CONGRUENCE {EFA.dimensions}

R Documentation

Factor solution congruence

Description

Aligns two factor loading matrices and computes the factor solution congruence and the root mean square residual.

Usage

CONGRUENCE(target, loadings, verbose)

Arguments

target	The target loading matrix.
loadings	The loading matrix that will be aligned with the target.
verbose	Should detailed results be displayed in console? TRUE (default) or FALSE

Details

The function first searches for the alignment of the factors from the two loading matrices that has the highest factor solution congruence. It then aligns the factors in "loadings" with the factors in "target" without changing the loadings. The alignment is based solely on the positions and directions of the factors. The function then produces the Tucker-Wrigley-Neuhaus factor solution congruence coefficient as an index of the degree of similarity between between the aligned loading matrices (see Guadagnoli & Velicer, 1991; and ten Berge, 1986, for reviews).

Value

A list with the following elements:

rcBefore	The factor solution congruence before factor alignment
rcAfter	The factor solution congruence after factor alignment
rcFactors	The congruence for each factor
rmsr	The root mean square residual
residmat	The residual matrix
loadingsNew	The aligned loading matrix

Author(s)

Brian P. O'Connor

References

Guadagnoli, E., & Velicer, W. (1991). A comparison of pattern matching indices. Multivariate Behavior Research, 26, 323-343.

ten Berge, J. M. F. (1986). Some relationships between descriptive comparisons of components from different studies. Multivariate Behavioral Research, 21, 29-40.

Examples

# Rosenberg Self-Esteem scale items
loadings <- PCA(data_RSE[1:150,],   corkind='pearson', Nfactors = 3, 
                rotate='VARIMAX', verbose=FALSE)

target   <- PCA(data_RSE[151:300,], corkind='pearson', Nfactors = 3, 
                rotate='VARIMAX', verbose=FALSE)
CONGRUENCE(target = target$loadingsV, loadings = loadings$loadingsV, verbose=TRUE)


# NEO-PI-R scales
loadings <- PCA(data_NEOPIR[1:500,], corkind='pearson', Nfactors = 3, 
                rotate='VARIMAX', verbose=FALSE)

target <- PCA(data_NEOPIR[501:1000,], corkind='pearson', Nfactors = 3, 
              rotate='VARIMAX', verbose=FALSE)
CONGRUENCE(target$loadingsV, loadings$loadingsV, verbose=TRUE)

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