EKC: Empirical Kaiser Criterion

In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

Empirical Kaiser Criterion

Description

The empirical Kaiser criterion incorporates random sampling variations of the eigenvalues from the Kaiser-Guttman criterion (KGC; see Auerswald & Moshagen , 2019; Braeken & van Assen, 2017). The code is based on Auerswald and Moshagen (2019).

Usage

EKC(
  x,
  N = NA,
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall")
)

Arguments

x	data.frame or matrix. data.frame or matrix of raw data or matrix with correlations.
N	numeric. The number of observations. Only needed if x is a correlation matrix.
use	character. Passed to stats::cor if raw data is given as input. Default is "pairwise.complete.obs".
cor_method	character. Passed to stats::cor. Default is "pearson".

Details

The Kaiser-Guttman criterion was defined with the intend that a factor should only be extracted if it explains at least as much variance as a single factor (see KGC). However, this only applies to population-level correlation matrices. Due to sampling variation, the KGC strongly overestimates the number of factors to retrieve (e.g., Zwick & Velicer, 1986). To account for this and to introduce a factor retention method that performs well with small number of indicators and correlated factors (cases where the performance of parallel analysis, see PARALLEL, is known to deteriorate) Braeken and van Assen (2017) introduced the empirical Kaiser criterion in which a series of reference eigenvalues is created as a function of the variables-to-sample-size ratio and the observed eigenvalues.

Braeken and van Assen (2017) showed that "(a) EKC performs about as well as parallel analysis for data arising from the null, 1-factor, or orthogonal factors model; and (b) clearly outperforms parallel analysis for the specific case of oblique factors, particularly whenever factor intercorrelation is moderate to high and the number of variables per factor is small, which is characteristic of many applications these days" (p.463-464).

The EKC function can also be called together with other factor retention criteria in the N_FACTORS function.

Value

A list of class EKC containing

eigenvalues	A vector containing the eigenvalues found on the correlation matrix of the entered data.
n_factors	The number of factors to retain according to the empirical Kaiser criterion.
references	The reference eigenvalues.
settings	A list with the settings used.

Source

Auerswald, M., & Moshagen, M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological Methods, 24(4), 468–491. https://doi.org/10.1037/met0000200

Braeken, J., & van Assen, M. A. (2017). An empirical Kaiser criterion. Psychological Methods, 22, 450 – 466. http://dx.doi.org/10.1037/ met0000074

Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432–442. http://dx.doi.org/10.1037/0033-2909.99.3.432

See Also

Other factor retention criteria: CD, HULL, KGC, PARALLEL, SMT

N_FACTORS as a wrapper function for this and all the above-mentioned factor retention criteria.

Examples

EKC(test_models$baseline$cormat, N = 500)

EFAtools documentation built on Jan. 6, 2023, 5:16 p.m.