# Studijny program: "Pravdepodobnost a matematicka statistika"
# Vyucujuci: Radoslav Harman, KAMS FMFI UK Bratislava
#
# Faktorova analyza (Factor analysis, FA)
# Priklad je zalozeny na knihe: Everitt, B: R and S+ Companion to MA

# Nacitat korelacnu maticu druguse.cor (RSPCMA)

# FA pomocou MMV
druguse.cor <- as.matrix(read.table(
               "http://www.iam.fmph.uniba.sk/ospm/Harman/data/drugcor.txt",
               header=TRUE))
print(druguse.cor)
library(corrplot)
corrplot(druguse.cor)

help(factanal)

druguse.fa <- factanal(covmat = druguse.cor, factors = 2, 
              rotation = "none", n.obs = 1634)
print(druguse.fa) 

druguse.fa <- factanal(covmat = druguse.cor, factors = 6,
              rotation = "none", n.obs = 1634)
print(druguse.fa)
print(druguse.fa$loadings)
print(druguse.fa$uniqueness)

varimax(druguse.fa$loadings)
V <- varimax(druguse.fa$loadings)$rotmat
print(druguse.fa$loadings %*% V)

druguse.fa <- factanal(covmat = druguse.cor, factors = 6,
              rotation="varimax", n.obs=1634)
print(druguse.fa)

druguse.fa <- factanal(covmat=druguse.cor, factors=6, method="mle",
              rotation="none", n.obs=1634, start=rep(0.5, 13))
print(druguse.fa)

druguse.fa <- factanal(covmat=druguse.cor, factors=6, method="mle",
              rotation="varimax", n.obs=1634, start=rep(0.5,13))
print(druguse.fa)

corrplot(t(druguse.fa$loadings[1:13,1:6]))

# Nepovinna Du: Urobit FA pre data decathlon z cviceni o PCA.
# Najst pocet faktorov, urobit varimaxnu rotaciu, interpretovat vysledky.
# Vypocitat faktorove skore, porovnat s PCA skore.