PROCRUSTES {EFA.dimensions}

Procrustes factor rotation

Description

Conducts Procrustes rotations of a factor loading matrix to a target factor matrix, and it computes the factor solution congruence and the root mean square residual (based on comparisons of the entered factor loading matrix with the Procrustes-rotated matrix).

Usage

PROCRUSTES(loadings, target, type, verbose)

Arguments

loadings

The loading matrix that will be aligned with the target.

target

The target loading matrix.

type

The options are 'orthogonal' or 'oblique' rotation.

verbose

Should detailed results be displayed in console? TRUE (default) or FALSE

Details

This function conducts Procrustes rotations of a factor loading matrix to a target factor matrix, and it computes the factor solution congruence and the root mean square residual (based on comparisons of the entered factor loading matrix with the Procrustes-rotated matrix). The orthogonal Procrustes rotation is based on Schonemann (1966; see also McCrae et al., 1996). The oblique Procrustes rotation is based on Hurley and Cattell (1962). The factor solution congruence is the Tucker-Wrigley-Neuhaus factor solution congruence coefficient (see Guadagnoli & Velicer, 1991; and ten Berge, 1986, for reviews).

Value

A list with the following elements:

loadingsPROC

The Procrustes-rotated loadings

congruence

The factor solution congruence after factor Procrustes rotation

rmsr

The root mean square residual

residmat

The residual matrix after factor Procrustes rotation

Author(s)

Brian P. O'Connor

References

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

Hurley, J. R., & Cattell, R. B. (1962). The Procrustes program: Producing direct rotation to test a hypothesized factor structure. Behavioral Science, 7, 258-262.

McCrae, R. R., Zonderman, A. B., Costa, P. T. Jr., Bond, M. H., & Paunonen, S. V. (1996). Evaluating replicability of factors in the revised NEO personality inventory: Confirmatory factor analysis versus Procrustes rotation. Journal of Personality and Social Psychology, 70, 552-566.

Schonemann, P. H. (1966). A generalized solution of the orthogonal Procrustes problem. Psychometrika, 31, 1-10.

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

Examples

# RSE data
PCAoutput_1 <- PCA(data_RSE[1:150,],   Nfactors = 2, rotation='promax', verbose=FALSE)

PCAoutput_2 <- PCA(data_RSE[151:300,], Nfactors = 2, rotation='promax', verbose=FALSE)

PROCRUSTES(target=PCAoutput_1$pattern, loadings=PCAoutput_2$pattern, 
           type = 'orthogonal', verbose=TRUE)