psych (version 1.0-58)

factor.congruence: Coefficient of factor congruence

Description

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

Usage

factor.congruence(x, y,digits=2)

Arguments

x

A matrix of factor loadings

y

A second matrix of factor loadings

digits

Round off to digits

Value

• A matrix of factor congruences.

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.

Input may either be matrices or factor analysis output (which includes a loadings object), or a mixture of the two.

Factor congruences are the cosines of pairs vectors defined by the loadings matrix and based at the origin. The correlations of factor loadings are cinoses of the vectors based at the mean loading for each factor.

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)
#factor.congruence(fa,pcv)
#
#factor.congruence(pcv,fa)
#    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)