Kaiser-Guttman criterion

Probably the most popular factor retention criterion. Kaiser and Guttman suggested to retain as many factors as there are sample eigenvalues greater than 1. This is why the criterion is also known as eigenvalues-greater-than-one rule.

Usage

efa_kgc(
  x,
  eigen_type = c("PCA", "SMC", "EFA"),
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  n_factors = 1,
  estimate_control = NULL,
  ...
)

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

Guttman, L. (1954). Some necessary conditions for common-factor analysis. Psychometrika, 19, 149 –161. http://dx.doi.org/10.1007/BF02289162

Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141–151. http://dx.doi.org/10.1177/001316446002000116

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.
eigen_type: character. On what the eigenvalues should be found. Can be either "PCA", "SMC", or "EFA", or some combination of them. If using "PCA", the diagonal values of the correlation matrices are left to be 1. If using "SMC", the diagonal of the correlation matrices is replaced by the squared multiple correlations (SMCs) of the indicators. If using "EFA", eigenvalues are found on the correlation matrices with the final communalities of an exploratory factor analysis solution (default is principal axis factoring extracting 1 factor) as diagonal.
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".
n_factors: numeric. Number of factors to extract if "EFA" is included in eigen_type. Default is 1.
estimate_control: an estimate_control() object with the estimation settings for the efa_fit() fit that provides the communalities when "EFA" is included in eigen_type. NULL (default) uses the efa_fit() defaults. The fit is unrotated, so no rotation settings apply.
...: Additional arguments passed to efa_fit(). For example, estimator, to change the estimator (PAF is default). The estimation tuning knobs are not passed here; they live in estimate_control.

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 eigenvalue type ("PCA", "SMC", and/or "EFA").
results: A list with one record per eigenvalue type, each holding the eigenvalues and the retained solution used for printing and plotting.
settings: A list of the settings used.

Details

Originally, the Kaiser-Guttman criterion was intended for the use with principal components, hence with eigenvalues derived from the original correlation matrix. This can be done here by setting eigen_type to "PCA". However, it is well-known that this criterion is often inaccurate and that it tends to overestimate the number of factors, especially for unidimensional or orthogonal factor structures (e.g., Zwick & Velicer, 1986).

The criterion's inaccuracy in these cases is somewhat addressed if it is applied on the correlation matrix with communalities in the diagonal, either initial communalities estimated from SMCs (done setting eigen_type to "SMC") or final communality estimates from an EFA (done setting eigen_type to "EFA"; see Auerswald & Moshagen, 2019). However, although this variant of the KGC is more accurate in some cases compared to the traditional KGC, it is at the same time less accurate than the PCA-variant in other cases, and it is still often less accurate than other factor retention methods, for example parallel analysis (efa_parallel()), the Hull method efa_hull(), or sequential \(chi^2\) model tests (efa_smt(); see Auerswald & Moshagen, 2019).

The efa_kgc function can also be called together with other factor retention criteria in the efa_retain() function.

Examples

efa_kgc(test_models$baseline$cormat, eigen_type = c("PCA", "SMC"))
#> ── Kaiser-Guttman criterion ────────────────────────────────────────────────────
#> 
#> • PCA eigenvalues: 3
#> • SMC eigenvalues: 1