efa_cd: Comparison data

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

Comparison data

Description

Factor retention method introduced by Ruscio and Roche (2012). The code was adapted from the CD code published by Auerswald and Moshagen (2019), available at https://osf.io/x5cz2/.

Usage

efa_cd(
  x,
  n_factors_max = NA,
  N_pop = 10000,
  N_samples = 500,
  alpha = 0.3,
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  max_iter = 50
)

Arguments

x	data.frame or matrix. Dataframe or matrix of raw data.
n_factors_max	numeric. The maximum number of factors to test against. Larger numbers will increase the duration the procedure takes, but test more possible solutions. If left NA (default) the maximum number of factors for which the model is still over-identified (df > 0) is used.
N_pop	numeric. Size of finite populations of comparison data. Default is 10000.
N_samples	numeric. Number of samples drawn from each population. Default is 500.
alpha	numeric. The alpha level used to test the significance of the improvement added by an additional factor. Default is .30.
cor_method	character. One of "pearson", "spearman", or "kendall", passed to stats::cor(). "poly" and "tetra" are not supported because CD compares the data against simulated continuous reference data. Default is "pearson".
max_iter	numeric. The maximum number of iterations after which the iterative PAF procedure inside the comparison-data generation is halted; it does not cap an EFA of x. Default is 50.

Details

Comparison data (CD) extends parallel analysis by reproducing the observed correlation matrix rather than generating random data: datasets with a known factor structure are generated with an increasing number of factors, and the smallest number for which adding a further factor no longer significantly improves the reproduction of the observed eigenvalues is retained (Ruscio & Roche, 2012).

Because it reproduces the observed correlation structure instead of a null model, CD was among the more accurate criteria across a broad range of conditions in Ruscio and Roche (2012). It is, however, the only criterion in this family that requires raw data, and by some margin the most computationally intensive one: a finite population of N_pop cases is generated and N_samples samples are drawn from it at every candidate factor count. It is therefore a good choice when the raw data are at hand and the runtime is acceptable, and a poor one for a quick look at a correlation matrix.

The comparison data are obtained by simulation, so the suggested number of factors varies slightly from run to run. Call base::set.seed() beforehand to make a run reproducible.

Note that if the data contains missing values, these will be removed for the comparison data procedure using stats::na.omit(). If missing data should be treated differently, e.g., by imputation, do this outside efa_cd() and then pass the complete data.

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 ("CD") with the suggested number of factors according to comparison data results.
results	A list with a single record holding the mean RMSE between the eigenvalues of the generated and the entered data per number of factors (used for the plot) and, in rmse_eigenvalues, the per-sample RMSE matrix (rows are samples, columns are factor counts; columns beyond the last tested factor count are left as zero).
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

Ruscio, J., & Roche, B. (2012). Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment, 24, 282–292. doi: 10.1037/a0025697

See Also

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

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

Examples

# determine n factors of the GRiPS
efa_cd(GRiPS_raw, N_pop = 500, N_samples = 20)

# determine n factors of the DOSPERT risk subscale
efa_cd(DOSPERT_raw, N_pop = 500, N_samples = 20)

EFAtools documentation built on Aug. 21, 2026, 5:16 p.m.