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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 and a plot()
function.
There is also many examples of correlation matrices available with the packages and other stopping rules as well, such as pa()
for parellel analysis.
The development version can be accessed through GitHub:
Here is an example using the ex_4factors_corr
correlation matrix from the Rnest
library. The factor structure is
and the correlation matrix is
\[\begin{bmatrix} 1&0.81&0.27&0.567&0.567&0.189&0&0&0&0&0&0 \\ 0.81&1&0.27&0.567&0.567&0.189&0&0&0&0&0&0 \\ 0.27&0.27&1&0.189&0.189&0.063&0&0&0&0&0&0 \\ 0.567&0.567&0.189&1&0.81&0.27&0&0&0&0&0&0 \\ 0.567&0.567&0.189&0.81&1&0.27&0&0&0&0&0&0 \\ 0.189&0.189&0.063&0.27&0.27&1&0&0&0&0&0&0 \\ 0&0&0&0&0&0&1&0.81&0.27&0.567&0.567&0.189 \\ 0&0&0&0&0&0&0.81&1&0.27&0.567&0.567&0.189 \\ 0&0&0&0&0&0&0.27&0.27&1&0.189&0.189&0.063 \\ 0&0&0&0&0&0&0.567&0.567&0.189&1&0.81&0.27 \\ 0&0&0&0&0&0&0.567&0.567&0.189&0.81&1&0.27 \\ 0&0&0&0&0&0&0.189&0.189&0.063&0.27&0.27&1 \\ \end{bmatrix}\]
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.
## At 95% confidence, Nest Eigenvalue Sufficiency Test (NEST) suggests 4 factors.
The first output tells hom many factors NEST suggest. We can also consult the summary with
##
## nest 0.0.0.1 ended normally
##
## Estimator ML
## Number of model parameters 66
## Resampling 1000
## Sample size 2500
## Stopped at 5
##
##
## Probabilities of factors
## Factor Eigenvalue Prob
## F1 3.228 < .001
## F2 3.167 < .001
## F3 1.007 .009
## F4 0.972 .009
## F5 0.860 .735
##
##
## At 95% confidence, Nest 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 95th percentile of the sampled eigenvalues.
It is also possible to use a correlation matrix directly. A sample size, n
must be supplied.
## At 95% confidence, Nest Eigenvalue Sufficiency Test (NEST) suggests 2 factors.
The nest()
function can use with many \(\alpha\) values if desired.
Scree plot of NEST with many \(\alpha\)
Caron, P.-O. (2023). 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. 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
Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S. Springer. https://www.stats.ox.ac.uk/pub/MASS4/
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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