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24 - Introduction to Exploratory Factor Analysis: An Applied Approach

from Part IV - Statistical Approaches

Published online by Cambridge University Press:  25 May 2023

By
Martin Sellbom  and
David Goretzko
Edited by
Austin Lee Nichols  and
John Edlund
Austin Lee Nichols
Affiliation:
Central European University, Vienna
John Edlund
Affiliation:
Rochester Institute of Technology, New York
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Summary

This chapter provides an overview of exploratory factor analysis (EFA) from an applied perspective. We start with a discussion of general issues and applications, including definitions of EFA and the underlying common factors model. We briefly cover history and general applications. The most substantive part of the chapter focuses on six steps of EFA. More specifically, we consider variable (or indicator) selection (Step 1), computing the variance–covariance matrix (Step 2), factor-extraction methods (Step 3), factor-retention procedures (Step 4), factor-rotation methods (Step 5), and interpretation (Step 6). We include a data analysis example throughout (with example code for R), with full details in an online supplement. We hope the chapter will provide helpful guidance to applied researchers in the social and behavioral sciences.

Keywords

Exploratory Factor AnalysisFactor AnalysisInternal StructureMeasurement ModelingLatent Variable Modeling
Type
Chapter
Information
The Cambridge Handbook of Research Methods and Statistics for the Social and Behavioral Sciences
Volume 1: Building a Program of Research
 , pp. 513 - 534
Publisher: Cambridge University Press
Print publication year: 2023

