EFA.dimensions (version 0.1.6)

NEVALSGT1: Number of eigenvalues greater than 1 in a correlation matrix.

Description

Returns the count of the number of eigenvalues greater than 1 in a correlation matrix. This value is often referred to as the "Kaiser", "Kaiser-Guttman", or "Guttman-Kaiser" rule for determining the number of components or factors in a correlation matrix.

The rationale is that a component with an eigenvalue of 1 accounts for as much variance as a single variable. Extracting components with eigenvalues of 1 or less than 1 would defeat the usual purpose of component and factor analyses. Furthermore, the reliability of a component will always be nonnegative when its eigenvalue is greater than 1. This rule is the default retention criteria in SPSS and SAS.

There are a number of problems with this rule of thumb. Monte Carlo investigations have found that its accuracy rate is not acceptably high (Zwick & Velicer, 1986)). The rule was originally intended to be an upper bound for the number of components to be retained, but it is most often used as the criterion to determine the exact number of components or factors. Guttman's original proof applies only to the population correlation matrix and the sampling error that occurs in specific samples results in the rule often overestimating the number of components. The rule is also considered overly mechanical, e.g., a component with an eigenvalue of 1.01 achieves factor status whereas a component with an eigenvalue of .999 does not.

This function is included in this package for curiosity and research purposes.

Usage

NEVALSGT1(data, corkind, verbose)

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', and 'polychoric'. Required only if the entered data is not a correlation matrix.

verbose

Should detailed results be displayed in console? The options are: TRUE (default) or FALSE.

Value

The number of eigenvalues greater than 1.

References

Kaiser, H. F. (1960). The application of electronic computer to factor analysis. Educational and Psychological Measurement, 20, 141-151. Guttman, L. (1954). Some necessary conditions for common factor analysis. Psychometrika, 19, 149-161. Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4, 272-299. Hayton, J. C., Allen, D. G., Scarpello, V. (2004). Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational Research Methods, 7, 191-205. Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.

Examples

# NOT RUN {
# test on the Harman correlation matrix
NEVALSGT1(data_Harman, corkind='pearson', verbose=TRUE)

# test on the Rosenberg Self-Esteem Scale (RSE) using Pearson correlations
NEVALSGT1(data_RSE, corkind='pearson', verbose=TRUE)

# test on the Rosenberg Self-Esteem Scale (RSE) using polychoric correlations
NEVALSGT1(data_RSE, corkind='polychoric', verbose=TRUE)
# }