CONGRUENCE: 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)

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

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

Author

Brian P. O'Connor

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).

An investigation by Lorenzo-Seva and ten Berge (2006) resulted in the following conclusion: A congruence coefficient "value in the range .85.94 corresponds to a fair similarity, while a value higher than .95 implies that the two factors or components compared can be considered equal."

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.

Lorenzo-Seva, U., & ten Berge, J. M. F. (2006). Tucker's congruence coefficient as a meaningful index of factor similarity. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 2(2), 5764.

Examples

Run this code

# \donttest{
# Rosenberg Self-Esteem scale items
loadings <- PCA(data_RSE[1:150,],   corkind='pearson', Nfactors = 3, 
                rotation='varimax', verbose=FALSE)

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


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

target <- PCA(data_NEOPIR[501:1000,], corkind='pearson', Nfactors = 3, 
              rotation='varimax', verbose=FALSE)
CONGRUENCE(target$loadingsROT, loadings$loadingsROT, verbose=TRUE)
# }

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