# R in Action (2nd ed): Chapter 14
# Principal components and factor analysis
# requires package psych
# install.packages(c("psych"))
#------------------------------

par(ask=TRUE)
set.seed(1234) # make results reproducible


## Principal components analysis of US Judge Ratings

library(psych)
fa.parallel(USJudgeRatings[,-1], fa="pc", 
            ntrials=100, show.legend=FALSE, 
            main="Scree plot with parallel analysis")
pc <- principal(USJudgeRatings[,-1], nfactors=1, score=TRUE)
pc

# principal components scores
head(pc$scores)

# correlation between PC score and number of lawyer contacts
cor(USJudgeRatings$CONT, pc$score)


## Principal components analysis Harman23.cor data

library(psych)
fa.parallel(Harman23.cor$cov, n.obs=302, fa="pc", 
            ntrials=100, show.legend=FALSE, 
            main="Scree plot with parallel analysis")
pc <- principal(Harman23.cor$cov, nfactors=2, rotate="none")
pc

# varimax rotation
rc <- principal(Harman23.cor$cov, nfactors=2, rotate="varimax")
rc

# principal components scoring coefficients
round(unclass(rc$weights), 2)


## Exploratory factor analysis of ability.cov data

options(digits=2)
library(psych)
covariances <- ability.cov$cov
# convert covariances to correlations
correlations <- cov2cor(covariances)
correlations

# determine number of factors to extract
fa.parallel(correlations, n.obs=112, fa="both", ntrials=100,
            main="Scree plots with parallel analysis")

# principal axis factoring without rotation
fa <- fa(correlations, nfactors=2, rotate="none", fm="pa")
fa

# factor extraction with orthogonal rotation
fa.varimax <- fa(correlations, nfactors=2, rotate="varimax", fm="pa")
fa.varimax

# factor extraction with oblique rotation
fa.promax <- fa(correlations, nfactors=2, rotate="promax", fm="pa")
fa.promax

# calculate factor loading matrix
P <- unclass(fa.promax$loading)
F <- P %*% fa.promax$Phi
colnames(F) <- c("PA1", "PA2")
F

# plot factor solution
factor.plot(fa.promax, labels=rownames(fa.promax$loadings))
fa.diagram(fa.promax, simple=FALSE)