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This function runs many existing procedures for determining how many factors to retain/extract from 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 model and select the solution with the fewer factors.

## Usage

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

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 psych::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

Package from which respective methods are used. Can be "all" or a vector containing "nFactors", "psych", "PCDimension", "fit" or "EGAnet". Note that "fit" (which actually also relies on the psych package) and "EGAnet" can be very slow for bigger datasets. Thus, the default is c("nFactors", "psych"). You must have the respective packages installed for the methods to be used.

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, the function will run all the procedures in try blocks, and will only return those that work and silently skip the ones that may fail.

n_max

If set to a value (e.g., 10), will drop from the results all methods that suggest a higher number of components. The interpretation becomes 'from all the methods that suggested a number lower than n_max, the results are ...'.

...

Arguments passed to or from other methods.

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, Scree (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          Scree (SE)     Scree_SE
#> 7          1    VSS complexity 1          VSS
#> 8          1       Velicer's MAP Velicers_MAP
#> 9          1                 BIC          BIC
#> 10         2            Bartlett      Barlett
#> 11         2            Anderson      Barlett
#> 12         2              Lawley      Barlett
#> 13         2          Scree (R2)     Scree_SE
#> 14         2      BIC (adjusted)          BIC
#> 15         3    VSS complexity 2          VSS
summary(result)
#>   n_Factors n_Methods
#> 1         1         9
#> 2         2         5
#> 3         3         1
# \dontrun{
# Setting package = 'all' will increase the number of methods (but is slow)
n_factors(mtcars, type = "PCA", package = "all")
#> # Method Agreement Procedure:
#>
#> The choice of 2 dimensions is supported by 12 (40.00%) methods out of 30 (Optimal coordinates, Parallel analysis, Kaiser criterion, VSS complexity 2, Fit_off, Random (F), Auer-Gervini (twice), Auer-Gervini (spectral), Auer-Gervini (kmeans-2), AuerGervini (kmeans-3), Auer-Gervini (T), AuerGervini (CPT)).
n_factors(mtcars, type = "FA", algorithm = "mle", package = "all")
#> # Method Agreement Procedure:
#>
#> The choice of 3 dimensions is supported by 11 (40.74%) methods out of 27 (Bartlett, CNG, Scree (SE), Scree (R2), EGA (glasso), EGA (TMFG), Velicer's MAP, BIC, RMSR, CRMS, BIC).
# }