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References

Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317–332.CrossRefGoogle Scholar
Arendasy, M. (2009) BFSI: Big-Five Struktur-Inventar (Test & Manual). Mödling, Schuhfried GmbH.Google Scholar
Asparouhov, T. & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16(3), 397–438.Google Scholar
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. https://doi.org/10.1037/met0000200Google Scholar
Bandalos, D. L. (2008). Is parceling really necessary? A comparison of results from item parceling and categorical variable methodology. Structural Equation Modeling, 15(2), 211–240.CrossRefGoogle Scholar
Barendse, M. T., Oort, F. J., & Timmerman, M. E. (2015). Using exploratory factor analysis to determine the dimensionality of discrete responses. Structural Equation Modeling, 22(1), 87–101.Google Scholar
Beauducel, A. (2001). On the generalizability of factors: The influence of changing contexts of variables on different methods of factor extraction. Methods of Psychological Research Online, 6(1), 69–96.Google Scholar
Beauducel, A. & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling, 13(2), 186–203.Google Scholar
Ben-Porath, Y. S. & Tellegen, A. (2008). Minnesota Multiphasic Personality Inventory-2 Restructured Form: Manual for Administration, Scoring and Interpretation. University of Minnesota Press.Google Scholar
Berger, J. L. & Karabenick, S. A. (2016). Construct validity of self-reported metacognitive learning strategies. Educational Assessment, 21(1), 19–33. https://doi.org/10.1080/10627197.2015.1127751Google Scholar
Braeken, J. & van Assen, M. A. (2017). An empirical Kaiser criterion. Psychological Methods, 22(3), 450–466. https://doi.org/10.1037/met0000074CrossRefGoogle ScholarPubMed
Beavers, A. S., Lounsbury, J. W., Richards, J. K., et al. (2013). Practical considerations for using exploratory factor analysis in educational research. Practical Assessment, Research, and Evaluation, 18(1). https://doi.org/10.7275/qv2q-rk76Google Scholar
Brown, T. A. (2014). Confirmatory Factor Analysis for Applied Research. Guilford Press.Google Scholar
Browne, M. W. (1977). Generalized least-squares estimators in the analysis of covariance structures. In Aigner, D. J. & Goldberger, A. S. (eds.), Latent Variables in Socio-Economic Models (pp. 205–226). North-Holland.Google Scholar
Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36(1), 111–150. https://doi.org/10.1207/S15327906MBR3601_05.Google Scholar
Cattell, R. B. (1943). The description of personality: Basic traits resolved into clusters. Journal of Abnormal and Social Psychology, 38, 476–506.Google Scholar
Cattell, R. B. (1945). The description of personality: Principles and findings in a factor analysis. The American Journal of Psychology, 58(1), 69–90.CrossRefGoogle Scholar
Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. https://doi.org/10.1207/s15327906mbr0102_10CrossRefGoogle ScholarPubMed
Cattell, R. B. & Tsujioka, B. (1964). The importance of factor-trueness and validity, versus homogeneity and orthogonality, in test scales. Educational and Psychological Measurement, 24(1), 3–30.Google Scholar
Clarkson, D. B. & Jennrich, R. I. (1988). Quartic rotation criteria and algorithms. Psychometrika, 53, 251–259.CrossRefGoogle Scholar
Conway, J. M. & Huffcutt, A. I. (2003). A review and evaluation of exploratory factor analysis practices in organizational research. Organizational Research Methods, 6(2), 147–168.Google Scholar
Crawford, C. B. & Ferguson, G. A. (1970). A general rotation criterion and its use inorthogonal rotation. Psychometrika, 35, 321–332.Google Scholar
De Winter, J. C. & Dodou, D. (2012). Factor recovery by principal axis factoring and maximum likelihood factor analysis as a function of factor pattern and sample size. Journal of Applied Statistics, 39(4), 695–710.Google Scholar
Detrick, P., Ben-Porath, Y. S., & Sellbom, M. (2016). Associations between MMPI-2-RF (restructured form) and Inwald Personality Inventory (IPI) scale scores in a law enforcement pre-employment screening sample. Journal of Police and Criminal Psychology, 31, 81–95.CrossRefGoogle Scholar
Dinno, A. (2009). Exploring the sensitivity of Horn’s parallel analysis to the distributional form of random data. Multivariate Behavioral Research, 44(3), 362–388. https://doi.org/10.1080/00273170902938969Google Scholar
DiStefano, C., & Morgan, G. B. (2014). A comparison of diagonal weighted least squares robust estimation techniques for ordinal data. Structural Equation Modeling, 21(3), 425–438.Google Scholar
Everitt, B. & Hothorn, T. (2011) Exploratory factor analysis. In An Introduction to Applied Multivariate Analysis with R (pp. 135–161). Springer. https://doi.org/10.1007/978-1-4419-9650-3_5CrossRefGoogle Scholar
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299. https://doi.org/10.1037/1082-989X.4.3.272.Google Scholar
Floyd, F. J. & Widaman, K. F. (1995). Factor analysis in the development and refinement of clinical assessment instruments. Psychological Assessment, 7(3), 286–299.Google Scholar
Goretzko, D. & Bühner, M. (2020). One model to rule them all? Using machine learning algorithms to determine the number of factors in exploratory factor analysis. Psychological Methods, 25(6), 776–786. https://doi.org/10.1037/met0000262Google Scholar
