#####################################################################
###  BMTRY 790: MACHINE LEARNING AND DATA MINING, Spring 2023  	###
###											###
###  Lecture 5: Penalized Regression, Part III				###
###											###
###  Body Fat Data Analysis                     			###
###				                                          ###
###  Looking at elastic netrelative to lasso using the body fat	###
###  data							        		###
#####################################################################

bodyfat<-read.csv("H:/public_html/BMTRY790_Spring2023/Datasets/Body_fat.csv")[,-1]
bodyfat2<-scale(bodyfat)
library(elasticnet)

###################################################
### 	Fitting Elastic Net Model to Bodyfat data	###
###################################################

### First conducting 10-fold CV to select our tuning parmaters ###
par(mfrow=c(2,3))
set.seed(3210)
menet0<-cv.enet(x=bodyfat2[,2:14], y=bodyfat2[,1], s=seq(0,1,length=100), lambda=0, mode="fraction")
set.seed(3210)
menet001<-cv.enet(x=bodyfat2[,2:14], y=bodyfat2[,1], s=seq(0,1,length=100), lambda=0.01, mode="fraction")
set.seed(3210)
menet01<-cv.enet(x=bodyfat2[,2:14], y=bodyfat2[,1], s=seq(0,1,length=100), lambda=0.1, mode="fraction")
set.seed(3210)
menet1<-cv.enet(x=bodyfat2[,2:14], y=bodyfat2[,1], s=seq(0,1,length=100), lambda=1, mode="fraction")
set.seed(3210)
menet10<-cv.enet(x=bodyfat2[,2:14], y=bodyfat2[,1], s=seq(0,1,length=100), lambda=10, mode="fraction")
set.seed(3210)
menet100<-cv.enet(x=bodyfat2[,2:14], y=bodyfat2[,1], s=seq(0,1,length=100), lambda=100, mode="fraction")


### Looking at minimum cv error for each choice of lambda_2
min(menet0$cv)
min(menet001$cv)
min(menet01$cv)
min(menet1$cv)
min(menet10$cv)
min(menet100$cv)

### Selecting the lambda_1 from the model with the smallest cv.error
fracL1<-menet0$s[which(menet0$cv==min(menet0$cv))]

### Comparing elastic net path to lasso path
mod.enet<-enet(x=bodyfat2[,2:14], y=bodyfat2[,1], lambda=0)
plot(mod.enet, use.color=T, main="Body Fat Example")
abline(v=fracL1, lty=2, col=2, lwd=2)

### extracting the model based on the selected lambda_2 and fraction of L1
predict(mod.enet, s=fracL1, type="coefficients", mode="fraction")