## 6. Multivariate and Tree-based Methods
## 6.1 Multivariate EDA, and Principal Components Analysis
pairs(possum[,6:14], col=palette()[as.integer(possum$sex)])
pairs(possum[,6:14], col=palette()[as.integer(possum$site)])
here<-!is.na(possum$footlgth)    # We need to exclude missing values
print(sum(!here))                # Check how many values are missing
possum.prc <- princomp(log(possum[here,6:14]))  # Principal components
# Print scores on second pc versus scores on first pc,
# by populations and sex, identified by site
xyplot(possum.prc$scores[,2] ~
     possum.prc$scores[,1] | possum$Pop[here]+possum$sex[here], 
     groups=possum$site,
     auto.key=list(columns=3))

## 6.2 Cluster Analysis

## 6.3 Discriminant Analysis
library(MASS)                 # Only if not already attached.
here<- !is.na(possum$footlgth)
possum.lda <- lda(site ~ hdlngth+skullw+totlngth+
+ taillgth+footlgth+earconch+eye+chest+belly,data=possum, subset=here)
options(digits=4)
possum.lda$svd   # Examine the singular values
>
plot(possum.lda, dimen=3)    
# Scatterplot matrix for scores on 1st 3 canonical variates, as in Figure22

## 6.4 Decision Tree models (Tree-based models)
library(rpart)
# Use fgl: Forensic glass fragment data; from MASS package
glass.tree <- rpart(type ~ RI+Na+Mg+Al+Si+K+Ca+Ba+Fe, data=fgl)
plot(glass.tree);  text(glass.tree)
summary(glass.tree)
## 6.5 Exercises
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## 6.6 References