mrfa {EFA.MRFA}

Minimum Rank Factor Analysis function

Description

Performs Minimum Rank Factor Analysis (MRFA) procedure, proposed by Ten Berge & Kiers (1991).

Usage

mrfa(SIGMA, dimensionality = 1, random = 10, conv1, conv2, display = TRUE,
    pwarnings = FALSE)

Arguments

SIGMA

Covariance/correlation matrix to be used in the analysis.

dimensionality

Common factors used to find communality estimates. The value has to be between 0 and the number of items minus 1, being the default option: 1 dimension to be retained. If 0 is selected, a more strict convergence criterion will be used.

random

Number of random starts.

conv1

Convergence criterion for MRFA. The default convergence criterion will be conv1=0.0001 . If the user determine a specific value, this will prevail.

conv2

Convergence criterion for glb step. The default convergence criterion will be conv2=0.001 . If the user determine a specific value, this will prevail.

display

Determines if the output will be displayed in the console, TRUE by default. If it is TRUE, the output is returned silently and if it is FALSE, the output is returned in the console.

pwarnings

Determines if the possible warnings occurred during the computation will be printed in the console.

Value

A

Factor loading matrix

Matrix

Covariance/Correlation matrix with optimal communalities in the diagonal

gam

Optimal communalities for each variable

Author(s)

David Navarro-Gonzalez

Urbano Lorenzo-Seva

References

ten Berge, J. M. F., & Kiers, H. A. L. (1991). A numerical approach to the approximate and the exact minimum rank of a covariance matrix. Psychometrika, 56(2), 309-315. doi: 10.1007/BF02294464

Examples

## perform MRFA using the correlation matrix of the IDAQ dataset, and using the default
## convergence criterion for MRFA and glb step.
mrfa(cor(IDAQ), dimensionality=3)