###############################################
##
## Generating data from the following model
## y=beta1*x+(beta1*x)^3+4*(beta1*x)^2+epsilon
##
###############################################

n<-400
beta1<-c(1,1,1)
beta2<-c(1,-1,-1)
X<-matrix(rnorm(n*3),n,3)
epsilon<-rnorm(n,0,1)
y<-X%*%beta1+(X%*%beta1)^3+4*(X%*%beta2)^2+epsilon

plot(y,X%*%beta1,xlab="first index",ylab="response")
plot(y,X%*%beta2,xlab="second index",ylab="response")

## Sliced inverse regression I

library("dr")
SIR<-dr(y~X[,1]+X[,2]+X[,3],slice.function=dr.slices.arc,nslices=20,chi2approx="wood",numdir=2,method="sir")
summary(SIR)

## Sliced inverse regression II

library("edrGraphicalTools")
SIRII<-edr(y,X,H=20,K=2,method="SIR-II")
summary(SIRII)