psych (version 1.0-25)

principal: Principal components analysis

Description

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. Unlike princomp, this returns a subset of just the best nfactors. The eigen vectors are rescaled by the sqrt of the eigen values to produce the component loadings more typical in factor analysis.

Usage

principal(r, nfactors = 0, residuals = FALSE,rotate=FALSE, digits=2)

Arguments

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

Value

• 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

Details

Useful for those cases where the correlation matrix is improper (perhaps because of SAPA techniques).

See Also

VSS,factor2cluster,factor.pa, factor.congruence

Examples

#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)