```
N <- 1000
X1 <- runif(N)
X2 <- 2*runif(N)
X3 <- ordered(sample(letters[1:4],N,replace=TRUE),levels=letters[4:1])
X4 <- factor(sample(letters[1:6],N,replace=TRUE))
X5 <- factor(sample(letters[1:3],N,replace=TRUE))
X6 <- 3*runif(N)
mu <- c(-1,0,1,2)[as.numeric(X3)]
SNR <- 10 # signal-to-noise ratio
Y <- X1**1.5 + 2 * (X2**.5) + mu
sigma <- sqrt(var(Y)/SNR)
Y <- Y + rnorm(N,0,sigma)
# introduce some missing values
X1[sample(1:N,size=500)] <- NA
X4[sample(1:N,size=300)] <- NA
data <- data.frame(Y=Y,X1=X1,X2=X2,X3=X3,X4=X4,X5=X5,X6=X6)
# fit initial model
gbm1 <-
gbm(Y~X1+X2+X3+X4+X5+X6, # formula
data=data, # dataset
var.monotone=c(0,0,0,0,0,0), # -1: monotone decrease,
# +1: monotone increase,
# 0: no monotone restrictions
distribution="gaussian", # see the help for other choices
n.trees=1000, # number of trees
shrinkage=0.05, # shrinkage or learning rate,
# 0.001 to 0.1 usually work
interaction.depth=3, # 1: additive model, 2: two-way interactions, etc.
bag.fraction = 0.5, # subsampling fraction, 0.5 is probably best
train.fraction = 0.5, # fraction of data for training,
# first train.fraction*N used for training
n.minobsinnode = 10, # minimum total weight needed in each node
cv.folds = 3, # do 3-fold cross-validation
keep.data=TRUE, # keep a copy of the dataset with the object
verbose=FALSE, # don't print out progress
n.cores=1) # use only a single core (detecting #cores is
# error-prone, so avoided here)
# check performance using an out-of-bag estimator
# OOB underestimates the optimal number of iterations
best.iter <- gbm.perf(gbm1,method="OOB")
print(best.iter)
# check performance using a 50% heldout test set
best.iter <- gbm.perf(gbm1,method="test")
print(best.iter)
# check performance using 5-fold cross-validation
best.iter <- gbm.perf(gbm1,method="cv")
print(best.iter)
# plot the performance # plot variable influence
summary(gbm1,n.trees=1) # based on the first tree
summary(gbm1,n.trees=best.iter) # based on the estimated best number of trees
# compactly print the first and last trees for curiosity
print(pretty.gbm.tree(gbm1,1))
print(pretty.gbm.tree(gbm1,gbm1$n.trees))
# make some new data
N <- 1000
X1 <- runif(N)
X2 <- 2*runif(N)
X3 <- ordered(sample(letters[1:4],N,replace=TRUE))
X4 <- factor(sample(letters[1:6],N,replace=TRUE))
X5 <- factor(sample(letters[1:3],N,replace=TRUE))
X6 <- 3*runif(N)
mu <- c(-1,0,1,2)[as.numeric(X3)]
Y <- X1**1.5 + 2 * (X2**.5) + mu + rnorm(N,0,sigma)
data2 <- data.frame(Y=Y,X1=X1,X2=X2,X3=X3,X4=X4,X5=X5,X6=X6)
# predict on the new data using "best" number of trees
# f.predict generally will be on the canonical scale (logit,log,etc.)
f.predict <- predict(gbm1,data2,best.iter)
# least squares error
print(sum((data2$Y-f.predict)^2))
# create marginal plots
# plot variable X1,X2,X3 after "best" iterations
par(mfrow=c(1,3))
plot(gbm1,1,best.iter)
plot(gbm1,2,best.iter)
plot(gbm1,3,best.iter)
par(mfrow=c(1,1))
# contour plot of variables 1 and 2 after "best" iterations
plot(gbm1,1:2,best.iter)
# lattice plot of variables 2 and 3
plot(gbm1,2:3,best.iter)
# lattice plot of variables 3 and 4
plot(gbm1,3:4,best.iter)
# 3-way plots
plot(gbm1,c(1,2,6),best.iter,cont=20)
plot(gbm1,1:3,best.iter)
plot(gbm1,2:4,best.iter)
plot(gbm1,3:5,best.iter)
# do another 100 iterations
gbm2 <- gbm.more(gbm1,100,
verbose=FALSE) # stop printing detailed progress
```

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