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Rnest: An R package for the Next Eigenvalue Sufficiency Test

The library Rnest offers the Next Eigenvalue Sufficiency Tests (NEST; Achim, 2017; 2020) to determine the number of dimensions in exploratory factor analysis. It provides a main function nest() to carry the analysis, a plot() function a many utilit. It has been showed to amongst the best stopping rule to determine the nuber of factor in factor analysis (Achim, 2021; Brandenburg & Papenberg, 2024; Caron, 2025).

There is many examples of correlation matrices available with the packages and other stopping rules as well, such as PA() for parallel analysis or MAP() for minimum average partial correlation.

As of version 1.0, Rnest is compatible with the tidyverse and the %>%.

Installation

The development version can be accessed through GitHub:

remotes::install_github(repo = "quantmeth/Rnest")
library(Rnest)

The CRAN package is also available.

installed.packages("Rnest")
library(Rnest)

Examples

Here is an example using the ex_4factors_corr correlation matrix from the Rnest library. The factor structure is

and the correlation matrix is

$$\begin{bmatrix} 1&.810&.270&.567&.567&.189&&&&&& \ .810&1&.270&.567&.567&.189&&&&&& \ .270&.270&1&.189&.189&.063&&&&&& \ .567&.567&.189&1&.810&.270&&&&&& \ .567&.567&.189&.810&1&.270&&&&&& \ .189&.189&.063&.270&.270&1&&&&&& \ &&&&&&1&.810&.270&.567&.567&.189 \ &&&&&&.810&1&.270&.567&.567&.189 \ &&&&&&.270&.270&1&.189&.189&.063 \ &&&&&&.567&.567&.189&1&.810&.270 \ &&&&&&.567&.567&.189&.810&1&.270 \ &&&&&&.189&.189&.063&.270&.270&1 \ \end{bmatrix}$$

From ex_4factors_corr, we can easily generate random data using the MASS packages (Venables & Ripley, 2002).

set.seed(1)
mydata <- MASS::mvrnorm(n = 2500,
                        mu = rep(0, ncol(ex_4factors_corr)),
                        Sigma = ex_4factors_corr)

We can then carry NEST.

res <- nest(mydata)
res
## Next Eigenvalue Sufficiency Test (NEST) suggests 4 factors.

The first output tells hom many factors NEST suggests. We can also consult the summary with

summary(res)
## 
## nest 1.1 ended normally  
##  
##    Estimator                       ML 
##    Missing data treatment          FIML 
##    Number of model parameters      66 
##    Resampling                      1000 
##    Sample size                     2500 
##    Stopped at                      5 
##  
##  
## Test that k factors are sufficient 
## 
##  k factor NextEig CritEig    Prob
##     k = 0   3.228   1.155  < .001
##     k = 1   3.167   1.113  < .001
##     k = 2   1.007   0.993    .010
##     k = 3   0.972   0.958    .009
##     k = 4   0.860   0.903    .727
## 
##  
## Next Eigenvalue Sufficiency Test (NEST) suggests 4 factors. 
## 
## Try plot(nest()) to see a graphical representation of the results. 
##

We can visualize the results using the generic function plot() using the nest() output.

plot(res)

The above figure shows the empirical eigenvalues in blue and the 95th percentile of the sampled eigenvalues.

It is also possible to use a correlation matrix directly. A sample size, n must be supplied.

nest(ex_4factors_corr, n = 240)
## Next Eigenvalue Sufficiency Test (NEST) suggests 2 factors.

The nest() function can use with many $\alpha$ values and presents parallel analysis results if desired.

res <- nest(ex_4factors_corr, n = 120, alpha = c(.01,.025,.05))
plot(res, pa = TRUE)

Recommended usage

Recommended usage : fiml estimation for correlation matrix and removing unique variables.

library(dplyr)
ex_3factors_doub_unique %>%
  genr8(n = 200) %>%        # to generate simulated data for the example
  cor_nest() %>%  
  remove_unique() %>%       
  nest() %>% 
  plot(pa = TRUE)

How to cite

Caron, P.-O. (2025). Rnest: An R package for the Next Eigenvalue Sufficiency Test. https://github.com/quantmeth/Rnest

References

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

Achim, A. (2020). Esprit et enjeux de l’analyse factorielle exploratoire. The Quantitative Methods for Psychology, 16(4), 213–247. https://doi.org/10.20982/tqmp.16.4.p213

Achim, A. (2021). Determining the number of factors using parallel analysis and its recent variants: Comment on Lim and Jahng (2019). Psychological Methods, 26(1), 69–73. https://doi.org/10.1037/met0000269

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. https://doi.org/10.1177/00131644241308528

Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S. Springer. https://www.stats.ox.ac.uk/pub/MASS4/

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Version

Install

install.packages('Rnest')

Monthly Downloads

447

Version

1.2

License

MIT + file LICENSE

Maintainer

P.-O. Caron

Last Published

June 19th, 2025

Functions in Rnest (1.2)

print.nest

Print results of NEST
tabachnick_fidell2019

A covariance matrix composed of 11 variables.
unique_variable

Probability of unique variables
loadings

Print Loadings in NEST
pa

Parallel analysis
plot.nest

Plot results of Next Eigenvalues Sufficiency Test (NEST)
shem

Split-Half Eigenvector Matching (SHEM)
summary.nest

Summary results of NEST
meek_bouchard

A correlation matrix from Meek-Bouchard.
nest

Next Eigenvalue Sufficiency Test (NEST)
remove_unique

Remove unique variables
MAP

Minimum average partial correlation (MAP)
TEST1

A problematic correlation matrix from Paquin.
Ledermann

Ledermann bound.
BartlettSphericity

Bartlett Sphericity Test
EKC

Empirical Kaiser Criterion (EKC)
genr8

Simplify the the generation from a multivariate normal distributions.
achim

A list of seven correlation matrices.
caron2019

A list of 15 correlation matrices composed of nine variables with three factors and different levels of correlations between factors.
briggs_maccallum2003

A list of three correlation matrices.
ex_2factors

A correlation matrix composed of 2 factors.
achim24

A correlation matrix composed of six factors.
caron2016

A list of six correlation matrices composed of nine variables with three factors and different levels of correlations between factors.
ex_4factors_corr

A correlation matrix composed of 4 correlated factors.
covFIML

Full Information Maximum Likelihood (FIML) correlation or covariance matrix
cov_nest

Compute covariance or correlation matrix with treatments for clusters and missing values
cormat.l

A list containing 120 lists of correlation matrices and their underlying characteristics.
ex_3factors_doub_unique

A correlation matrix composed of two factors, a doublet factor and a unique variable.
cormat

A list containing 120 correlation matrices.
ex_mqr

A correlation matrix from chapter 19 Explorer of Méthodes quantitatives avec R (MQR).