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
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
CONGRUENCE(target$loadingsV, loadings$loadingsV, verbose=TRUE)