Regression tree with simulated data - rpart package - r

Question

I have simulated some data to create a regression tree with 3 terminal nodes:
set.seed(1988)
n=1000
X1<-rnorm(n,mean=0,sd=2)
X2<-rnorm(n,mean=0,sd=2)
e<-rnorm(n)
Y=5*I(X1<1)*I(X2<0.2)+4*I(X1<1)*I(X2>=0.2)+3*I(X1>=1)+e
mydat=as.data.frame(cbind(Y,X1,X2))
So, I want first to split by X1<1, and for X1<1 I want to split by X2<0.2. The values of Y in the leaves are the coefficient of the indicator.
If I run the procedure implemented in the RPART package everything is ok in the case above.
mytree<-rpart(Y~.,data=mydat)
mytree
Output:
node), split, n, deviance, yval
* denotes terminal node
1) root 1000 1627.0670 4.043696
2) X1>=0.9490461 326 373.8485 3.124825 *
3) X1< 0.9490461 674 844.8367 4.488135
6) X2>=0.2488142 327 312.7506 3.970742 *
7) X2< 0.2488142 347 362.0582 4.975708 *
It runs also if I try with coefficient all negative.
But when I try to generate some negative and some positive values in the final terms (it means in the "interaction" of the tree, so where the split is divided at a second level), RPART change the order of the split and the value in the leaves are not correct:
Y=-5*I(X1<1)*I(X2<0.2)+4*I(X1<1)*I(X2>=0.2)+3*I(X1>=1)+e
mydat=as.data.frame(cbind(Y,X1,X2))
mytree<-rpart(Y~.,data=mydat)
mytree
Output:
node), split, n, deviance, yval
* denotes terminal node
1) root 1000 17811.4000 0.6136962
2) X2< 0.1974489 515 8116.5350 -2.3192910
4) X1< 1.002815 343 359.7394 -5.0305350 *
5) X1>=1.002815 172 207.4313 3.0874360 *
3) X2>=0.1974489 485 560.3419 3.7281050 *
Anyone have some idea for that problem?
Thanks

Answer 1

You need to tune the complexity parameter cp. See the code below.
# Data Generating Process
set.seed(1988)
n=1000
X1<-rnorm(n,mean=0,sd=2)
X2<-rnorm(n,mean=0,sd=2)
e<-rnorm(n)
Y=-5*I(X1<1)*I(X2<0.2)+4*I(X1<1)*I(X2>=0.2)+3*I(X1>=1)+e
mydat=as.data.frame(cbind(Y,X1,X2))
library(rpart)
mytree<-rpart(Y~.,data=mydat, cp=0.0001)
# Plot the cross-validation error vs the complexity parameter
plotcp(mytree)
# Find the optimal value of the complexity parameter cp
optcp <- mytree$cptable[which.min(mytree$cptable[,4]),1]
# Prune the tree using the optial complexity parameter
mytree <- prune(mytree,optcp)
The pruned tree correctly represents the underlying data generating process
library(rattle)
fancyRpartPlot(mytree)