Coefficient of factor congruence

Description

Given two sets of factor loadings, report their degree of congruence.

Usage

factor.congruence(x, y, loading=TRUE)

Arguments

Details

Find the coefficient of factor congruence between two sets of factor loadings.

It is an interesting exercise to compare factor congruences with the correlations of factor loadings. Factor congruences are based upon the raw cross products, while correlations are based upon centered cross products.

Value

A matrix of factor congruences.

Author(s)

revelle@northwestern.edu
http://personality-project.org/revelle.html

References

Gorsuch, Richard, (1983) Factor Analysis. Lawrence Erlebaum Associates.
Revelle, W. (In preparation) An Introduction to Psychometric Theory with applications in R (http://personality-project.org/r/book/)

See Also

principal, factor.pa

Examples

#fa <- factanal(x,4,covmat=Harman74.cor$cov)
#pc <- principal(Harman74.cor$cov,4)
#pcv <- varimax(pc$loading)
#round(factor.congruence(fa,pcv),2)
#
#round(factor.congruence(pcv,fa),2)
#    Factor1 Factor2 Factor3 Factor4
#PC1    1.00    0.60    0.45    0.55
#PC2    0.44    0.49    1.00    0.56
#PC3    0.54    0.99    0.44    0.55
#PC4    0.47    0.52    0.48    0.99

#compare with 
#round(cor(fa$loading,pcv$loading),2)


## The function is currently defined as
#function (x,y,loading=TRUE) {
# if (loading) {x <- x$loadings
#      y <- y$loadings }
      
#  nx<- dim(x)[2]
#  ny<- dim(y)[2]
#  cross<- t(y) %*% x   #inner product will have dim of ny * nx
#   sumsx<- sqrt(1/diag(t(x) %*%x))   
 #  sumsy<- sqrt(1/diag(t(y) %*%y)) 

 #  result<- matrix(rep(0,nx*ny),ncol=nx)
#    result<-  sumsy * (cross * rep(sumsx, each = ny))
#  return(t(result))
#   }