Regression tree analysis: generating split confidence for specific splits

Question

I'm trying to generate bootstrap confidence 'intervals' for particular split(s) of a regression tree using rpart (to generate tree) and boot (to bootstrap) - elaborating on this question/answer.

Example:

data(iris)

library(rpart)
r1<-rpart(Sepal.Length ~ ., cp = 0.05, data=iris)
plot(r1)
text(r1)

library(boot)

trainData <- iris[-150L, ]
predictData <- iris[150L, ]

rboot <- boot(trainData, function(data, idx) {
  bootstrapData <- data[idx, ]
  r1 <- rpart(Sepal.Length ~ ., bootstrapData, cp = 0.05)
  predict(r1, newdata = predictData)
}, 1000L)

Generate quantiles, as rpart has no CI function:

quantile(rboot$t, c(0.025, 0.975))
  2.5%    97.5% 
  5.871393 6.766842

That's ok, BUT, how can I obtain 'quantile' estimates per split in terms of the predictor. For example, quantiles for either side of "Petal.Length<3.4"?

Answer 1

Here's one solution (courtesy of a non-member). Only problem is the no. of splits fluctuates between booting runs, perhaps as a function of small n.

Fit model

library(boot)
library(rpart)
library(lattice)

data(iris)
names(iris)

iris2 <- iris[,c(1,3)]

r1 <- rpart(Sepal.Length ~ Petal.Length, cp = 0.05, data=iris2)
r1$splits
r1$frame

plot tree

plot(r1)
text(r1)

manual booting

n.boot <- 10000

enter no. of splits to look at

n.split <- 3 #change this according to no. of splits on tree

store_matrix <- array(0,c(n.boot,n.split))` #column 1 will contain split, col 2 split 2, etc
trainData <- iris2

for (i in 1:n.boot) { 
iboot <- sample(1:nrow(trainData), replace = TRUE)
bootdata <- trainData[iboot,]
r <- rpart(Sepal.Length ~ Petal.Length, bootdata, cp = 0.05)
r
r$frame
r$split
store_matrix[i,] <- r$splits[1:n.split,4]
}

generate interval and width

split.n <- 2 #choose which split to look at

store1 <- store_matrix[,split.n] #select the distribution of split estimates for a specific split
(split_estimate <- r1$splits[split.n,4]) #check its the correct split
[1] 3.4

q1 <- quantile(na.omit(as.numeric(store1)), c(0.025, 0.975))    
quantile(na.omit(as.numeric(store1)), c(0.025, 0.975)); as.numeric(q1)[2] - as.numeric(q1)[1]  
2.5% 97.5% 
1.45  5.65 
[1] 4.2