| principal {psych} | R Documentation |
Does an eigen value decomposition and returns eigen values, loadings, and degree of fit for a specified number of components. Basically just is doing a principal components for n principal components. Can show the residual correlations as well. The quality of reduction in the squared correlations is reported by comparing residual correlations to original correlations.
principal(r, nfactors = 0, residuals = FALSE,rotate=FALSE, digits=2)
r |
a correlation matrix |
nfactors |
Number of components to extract |
residuals |
FALSE, do not show residuals, TRUE, report residuals |
rotate |
|
digits |
digits =2 Accuracy of answers as well as display |
Useful for those cases where the correlation matrix is improper (perhaps because of SAPA techniques).
values |
Eigen Values of all components – useful for a scree plot |
loadings |
A standard loading matrix |
fit |
Fit of the model to the correlation matrix |
residual |
Residual matrix – if requested |
William Revelle
VSS,factor2cluster,factor.pa, factor.congruence
#Four principal components of the Harmon 24 variable problem
#compare to a four factor principal axes solution using factor.congruence
pc <- principal(Harman74.cor$cov,4,rotate=TRUE)
pa <- factor.pa(Harman74.cor$cov,4,rotate=TRUE)
round(factor.congruence(pc,pa),2)
## The function is currently defined as
function(r,nfactors=0,residuals=FALSE,rotate=FALSE,digits=2) {
n <- dim(r)[1]
if (n!=dim(r)[2]) r <- cor(r,use="pairwise") # if given a rectangular matrix, the find the correlations first
if (!residuals) { result <- list(values=c(rep(0,n)),loadings=matrix(rep(0,n*n),ncol=n),fit=0)} else { result <- list(values=c(rep(0,n)),loadings=matrix(rep(0,n*n),ncol=n),residual=matrix(rep(0,n*n),ncol=n),fit=0)}
eigens <- eigen(r) #call the eigen value decomposition routine
result$values <- round(eigens$values,digits)
if(nfactors >0) {loadings <- eigen.loadings(eigens)[,1:nfactors] } else {loadings <- eigen.loadings(eigens)
nfactors <- n}
if(nfactors >1) {
maxabs <- apply(apply(loadings,2,abs),2,which.max)
sign.max <- vector(mode="numeric",length=nfactors)
for (i in 1: nfactors) {sign.max[i] <- sign(loadings[maxabs[i],i])}
loadings <- loadings
} else {if(nfactors >0) {mini <- min(loadings)
maxi <- max(loadings)
if (abs(mini) > maxi) {loadings <- -loadings }
loadings <- as.matrix(loadings)
}}
colnames(loadings) <- paste("PC",1:nfactors,sep='')
rownames(loadings) <- rownames(r)
if(rotate) {loadings <- varimax(loadings)$loadings }
residual<- factor.residuals(r,loadings)
r2 <- sum(r*r)
rstar2 <- sum(residual*residual)
if (residuals) {result$residual <-residual}
result$fit <- round(1-rstar2/r2,digits)
result$loadings <- round(loadings,digits)
return(result)
}