What is the meaning of component err.rate of class randomForest? - r

Question

I'm using the function randomForest from package randomForest. One of the objects of class randomForest is err.rate which is
(classification only) vector error rates of the prediction on the input data, the i-th element being the (OOB) error rate for all trees up to the i-th.
Could you please explain what is the meaning of this component? Thank you so much for your help!
I take the dataset Sonar, Mines vs. Rocks as an code example.
library(mlbench)
data(Sonar)
library(boot)
library(randomForest)
n <- 208
ntrain <- 100
ntest <- 108
train.idx <- sample(1:n, ntrain, replace = FALSE)
train.set <- Sonar[train.idx, ]
test.set <- Sonar[-train.idx, ]
rf <- randomForest(Class ~ ., data = train.set, keep.inbag = TRUE, importance = TRUE)
head(rf$err.rate)
Here is the result of the code
OOB M R
[1,] 0.1891892 0.1500000 0.2352941
[2,] 0.2931034 0.2307692 0.3437500
[3,] 0.2739726 0.2647059 0.2820513
[4,] 0.2911392 0.2894737 0.2926829
[5,] 0.2413793 0.2682927 0.2173913
[6,] 0.2555556 0.2142857 0.2916667
[7,] 0.2553191 0.2444444 0.2653061
[8,] 0.2268041 0.1956522 0.2549020
[9,] 0.2783505 0.2608696 0.2941176

Answer 1

One component of randomForest is bagging where you get a consensus prediction from i number of trees.
As you increase the number of trees, the OOB error is computed at each step. The OOB error is not calculated from comparing the prediction obtained from 1 tree onto OOB samples with respect to that tree, but rather you use the averaged prediction across trees from which this sample is not used. I recommend checking this for an overview.
So in the example you have, we can visualize this:
library(ggplot2)
library(tidyr)
plotdf <- pivot_longer(data.frame(ntrees=1:nrow(rf$err.rate),rf$err.rate),-ntrees)
ggplot(plotdf,aes(x=ntrees,y=value,col=name)) +
geom_line() + theme_bw()
M and R are lines for error in prediction for that specific label, and OOB (your first column) is simply the average of the two. As the number of trees increase, your OOB error gets lower because you get a better prediction from more trees.
The nice thing about randomForest is that you don't need the cross-validation, because the OOB estimate is usually quite indicative. Below we can try to show that we get the same result:
set.seed(12)
# split in 5 parts
trn = split(1:nrow(Sonar),sample(1:nrow(Sonar) %% 5))
sim = vector("list",5)
# the number of trees we incrementally grow
ntrees = c(1,20*(1:50)+1)
for(CV in 1:5){
idx = trn[[CV]]
train.set <- Sonar[-idx, ]
test.set <- Sonar[idx, ]
# first forest, n=1, but works
mdl <- randomForest(Class ~ ., data = train.set, ntree=1,
keep.inbag = TRUE, importance = TRUE,keep.forest=TRUE)
err_rate <- vector("numeric",51)
err_rate[1] <- mean(predict(mdl,test.set)!=test.set$Class)
#growing the tree
for(i in 1:50){
mdl <- grow(mdl,10)
err_rate[i+1] <- mean(predict(mdl,test.set)!=test.set$Class)
}
sim[[CV]] <- data.frame(ntrees=ntrees,err_rate=err_rate,CV=CV)
}
sim = do.call(rbind,sim)
#plot
ggplot(sim,aes(x=ntrees,y=err_rate)) + geom_line(aes(group=CV),alpha=0.2) +
stat_summary(fun.y=mean,geom="line",col="blue")+theme_bw()