Number of components/factors to retain in PCA/FA

This function runs many existing procedures for determining how many factors to retain for your factor analysis (FA) or dimension reduction (PCA). It returns the number of factors based on the maximum consensus between methods. In case of ties, it will keep the simplest models and select the solution with the less factors.

n_factors(
  x,
  type = "FA",
  rotation = "varimax",
  algorithm = "default",
  package = c("nFactors", "psych"),
  cor = NULL,
  safe = TRUE,
  ...
)

n_components(
  x,
  type = "PCA",
  rotation = "varimax",
  algorithm = "default",
  package = c("nFactors", "psych"),
  cor = NULL,
  safe = TRUE,
  ...
)

Arguments

x	A data frame.
type	Can be `"FA"` or `"PCA"`, depending on what you want to do.
rotation	Only used for VSS (Very Simple Structure criterion, see `VSS`). The rotation to apply. Can be `"none"`, `"varimax"`, `"quartimax"`, `"bentlerT"`, `"equamax"`, `"varimin"`, `"geominT"` and `"bifactor"` for orthogonal rotations, and `"promax"`, `"oblimin"`, `"simplimax"`, `"bentlerQ"`, `"geominQ"`, `"biquartimin"` and `"cluster"` for oblique transformations.
algorithm	Factoring method used by VSS. Can be `"pa"` for Principal Axis Factor Analysis, `"minres"` for minimum residual (OLS) factoring, `"mle"` for Maximum Likelihood FA and `"pc"` for Principal Components. `"default"` will select `"minres"` if `type = "FA"` and `"pc"` if `type = "PCA"`.
package	These are the packages from which methods are used. Can be `"all"` or a vector containing `"nFactors"`, `"psych"` and `"EGAnet"`. However, `"EGAnet"` can be very slow for bigger datasets. Thus, by default, `c("nFactors", "psych")` are selected.
cor	An optional correlation matrix that can be used (note that the data must still be passed as the first argument). If `NULL`, will compute it by running `cor()` on the passed data.
safe	If `TRUE`, will run all the procedures in try blocks, and will only return those that work and silently skip the ones that may fail.
...	Arguments passed to or from other methods.

Value

A data frame.

Details

n_components is actually an alias for n_factors, with different defaults for the function arguments.

Note

There is also a plot()-method implemented in the see-package. n_components() is a convenient short for n_factors(type = "PCA").

References

Bartlett, M. S. (1950). Tests of significance in factor analysis. British Journal of statistical psychology, 3(2), 77-85.
Bentler, P. M., & Yuan, K. H. (1996). Test of linear trend in eigenvalues of a covariance matrix with application to data analysis. British Journal of Mathematical and Statistical Psychology, 49(2), 299-312.
Cattell, R. B. (1966). The scree test for the number of factors. Multivariate behavioral research, 1(2), 245-276.
Finch, W. H. (2019). Using Fit Statistic Differences to Determine the Optimal Number of Factors to Retain in an Exploratory Factor Analysis. Educational and Psychological Measurement.
Zoski, K. W., & Jurs, S. (1996). An objective counterpart to the visual scree test for factor analysis: The standard error scree. Educational and Psychological Measurement, 56(3), 443-451.
Zoski, K., & Jurs, S. (1993). Using multiple regression to determine the number of factors to retain in factor analysis. Multiple Linear Regression Viewpoints, 20(1), 5-9.
Nasser, F., Benson, J., & Wisenbaker, J. (2002). The performance of regression-based variations of the visual scree for determining the number of common factors. Educational and psychological measurement, 62(3), 397-419.
Golino, H., Shi, D., Garrido, L. E., Christensen, A. P., Nieto, M. D., Sadana, R., & Thiyagarajan, J. A. (2018). Investigating the performance of Exploratory Graph Analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial.
Golino, H. F., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PloS one, 12(6), e0174035.
Revelle, W., & Rocklin, T. (1979). Very simple structure: An alternative procedure for estimating the optimal number of interpretable factors. Multivariate Behavioral Research, 14(4), 403-414.
Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321-327.

Examples

library(parameters)

n_factors(mtcars, type = "PCA")
#> # Method Agreement Procedure:
#> 
#> The choice of 3 dimensions is supported by 5 (29.41%) methods out of 17 (Bartlett, CNG, SE Scree, R2, Velicer's MAP).

result <- n_factors(mtcars[1:5], type = "FA")
as.data.frame(result)
#>    n_Factors              Method       Family
#> 1          1             Bentler      Bentler
#> 2          1 Optimal coordinates        Scree
#> 3          1 Acceleration factor        Scree
#> 4          1   Parallel analysis        Scree
#> 5          1    Kaiser criterion        Scree
#> 6          1            SE Scree     Scree_SE
#> 7          1    VSS complexity 1          VSS
#> 8          1       Velicer's MAP Velicers_MAP
#> 9          1                 BIC          BIC
#> 10         1                 TLI          Fit
#> 11         1               RMSEA          Fit
#> 12         1                 BIC          Fit
#> 13         2            Bartlett      Barlett
#> 14         2            Anderson      Barlett
#> 15         2              Lawley      Barlett
#> 16         2                  R2     Scree_SE
#> 17         2      BIC (adjusted)          BIC
#> 18         2                CRMS          Fit
#> 19         3    VSS complexity 2          VSS
summary(result)
#>   n_Factors n_Methods
#> 1         1        12
#> 2         2         6
#> 3         3         1
# \donttest{
n_factors(mtcars, type = "PCA", package = "all")
#> Registered S3 methods overwritten by 'huge':
#>   method    from   
#>   plot.sim  BDgraph
#>   print.sim BDgraph
#> # Method Agreement Procedure:
#> 
#> The choice of 1 dimensions is supported by 5 (26.32%) methods out of 19 (t, p, Acceleration factor, EGA (glasso), VSS complexity 1).
n_factors(mtcars, type = "FA", algorithm = "mle", package = "all")
#> # Method Agreement Procedure:
#> 
#> The choice of 3 dimensions is supported by 7 (28.00%) methods out of 25 (Bartlett, CNG, SE Scree, R2, Velicer's MAP, BIC, BIC).
# }