Skip to contents

Scree plot

Source: R/efa_scree.R
efa_scree.Rd

The scree plot was originally introduced by Cattell (1966) to perform the scree test. In a scree plot, the eigenvalues of the factors / components are plotted against the index of the factors / components, ordered from 1 to N factors components, hence from largest to smallest eigenvalue. According to the scree test, the number of factors / components to retain is the number of factors / components to the left of the "elbow" (where the curve starts to level off) in the scree plot.

Usage

efa_scree(
  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

Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. https://doi.org/10.1207/s15327906mbr0102_10

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). The scree plot is a visual criterion, so it returns no numeric suggestion. Its main fields are:

results

A list with one record per requested eigenvalue type, each holding the eigenvalues used for the scree plot.

settings

A list of the settings used.

Details

As the scree test requires visual examination, the test has been especially criticized for its subjectivity and with this low inter-rater reliability. Moreover, a scree plot can be ambiguous if there are either no clear "elbow" or multiple "elbows", making it difficult to judge just where the eigenvalues do level off. Finally, the scree test has also been found to be less accurate than other factor retention criteria. For all these reasons, the scree test has been recommended against, at least for exclusive use as a factor retention criterion (Zwick & Velicer, 1986)

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

See also

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

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

Examples

efa_scree(test_models$baseline$cormat, eigen_type = c("PCA", "SMC"))
#> ── Scree plot ──────────────────────────────────────────────────────────────────
#> Eigenvalues found using PCA and SMC.
#> 
#> ℹ Scree plot is a visual criterion; inspect the plot to identify the elbow.