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README

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 %>%.

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)

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.

## Next Eigenvalue Sufficiency Test (NEST) suggests 4 factors.

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

## 
## 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.

Scree plot of NEST

The above figure shows the empirical eigenvalues in blue and the 95^th 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)

Scree plot of NEST with many \(\alpha\)

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)

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

Achim, A. (2017). Testing the number of required dimensions in exploratory factor analysis.

,

(1), 64–74.

Achim, A. (2020). Esprit et enjeux de l’analyse factorielle exploratoire.

,

(4), 213–247.

Achim, A. (2021). Determining the number of factors using parallel analysis and its recent variants: Comment on Lim and Jahng (2019).

,

(1), 69–73.

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.

,

(1), 21–47.

Caron, P.-O. (2025). A comparison of the next eigenvalue sufficiency test to other stopping rules for the number of factors in factor analysis.

.

Venables, W. N., & Ripley, B. D. (2002).

. Springer.

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