#A seguinte sintaxes reproduz os analises do exemplo 3.17.1 do livro de 
#Bartholomew, Knox e Moustaki (2011)

mycovmat=matrix(c(
  26.641, 5.991, 33.52,  6.023, 20.755,  29.701,
  5.991,  6.700, 18.137, 1.782  , 4.936,   7.204,
  33.52, 18.137, 149.831,19.424 , 31.430,  50.753, 
  6.023,  1.782, 19.424,  12.711, 4.757,    9.075,
  20.755, 4.936, 31.430,  4.757 , 52.604,   66.762,
  29.701, 7.204, 50.753,  9.075 , 66.762, 135.292),nrow=6)
mycovmat

mycorrmat=matrix(c(
  1     ,    0.466, 0.552, 0.340, 0.576, 0.510,
  0.446 ,   1     , 0.572, 0.193, 0.263, 0.239,
  0.552 ,  0.572  ,  1   , 0.445, 0.354, 0.356, 
  0.340 ,  0.193  , 0.445, 1    , 0.184, 0.219,
  0.576 ,  0.263  , 0.354, 0.184, 1    , 0.794,
  0.510 ,  0.239  , 0.356, 0.219, 0.794 ,   1  ),nrow=6)
mycorrmat

help(factanal)
#fit <- factanal(covmat=mycovmat, factors=2, n.obs=112)
fit <- factanal(covmat=mycorrmat, factors=2)
fit

summary(fit) # print variance accounted for 
fit$loadings # uniquenesses 
fit$uniquenesses # uniquenesses 
1-fit$uniquenesses # uniquenesses 
fit$factors

library(psych)
help(fa)

fitml <- fa(mycorrmat,fm="ml", nfactors=2,rotate="none")
fitml

fituls<- fa(mycorrmat, factors=2)

#rotation 
fitrotml1 <- fa(mycorrmat,fm="ml", nfactors=2)
fitrotml2 <- fa(mycorrmat,fm="ml", nfactors=2,rotate="oblimin")
fitrotml1
fitrotml2
fitminres <- fa(mycorrmat,fm="minres", nfactors=2)
fitminres
fitwls <- fa(mycorrmat, fm="wls",nfactors=2)
fitwls
fitgls <- fa(mycorrmat, fm="gls",nfactors=2)
fitgls
fitpa <- fa(mycorrmat,fm="pa", nfactors=2)
fitpa