Y: Response vector
n=dim(X)[1]
nvar=dim(X)[2]
```
0.5\*length(diffmat[diffmat==0]))/(m\*n)

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plot(t,ROC,type='s',col='red',xlab="1-esp",ylab="sen")

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auc=round(auc,digits=3)

**9. References**

abline(a=0,b=1,col='grey')

lines(t,ROC,col='blue',type='s') text(0.9,0.1,paste("auc=",auc)) result=list(t=t,ROC=ROC,auc=auc)}

```
variables=1:nvar
auc0=NULL; formula0=NULL; inside=NULL
nvars=NULL;aucs=NULL;ROCs=NULL
test<-seq(1,n,4)
Wtraining=rep(1,n);Wtraining[test]=0
for (ivar in 1:nvar) {
 ii=! (variables %in% inside)
 variables=variables[ii]
 auc=NULL
 for (j in 1:length(variables)) {
  if (option=="gam") {formula=paste("+s(X[,",j,"])",sep="")}
else {formula=paste("+(X[,",j,"])",sep="")}
  formula=paste(formula0,formula,sep="")
  formula=paste("Y~",formula,sep="")
  if (option=="gam") {modelo=gam(as.formula(formula),
   family="binomial",weights=Wtraining)}
else {modelo=glm(as.formula(formula),family="binomial",
  weights=Wtraining)}
  muhat=predict(modelo,type="response")
  a=EmpiricalROC(Y[Wtraining==0],muhat[Wtraining==0])
  aux=a$auc
  nvars=c(nvars,ivar);aucs=c(aucs,aux);auc=c(auc,aux)
  jj=length(a$t)
  ROCs=rbind(ROCs,cbind(rep(ivar,jj),rep(aux,jj),a$t,a$ROC))}
  inside=c(inside,variables[which.max(auc)])
  auc0=c(auc0,max(auc))
  if (option=="gam") {formula0=paste("s(X[,",inside,"])",
   sep="",collapse="+")}
  else { formula0=paste("(X[,",inside,"])",sep="",collapse="+")}}
return(list(aucs=cbind(nvars,aucs),
aucopt=cbind(1:nvar,auc0),models=inside,roc=ROCs))
}
##################################################################