidden email]]

Sent: 16 May 2017 00:43

To:

[hidden email]; Marshall, Jonathan

Subject: Re: Odd results from rpart classification tree

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,

[hidden email] 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

>

>

______________________________________________

[hidden email] mailing list -- To UNSUBSCRIBE and more, see

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.