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EFAtools: An R package with fast and flexible implementations of exploratory factor analysis tools

---
doi: "10.21105/joss.02521"
title: "EFAtools: An R package with fast and flexible implementations of exploratory factor analysis tools"
source_url: "https://joss.theoj.org/papers/10.21105/joss.02521.pdf"
license_spdx: "CC-BY-4.0"
converter: "docling 2.129.0"
retrieved: "2026-09-29"
---
## [DOI: 10.21105/joss.02521](https://doi.org/10.21105/joss.02521)

## Software

- [Review](https://github.com/openjournals/joss-reviews/issues/2521)
- [Repository](https://github.com/mdsteiner/EFAtools)
- [Archive](https://doi.org/10.5281/zenodo.4032509)

Editor:

[Frederick Boehm](https://fboehm.us/)

## Reviewers:

- [@jacobsoj](https://github.com/jacobsoj)
- [@chainsawriot](https://github.com/chainsawriot)

Submitted:

19 July 2020

Published:

16 September 2020

## License

Authors of papers retain copyright and release the work under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

## EFAtools: An R package with fast and flexible implementations of exploratory factor analysis tools

## Markus D. Steiner 1 and Silvia Grieder 2

1 Center for Cognitive and Decision Sciences, Department of Psychology, University of Basel, Switzerland 2 Division of Developmental and Personality Psychology, Department of Psychology, University of Basel, Switzerland

## Summary

In the social sciences, factor analysis is a widely used tool to identify latent constructs underlying task performance or the answers to questionnaire items. Exploratory factor analysis (EFA) is a data-driven approach to factor analysis and is used to extract a smaller number of common factors that represent or explain the common variance of a larger set of manifest variables (see, e.g., Watkins, 2018 for an overview). Several decisions have to be made in advance when performing an EFA, including the number of factors to extract, and the extraction and rotation method to be used. After a factor solution has been found, it is useful to subject the resulting factor solution to an orthogonalization procedure to achieve a hierarchical factor solution with one general and several specific factors. This situation especially applies to data structures in the field of intelligence research where usually high, positive factor intercorrelations occur. From this orthogonalized, hierarchical solution, the variance can then be partitioned to estimate the relative importance of the general versus the specific factors using omega reliability coefficients (e.g., McDonald, 1999).

EFAtools is an R package (R Core Team, 2020) that enables fast and flexible analyses in an EFA framework, from tests for suitability of the data for factor analysis and factor retention criteria to hierarchical factor analysis with Schmid-Leiman transformation (Schmid & Leiman, 1957) and McDonald's omegas (e.g., McDonald, 1999). The package's core functionalities are listed in Table 1.

## Statement of Need

Compared to other R packages with which EFA can be performed, EFAtools has several advantages, including fast implementations using Rcpp (Eddelbuettel & Balamuta, 2017; Eddelbuettel & Sanderson, 2014), more flexibility in the adjustment of implementation features, the ability to reproduce the R psych (Revelle, 2020) and SPSS (IBM, 2015) implementations of some analyses methods (see vignette Replicate SPSS and R psych results with EFAtools ), as well as the inclusion of recommended implementations for these methods based on simulation analyses (Grieder & Steiner, 2020). Finally, the package includes the implementation of the, as of yet, most comprehensive set of factor retention criteria in R, including recently developed criteria such as the Hull method (Lorenzo-Seva, Timmerman, & Kiers, 2011), comparison data (Ruscio & Roche, 2012), and the empirical Kaiser criterion (Braeken & van Assen, 2016). As recommended by Auerswald & Moshagen (2019), multiple factor retention criteria should be examined simultaneously to check their convergence, which now is easily possible with a comprehensive function in EFAtools incorporating all implemented factor retention criteria for simultaneous application. Minor advantages over and above the existing implementations in R

include that when intending to perform a Schmid-Leiman transformation, this can be done on an obliquely rotated solution obtained with functions from the EFAtools or the psych package instead of being forced to perform the whole EFA procedure again. Moreover, our implementation of McDonald's omegas calculations include the possibility of manual variable-to-factor correspondences (as are needed for variance partitioning for predetermined / theoretical composites) in addition to automatically determined variable-to-factor correspondences (as done, for example, in the psych package). Further, the EFAtools function to compute McDonald's omegas can easily be applied on EFAtools and psych Schmid-Leiman solutions as well as on lavaan (Rosseel, 2012) second-order, bifactor, and single factor solutions (including solutions from multiple group analyses).

