efa_kgc: Kaiser-Guttman criterion

Description

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,
  ...
)

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.

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. Default is c("PCA", "SMC", "EFA"), i.e. all three; "EFA" is the only one that fits a model.
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). 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, and the standard-error arguments (se, b_boot, ci, seed) are not accepted because the fit is an internal step that keeps only its communalities.

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 several of the other criteria available here, such as parallel analysis (efa_parallel()), the Hull method (efa_hull()), the empirical Kaiser criterion (efa_ekc()), or sequential \(chi^2\) model tests (efa_smt(); see Auerswald & Moshagen, 2019). Which criteria are informative depends on the data at hand, so rather than substituting one for another, run several of them together and compare their suggestions.

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

Examples

Run this code

efa_kgc(test_models$baseline$cormat, eigen_type = c("PCA", "SMC"))