## Chapter 11 
##                                Note 

## Sec 11.1: The Uses of Tree-based Methods 
## ss 11.1.1: Problems for which tree-based regression may be used 
##              When are tree-based methods appropriate? 

## Sec 11.2: Detecting Email Spam~-- an Example 
## Footnote code 
## Sample 50 rows from data frame spam7 (DAAG) 
## To get another sample and to obtain one of the plots, type: 
spam.sample <- spam7[sample(seq(1,4601),500,replace=FALSE), ] 
boxplot(split(spam.sample$crl.tot, spam.sample$yesno)) 
library(rpart) 
spam.rpart <- rpart(formula = yesno ~ crl.tot + dollar + bang + 
                    money + n000 + make,  method="class", data=spam7) 
plot(spam.rpart)     # Draw tree 
text(spam.rpart)     # Add labeling 

## ss 11.2.1: Choosing the number of splits 

## Sec 11.3: Terminology and Methodology 
## Footnote code 
## Code to plot such a tree is 
Criterion <- factor(paste("Leaf", 1:5)) 
Node <- c(1,2,3,4,5) 
demo.df <- data.frame(Criterion = Criterion, Node = Node) 
demo.rpart <- rpart(Node ~ Criterion, data = demo.df,  
                    control = list(minsplit = 2, minbucket = 1)) 
plot(demo.rpart, uniform=TRUE) 
text(demo.rpart) 

## ss 11.3.1: Choosing the split~-- regression trees 
## ss 11.3.2: Within and between sums of squares 
## ss 11.3.3: Choosing the split~-- classification trees 
## ss 11.3.4: Tree-based regression versus loess regression smoothing 
## loess fit to Mileage vs Weight: data frame car.test.frame (rpart) 
car.lo <- loess(Mileage ~ Weight, car.test.frame) 
plot(car.lo, xlab="Weight", ylab="Miles per gallon") 
lines(seq(1850,3850), predict(car.lo, data.frame(Weight=seq(1850,3850)))) 
car.tree <- rpart(Mileage ~ Weight, data=car.test.frame, 
                  control = list(minsplit = 10, minbucket = 5, 
                  cp = 0.0001), method="anova") 
plot(car.tree, uniform = TRUE) 
text(car.tree, digits = 3, use.n = TRUE) 
car.tree <- rpart(Mileage ~ Weight, data = car.test.frame) 
plot(car.tree, uniform = FALSE) 
text(car.tree, digits = 3, use.n = TRUE) 

## Sec 11.4: Predictive Accuracy, and the Cost-complexity Tradeoff 

## ss 11.4.1: Cross-validation 
## ss 11.4.2: The cost-complexity parameter 
## ss 11.4.3: Prediction error versus tree size 

## Sec 11.5: Data for female heart attack patients 
summary(mifem)     # data frame mifem (DAAG) 
mifem.rpart <- rpart(outcome ~ ., method="class",   
                     data = mifem, cp = 0.0025) 
plotcp(mifem.rpart)  # Cross-validated error vs cp 
printcp(mifem.rpart) # Tabular version of the same information 
mifemb.rpart <- prune(mifem.rpart, cp=0.03) 
plot(mifemb.rpart) 
par(xpd=TRUE)        # May be needed so that labels appear 
text(mifemb.rpart, use.n=T, digits=3) 
par(xpd=FALSE) 

## ss 11.5.1: The one-standard-deviation rule 
## ss 11.5.2: Printed Information on Each Split 
print(mifemb.rpart) 

## Sec 11.6: Detecting Email Spam~-- the Optimal Tree 
spam7a.rpart <- rpart(formula = yesno ~ crl.tot + dollar +  
                      bang + money + n000 + make,  
                      method="class", data = spam7, cp = 0.001) 
printcp(spam7a.rpart) 
## Footnote code 
## Use of prune.rpart() with cp between 0.00276 and 0.00386  
## will prune back to nsplit=16.  Specify: 
spam7b.rpart <- prune(spam7a.rpart, cp=0.003) 
plot(spam7b.rpart, uniform=TRUE) 
text(spam7b.rpart, cex=0.75) 

##  How does the one standard error rule affect accuracy estimates? 
acctree.mat <- matrix(0, nrow=100, ncol=6) 
for(i in 1:100)acctree.mat[i,] <- compareTreecalcs(data=spam7,  
                                                    fun="rpart") 

##               How is the standard error calculated? 
##              When are tree-based methods appropriate? 

## Sec 11.7: The \textit{randomForest} Package 
library(randomForest) 
spam7.rf <- randomForest(yesno ~ ., data=spam7, importance=TRUE) 
print(spam7.rf) 
tuneRF(x=spam7[, -7], y=spam7$yesno, trace=FALSE) 
importance(spam7.rf) 

## ss 11.7.1: Comparison between \texttt{rpart()} and \texttt{randomForest()} 
## Footnote code 
acctree.mat <- matrix(0, nrow=100, ncol=8) 
colnames(acctree.mat) <- c("rpSEcvI", "rpcvI", "rpSEtest", "rptest", 
                           "n.SErule", "nre.min.12", "rfcvI", "rftest") 
for(i in 1:100)acctree.mat[i,] <-  
   compareTreecalcs(data=spam7, fun=c("rpart", "randomForest")) 
acctree.df <- data.frame(acctree.mat) 
lims <- range(acctree.mat[, c(4,7,8)], na.rm=TRUE) 
plot(rfcvI ~ rftest, data=acctree.df); abline(0,1)    # Panel A 
plot(rptest ~ rftest, data=acctree.df); abline(0,1)   # Panel B 

##                       Efficient computation 
##  Differences between \texttt{rpart()} and \texttt{randomForest()} 

## Sec 11.8: Additional Notes on Tree-Based Methods 
##     The combining of tree-based methods with other approaches 
##               Models with a complex error structure 
##                   Pruning as variable selection 
##                        Other types of tree 
##                       Factors as predictors 
##        Summary of pluses and minuses of tree-based methods 

## Sec 11.9: Further Reading