PCA with Wuensch's beer data. http://core.ecu.edu/psyc/wuenschk/SPSS/SPSS-Data.htm

library(psych)

beer <- read.table("http://www.unt.edu/rss/class/mike/data/beer.txt",header=TRUE, sep="", na.strings="NA", dec=".", strip.white=TRUE)
beer2 = beer[,1:7] #just the attribute variables
beer2
fit <- principal(beer2, nfactors=3,rotate="varimax", scores=T)
fit 
plot(fit)  #Need R 2.8.1
fit$scores

#VSS(beer2, rotate="varimax",n=5,pc = "pc")   This function tries out several approaches to determine the best number of factors to retain.  You will need an updated version of R to use it however. 




#Conceptual tie-in: PCA regression
RegModel.1 <- lm(SES~ALCOHOL+AROMA+COLOR+COST+REPUTAT+SIZE+TASTE, data=beer)
summary(RegModel.1)


library(pls)
beer.pcr <- pcr(SES ~ COST+SIZE+ALCOHOL+REPUTAT+AROMA+COLOR+TASTE, 3,  data = beer)
summary(beer.pcr)
coef(beer.pcr, intercept=T)  #coefs for original data
loadings(beer.pcr)  #only difference from above is this uses the covariance matrix.  essentially it returns output from princomp function, and can be verified as below.
loadingplot(beer.pcr, comps=1:3, legend="topleft")
corrplot(beer.pcr, comps=1:3)


#Doing it the hard way, PCA then lm for verification
beer3=na.omit(beer)
test=princomp(beer3[,1:7], scale=T)
summary(test)
test$loadings
test$scores  

pcreg2=lm(beer3$SES~test$scores[,"Comp.1"]+test$scores[,"Comp.2"]+test$scores[,"Comp.3"])
summary(pcreg2)


#Partial Least Squares
beer.pls <- plsr(SES ~ COST+SIZE+ALCOHOL+REPUTAT+AROMA+COLOR+TASTE, 3,  data = beer)
summary(beer.pls)
coef(beer.pls, intercept=T)  #coefs for original data
loadings(beer.pls)  #only difference from above is this uses the covariance matrix.  essentially it returns output from princomp function, and can be verified as below.
loadingplot(beer.pls, comps=1:3, legend="topleft")
corrplot(beer.pls, comps=1:3)