EFAtools (version 0.6.0)

NEST: 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,
  ...
)

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.

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.

Examples

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

# with raw data
NEST(GRiPS_raw)