fil = "http://www.uio.no/studier/emner/matnat/math/STK2100/data/spam_data.txt"
spam = read.table(fil,header=T)

fit = glm(y~.-train,data=spam,subset=spam$train,family=binomial)
pred = predict(fit,spam[!spam$train,],type="response")>0.5

x.prcomp = prcomp(spam[,1:57],retx=TRUE,scale=TRUE)
d = data.frame(x.prcomp$x,y=spam$y,train=spam$train)

fit.pc = glm(y~.-train,data=d[,c(1:2,58,59)],family=binomial,subset=d$train)
pred.pc = predict(fit.pc,d[!d$train,],type="response")>0.5

plot.ts(x.prcomp$rotation[,1])

library(gam)
fit.gam = gam(y~s(x1)+s(x2)+s(x3),data=spam,
              subset=spam$train,family=binomial)
pred.gam = predict(fit.gam,spam[!spam$train,],type="response")>0.5

plot(fit.gam,se=T)

fit.pc.gam = gam(y~s(PC1)+s(PC2)+s(PC3),data=d,
                  subset=d$train,family=binomial)
pred.pc.gam = predict(fit.pc.gam,d[!d$train,],type="response")>0.5

nam = names(d)[1:57]
k=20
formula = as.formula(paste("y",paste(paste("s(",nam[1:k],")",sep=""), 
                                     collapse="+"), sep="~"))
print(formula)
fit.pc.gam = gam(formula,data=d,subset=d$train,family=binomial)
pred.pc.gam = predict(fit.pc.gam,d[!d$train,],type="response")>0.5