NEST: Next eigenvalue sufficiency test (NEST)

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

Next eigenvalue sufficiency test (NEST)

Description

NEST uses many synthetic datasets to generate reference eigenvalues against which to compare the empirical eigenvalues. This is similar to parallel analysis, but other than parallel analysis, NEST does not just rely on synthetic eigenvalues based on an identity matrix as null model. It was introduced by Achim (2017), see also Brandenburg and Papenberg (2024) and Caron (2025) for further simulation studies including NEST.

Usage

NEST(
  x,
  N = NA,
  alpha = 0.05,
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall"),
  n_datasets = 1000,
  ...
)

Arguments

x	data.frame or matrix. data.frame or matrix of raw data or matrix with correlations.
N	numeric. The number of observations. Only needed if x is a correlation matrix.
alpha	numeric. The alpha level to use (i.e., 1-alpha percentile of eigenvalues is used for reference values).
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_datasets	numeric. The number of datasets to simulate. Default is 1000.
...	Additional arguments passed to EFA. For example, the extraction method can be changed here (default is "PAF"). PAF is more robust, but it will take longer compared to the other estimation methods available ("ML" and "ULS").

Details

NEST compares the first empirical eigenvalue against the first eigenvalues of n_dataset synthetic datasets based on a null model (i.e., with uncorrelated variables; same as in parallel analysis, see PARALLEL). The following eigenvalues are compared against synthetic datasets based on an EFA-model with one fewer factors than the position of the respective empirical eigenvalue. E.g, the second empirical eigenvalue is compared against synthetic data based on a one-factor model. The alpha-level defines against which percentile of the synthetic eigenvalue distribution to compare the empirical eigenvalues against, i.e., an alpha of .05 (the default) uses the 95th percentile as reference value.

For details on the method, including simulation studies, see Achim (2017), Brandenburg and Papenberg (2024), and Caron (2025).

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

Value

A list of class NEST containing the following objects

eigenvalues	A vector containing the empirical eigenvalues of the entered data.
n_factors	The number of factors to retain according to the NEST procedure.
references	A vector containing the reference eigenvalues.
prob	For the first n_factors + 1 empirical eigenvalues, the proportion <= the set of n_datasets reference eigenvalues.
settings	A list of control settings used in the print function.

Source

Achim, A. (2017). Testing the number of required dimensions in exploratory factor analysis. The Quantitative Methods for Psychology, 13(1), 64–74. https://doi.org/10.20982/tqmp.13.1.p064

Brandenburg, N., & Papenberg, M. (2024). Reassessment of innovative methods to determine the number of factors: A simulation-based comparison of exploratory graph analysis and Next Eigenvalue Sufficiency Test. Psychological Methods, 29(1), 21–47. https://doi.org/10.1037/met0000527

Caron, P.-O. (2025). A Comparison of the Next Eigenvalue Sufficiency Test to Other Stopping Rules for the Number of Factors in Factor Analysis. Educational and Psychological Measurement, Online-first publication. https://doi.org/10.1177/00131644241308528

Examples

# with correlation matrix
NEST(test_models$baseline$cormat, N = 500)

# with raw data
NEST(GRiPS_raw)

EFAtools documentation built on June 19, 2025, 9:07 a.m.