KGC: Kaiser-Guttman Criterion

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

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

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"),
  n_factors = 1,
  ...
)

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. Passed to stats::cor. Default is "pearson".
n_factors	numeric. Number of factors to extract if "EFA" is included in eigen_type. Default is 1.
...	Additional arguments passed to EFA. For example, to change the extraction method (PAF is default).

Details

Originally, the Kaiser-Guttman criterion was intended for the use with prinicpal 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 (PARALLEL), the Hull method HULL, or sequential chi^2 model tests (SMT; see Auerswald & Moshagen, 2019).

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

Value

A list of class KGC containing

eigen_PCA	A vector containing the eigenvalues found with PCA.
eigen_SMC	A vector containing the eigenvalues found with SMCs.
eigen_EFA	A vector containing the eigenvalues found with EFA.
n_fac_PCA	The number of factors to retain according to the Kaiser- Guttmann criterion with PCA eigenvalues type.
n_fac_SMC	The number of factors to retain according to the Kaiser- Guttmann criterion with SMC eigenvalues type.
n_fac_EFA	The number of factors to retain according to the Kaiser- Guttmann criterion with EFA eigenvalues type.
settings	A list of 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

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

See Also

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

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

Examples

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

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