FACTORABILITY {EFA.dimensions}

Factorability of a correlation matrix

Description

Three methods for assessing the factorability of a correlation matrix

Usage

FACTORABILITY(data, corkind='pearson', Ncases=NULL, verbose=TRUE)

Arguments

data

An all-numeric dataframe where the rows are cases & the columns are the variables, or a correlation matrix with ones on the diagonal. The function internally determines whether the data are a correlation matrix.

corkind

The kind of correlation matrix to be used if data is not a correlation matrix. The options are 'pearson', 'kendall', 'spearman', 'gamma', and 'polychoric'. Required only if the entered data is not a correlation matrix.

Ncases

The number of cases for a correlation matrix. Required only if the entered data is a correlation matrix.

verbose

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

Details

This function provides results from three methods of assessing whether a dataset or correlation matrix is suitable for factor analysis:

1 – whether the determinant of the correlation matrix is > 0.00001;

2 – Bartlett's test of whether a correlation matrix is significantly different an identity matrix; and

3 – the Kaiser-Meyer-Olkin measure of sampling adequacy.

Value

A list with the following elements:

chisq

The chi-squared value for Bartlett,s test

df

The degrees of freedom for Bartlett,s test

pvalue

The significance level for Bartlett,s test

Rimage

The image correlation matrix

KMO

The overall KMO value

KMOvars

The KMO values for the variables

Author(s)

Brian P. O'Connor

References

Bartlett, M. S. (1951). The effect of standardization on a chi square approximation in factor analysis, Biometrika, 38, 337-344.

Cerny, C. A., & Kaiser, H. F. (1977). A study of a measure of sampling adequacy for factor-analytic correlation matrices. Multivariate Behavioral Research, 12(1), 43-47.

Dziuban, C. D., & Shirkey, E. C. (1974). When is a correlation matrix appropriate for factor analysis? Psychological Bulletin, 81, 358-361.

Kaiser, H. F., & Rice, J. (1974). Little Jiffy, Mark IV. Educational and Psychological Measurement, 34, 111-117.

Examples

FACTORABILITY(data_RSE, corkind='pearson')

FACTORABILITY(data_Field, corkind='pearson')