# Play with sample size and model structure
# I.e, change ns, the model coefficients, the noise error
# Run several times to see what happens across simulations
ns<-100
xx<-mvrnorm(ns,Sigma=as.matrix(cbind(c(1,.9),c(.9,1))),mu=rep(0,2))
xx<-cbind(xx,mvrnorm(ns,Sigma=as.matrix(cbind(c(1,.9),c(.9,1))),mu=rep(0,2)))
xx<-cbind(xx,mvrnorm(ns,Sigma=diag(rep(1,100)),mu=rep(0,100)))
# 104 variables
y<--1*xx[,1]+1*xx[,3]+1*xx[,4]+xx[,5]+rnorm(ns)*1
df<-as.data.frame(cbind(xx,y))
names(df)<-c(as.character(seq(1,104)),"y")

####

library(glmnet)

gg<-glmnet(x=xx,y=y)
plot(gg,xvar="lambda")

cv.gg<-cv.glmnet(x=xx,y=y)
plot(cv.gg)
names(cv.gg)

coef(cv.gg,s="lambda.1se")
coef(cv.gg,s="lambda.min")

#### adaptive lasso
gamma<-1
ggl<-glmnet(x=xx,y=y,lambda=cv.gg$lambda.min)
ggr<-glmnet(x=xx,y=y,lambda=cv.gg$lambda.min,alpha=0)
xx2<-xx%*%diag(abs(coef(ggr)[-1])^gamma)
gg2<-glmnet(x=xx2,y=y,lambda=cv.gg$lambda.min)
cc<-coef(gg2)[-1]/coef(ggr)[-1]
coef(ggl)[2:10]
coef(gg2)[2:10]
# try different gamma


########
library(hdi)
ll<-lasso.proj(x=xx,y=y)
ll$pval
ll$pval.corr
# are the pvalues identifying the true model?

ll<-ridge.proj(x=xx,y=y)
ll$pval
ll$pval.corr

cc<-ll$clusterGroupTest()
plot(cc)
cc$pval
cc$clusters