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Empirical Kaiser criterion

Source: R/efa_ekc.R
efa_ekc.Rd

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

Usage

efa_ekc(
  x,
  N = NA,
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  type = "BvA2017"
)

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

Caron, P.-O. (2025). A Comparison of the Next Eigenvalue Sufficiency Test to Other Stopping Rules for the Number of Factors in Factor Analysis. Educational and Psychological Measurement, Online-first publication. https://doi.org/10.1177/00131644241308528

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

Arguments

x

data.frame or matrix. Dataframe 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. Correlation computed from raw data: "pearson", "spearman", or "kendall" (passed to stats::cor()), or "poly" / "tetra" for polychoric / tetrachoric correlations of ordinal / binary data (a two-step estimator with no empty-cell continuity correction). Default is "pearson".

type

character. The calculation of EKC. type "BvA2017" is the original implementation; type "AM2019" differs from the original implementation but was used in simulation studies (Auerswald & Moshagen, 2019; Caron, 2025). See details. Use type = c("BvA2017", "AM2019") for both implementations. Make sure to report which version you used.

Value

An object of class efa_retention (see print.efa_retention() and plot.efa_retention() for the print and plot methods). Its main fields are:

n_factors

A named numeric vector with the suggested number of factors for each requested implementation ("BvA2017" and/or "AM2019").

results

A list with one record per implementation, each holding the eigenvalues, the reference eigenvalues, and the retained solution used for printing and plotting.

settings

A list with the settings used.

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 efa_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 efa_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).

In EFAtools version <= 0.5.0 only the implementation of Auerswald and Moshagen (2019) was implemented (now available with type = "AM2019"). However, this implementation, that was probably also used in Caron (2025), differs from the original implementation by Braeken and van Assen (2017) in that it corrects by the reference values, i.e., without using the empirical eigenvalues used in the original implementation. Thanks to Luis Eduardo Garrido for pointing this out and to Johan Braeken for sharing sample code, based on which the original version is now implemented and used by default with type = "BvA2017".

While the adapted version performed relatively well in the simulation studies by Auerswald and Moshagen (2019) and Caron (2025), the theoretical derivations of the EKC as introduced by Braeken and van Assen (2017) may no longer hold. Currently we are unaware of studies comparing the two implementations, but based on our own brief comparisons across multiple datasets, the two implementations appear to often differ substantially regarding the number of factors suggested.

As both implementations exist in different packages and studies, we provide both versions here. Be sure to state clearly which version you use when reporting your results to avoid confusion and ensure reproducibility.

See also

efa_retain() as a wrapper function for this and the other factor retention criteria.

Other factor retention criteria: efa_cd(), efa_hull(), efa_kgc(), efa_map(), efa_nest(), efa_parallel(), efa_retain(), efa_scree(), efa_smt()

Examples

# original implementation
efa_ekc(test_models$baseline$cormat, N = 500)
#> ── Empirical Kaiser Criterion ──────────────────────────────────────────────────
#> 
#> • Original implementation (Braeken & van Assen, 2017): 3
#> 
#> ℹ Multiple implementations of EKC exist; make sure to report which one you used (see the efa_ekc help page for details).