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###  BMTRY 790: MACHINE LEARNING AND DATA MINING, Spring 2023  	###
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###  Lecture 6: Alternative Regression Methods				###
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###  Body Fat Data Analysis                     			###
###				                                          ###
###  Looking at principal component regression and partial		###
###  least squares regression examples using the body fat		###
###  data							        		###
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bodyfat<-read.csv("H:/public_html/BMTRY790_Spring2023/Datasets/Body_fat.csv")[,-1]
bodyfat2<-as.data.frame(scale(bodyfat))
library(pls)


### Fitting a Principal Component Model ###
bf.pcr <- pcr(PBF ~ ., data=bodyfat2, validation = "CV")
summary(bf.pcr)
plot(bf.pcr, plottype="validation")
plot(bf.pcr, plottype="coefficients")
plot(bf.pcr, plottype="correlation")
scoreplot(bf.pcr)
scoreplot(bf.pcr, comp=1:5)
loadingplot(bf.pcr)
corrplot(bf.pcr, comp=1:3)
plot(bf.pcr, "loadings",comps=1:3, legendpos="bottomright")
loadingplot(bf.pcr)
coef(bf.pcr, comp=1:2)
scores(bf.pcr)
loadings(bf.pcr)

### Comparison to OLS fit
bf.ols<-lm(PBF ~ ., data=bodyfat2)
pbf.ols<-predict(bf.ols)
par(mfrow=c(1,2))
bf.pcr <- pcr(PBF ~ ., data=bodyfat2, validation = "CV")
pbf8<-fitted(bf.pcr, ncomp=8)[,,8]; pbf.fullpcr<-fitted(bf.pcr, ncomp=13)[,,13]
plot(pbf.ols, pbf.fullpcr, xlab="predictions from OLS", ylab="predictions from full PCR", pch=16, col=3)
points(pbf.ols, pbf8, pch=1, col=2)



### Fitting a Partial Least Squares Model ###
bf.plsr <- plsr(PBF ~ ., method="simpls", data=bodyfat2, validation = "CV")
summary(bf.plsr)

plot(bf.plsr, plottype="validation")
par(mfrow=c(1,2))
plot(bf.plsr, plottype="coefficients", 1:3, legendpos="topright")
plot(bf.plsr, plottype="loadings", 1:3, legendpos="topright")

plot(bf.plsr, plottype="correlation", 1:3, pch=16, col=2)
plot(bf.plsr, "score", 1:3)

par(mfrow=c(2,2))
plot(bf.plsr, "prediction", ncomp=1); plot(bf.plsr, "prediction", ncomp=4)
plot(bf.plsr, "prediction", ncomp=8); plot(bf.plsr, "prediction", ncomp=13)

### Comparison to OLS fit
bf.ols<-lm(PBF ~ ., data=bodyfat2)
pbf.ols<-predict(bf.ols)

bf.plsr <- plsr(PBF ~ ., data=bodyfat2, validation = "CV")
pbf6<-fitted(bf.plsr, ncomp=6)[,,6]
pbf.fullplsr<-fitted(bf.plsr, ncomp=13)[,,13]

plot(pbf.ols, pbf.fullplsr, xlab="predictions from OLS", 
         ylab="predictions from full PLSR", pch=16, col=3)
points(pbf.ols, pbf6, pch=1, col=2)