## Development and Purpose

EFAtools was designed for use in the social sciences in general and is especially suitable for research on cognitive abilities or other hierarchically organized constructs as well as for more time-consuming applications such as in simulation analyses. Its development arose from the need for a tool for easy replication and comparison of EFA solutions from different programs, namely R and SPSS (Grieder & Steiner, 2020), and has already been used in another publication (Grieder & Grob, 2019). The package was then expanded for a broader, easy, fast, and flexible use of EFA tools such that it is now suitable for most projects within the EFA framework.

Table 1: Core functionalities of EFAtools .

| Topic                           | Method                                                                                                                        | Function                                   |
|---------------------------------|-------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------|
| Suitability for factor analysis | Bartlett's test of sphericity Kaiser-Meyer-Olkin criterion                                                                    | BARTLETT() KMO()                           |
| Factor retention criteria       | Comparison data Empirical Kaiser criterion Hull method Kaiser-Guttman criterion Parallel analysis Scree plot                  | CD() EKC() HULL() KGC() PARALLEL() SCREE() |
| Factor extraction methods       | Sequential model tests RMSEA lower bound criterion AIC criterion Principal axis factoring Maximum likelihood                  | SMT() SMT() SMT() EFA() EFA()              |
| Rotation methods                | Unweighted least squares Orthogonal: Varimax,                                                                                 | EFA() EFA()                                |
| Factor scores                   | equamax, quartimax, geominT, bentlerT, bifactorT Oblique: Promax, oblimin, quartimin, simplimax, bentlerQ, geominQ, bifactorQ | EFA()                                      |
|                                 | Different methods for calculating factor scores                                                                               | FACTOR_SCORES()                            |
| Hierarchical factor analysis    | Schmid-Leiman transformation McDonald's omegas                                                                                | SL() OMEGA()                               |

Note . All functions for suitability for factor analysis and factor retention criteria can be called in any desired combination using the N\_FACTORS() function.

## Installation

The EFAtools package can be installed from CRAN using install.packages("EFAtools ") . Moreover, the development version can be installed from GitHub (https://github.com/ mdsteiner/EFAtools) using devtools::install\_github("mdsteiner/EFAtools", buil d\_vignettes = TRUE) .

## Acknowledgements

We thank Dirk Wulff for helpful suggestions concerning the C++ implementations.

## References

- Auerswald, M., & Moshagen, M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological Methods , 24 (4), 468-491. doi:10.1037/met0000200
- Braeken, J., & van Assen, M. A. L. M. (2016). An empirical Kaiser criterion. Psychological Methods , 22 (3), 450-466. doi:10.1037/met0000074
- Eddelbuettel, D., & Balamuta, J. J. (2017). Extending R with C++: A brief introduction to Rcpp. PeerJ Preprints , 5 , e3188v1. doi:10.7287/peerj.preprints.3188v1
- Eddelbuettel, D., & Sanderson, C. (2014). RcppArmadillo: Accelerating R with highperformance C++ linear algebra. Computational Statistics and Data Analysis , 71 , 1054-1063. doi:10.1016/j.csda.2013.02.005
- Grieder, S., & Grob, A. (2019). Exploratory factor analysis of the Intelligence and Development Scales-2: Implications for theory and practice. Assessment. Advance online publication. doi:10.1177/1073191119845051
- Grieder, S., & Steiner, M. D. (2020). Algorithmic jingle jungle: A comparison of implementations of Principal Axis Factoring and promax rotation in R and SPSS . PsyArXiv. doi:10.31234/osf.io/7hwrm
- IBM, C. (2015). IBM SPSS Statistics for Macintosh, Version 23.0 . Armonk, NY.
- Lorenzo-Seva, U., Timmerman, M. E., & Kiers, H. A. L. (2011). The Hull Method for selecting the number of common factors. Multivariate Behavioral Research , 46 (2), 340364. doi:10.1080/00273171.2011.564527
- McDonald, R. P. (1999). Test theory: A unified treatment . Mahwah, NJ: Erlbaum. ISBN: 978-1-4106-0108-7
- R Core Team. (2020). R: A language and environment for statistical computing . Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.R-project. org/
- Revelle, W. (2020). Psych: Procedures for psychological, psychometric, and personality research . Evanston, IL: Northwestern University. Retrieved from https://CRAN.R-project. org/package=psych
- Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software , 48 (2), 1-36. doi:10.18637/jss.v048.i02
- Ruscio, J., & Roche, B. (2012). Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment , 24 (2), 282-292. doi:10.1037/a0025697

Schmid, J., & Leiman, J. M. (1957). The development of hierarchical factor solutions. Psychometrika , 22 , 53-61. doi:10.1007/BF02289209

Watkins, M. W. (2018). Exploratory factor analysis: A guide to best practice. Journal of Black Psychology , 44 , 219-246. doi:10.1177/0095798418771807