Goretzko, D., Pham, T. T. H., & Bühner, M. (2021). Exploratory factor analysis: Current use, methodological developments and recommendations for good practice. Current Psychology, 40(1), 3510–3521. https://doi.org/10.1007/s12144-019-00300-2Google Scholar
Gorsuch, R. L. (1983). Factor Analysis. Erlbaum.Google Scholar
Graham, J. R., Ben-Porath, Y. S., & McNulty, J. L. (1999). MMPI-2 Correlates for Outpatient Mental Health. University of Minnesota Press.Google Scholar
Harman, H. H. (1976). Modern Factor Analysis, 3rd ed. University of Chicago Press.Google Scholar
Harman, H. H. & Jones, W. H. (1966). Factor analysis by minimizing residuals (minres). Psychometrika, 31, 351–368. https://doi.org/10.1007/BF02289468Google Scholar
Hendrickson, A. E. & White, P. O. (1964). Promax: A quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 17(1), 65–70. https://doi.org/10.1111/j.2044-8317.1964.tb00244.xGoogle Scholar
Henson, R. K. & Roberts, J. K. (2006). Use of exploratory factor analysis in published research: Common errors and some comment on improved practice. Educational and Psychological Measurement, 66(3), 393–416.Google Scholar
Holzinger, K. J. (1946). A comparison of the principal-axis and centroid factor. Journal of Educational Psychology, 37(8), 449–472. https://doi.org/10.1037/h0056539Google Scholar
Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185. https://doi.org/10.1007/BF02289447Google Scholar
Howard, M. C. (2016). A review of exploratory factor analysis decisions and overview of current practices: What we are doing and how can we improve?. International Journal of Human-Computer Interaction, 32(1), 51–62.CrossRefGoogle Scholar
Jennrich, R. I. (1979). Admissible values of γ in direct oblimin rotation. Psychometrika, 44, 173–177.CrossRefGoogle Scholar
Jokiniemi, K., Pietilä, A. M., & Mikkonen, S. (2021). Construct validity of clinical nurse specialist core competency scale: An exploratory factor analysis. Journal of Clinical Nursing, 30(13–14), 1863–1873.Google Scholar
Jöreskog, K. G., Olsson, U. H., Wallentin, F. Y. (2016) Exploratory factor analysis (EFA). In Multivariate Analysis with LISREL. Springer Series in Statistics (pp. 257–282). Springer. https://doi.org/10.1007/978-3-319-33153-9_6Google Scholar
Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200.Google Scholar
Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20(1), 141–151. https://doi.org/10.1177/001316446002000116Google Scholar
Kaiser, H. F. (1974). A note on the equamax criterion. Multivariate Behavioral Research, 9(4), 501–503.Google Scholar
Kaiser, H. F. & Rice, J. (1974). Little jiffy, mark IV. Educational and Psychological Measurement, 34(1), 111–117.Google Scholar
Kirkegaard, E. O. (2016). Some new methods for exploratory factor analysis of socioeconomic data. Open Quantitative Sociology & Political Science, 1(1), November 7. https://doi.org/10.26775/OQSPS.2016.11.07Google Scholar
Krueger, R. F. (2013). Personality disorders are the vanguard of the post-DSM-5.0 era. Personality Disorders: Theory, Research, and Treatment, 4(4), 355–362. https://doi.org/10.1037/per0000028Google Scholar
Li, C. H. (2016). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936–949.Google Scholar
Lim, S. & Jahng, S. (2019). Determining the number of factors using parallel analysis and its recent variants. Psychological Methods, 24(4), 452–467. https://doi.org/10.1037/met0000230CrossRefGoogle ScholarPubMed
Little, T. D., Rhemtulla, M., Gibson, K., & Schoemann, A. M. (2013). Why the items versus parcels controversy needn’t be one. Psychological Methods, 18(3), 285–300. https://doi.org/10.1037/a0033266Google Scholar
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), 340–364. https://doi.org/10.1080/00273171.2011.564527Google Scholar
Marsh, H. W., Lüdtke, O., Nagengast, B., Morin, A. J., & Von Davier, M. (2013). Why item parcels are (almost) never appropriate: Two wrongs do not make a right – Camouflaging misspecification with item parcels in CFA models. Psychological Methods, 18(3), 257–284.Google Scholar
Montoya, A. K. & Edwards, M. C. (2021). The poor fit of model fit for selecting number of factors in exploratory factor analysis for scale evaluation. Educational and Psychological Measurement, 81(3), 413–440.CrossRefGoogle ScholarPubMed
Mulaik, S. A. (2010). Foundations of Factor Analysis. CRC Press.Google Scholar
Park, H. S., Dailey, R., & Lemus, D. (2002). The use of exploratory factor analysis and principal components analysis in communication research. Human Communication Research, 28(4), 562–577.Google Scholar
Pearson, K. (1909). Determination of the coefficient of correlation. Science, 30(757), 23–25.Google Scholar
Preacher, K. J., Zhang, G., Kim, C., & Mels, G. (2013). Choosing the optimal number of factors in exploratory factor analysis: A model selection perspective. Multivariate Behavioral Research, 48(1), 28–56. doi:10.1080/00273171.2012.710386Google Scholar
Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. https://doi.org/10.1037/a0029315.Google Scholar
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. https://doi.org/10.1037/a0025697Google Scholar
Sass, D. A. & Schmitt, T. A. (2010). A comparative investigation of rotation criteria within exploratory factor analysis. Multivariate Behavioral Research, 45(1), 73–103. https://doi.org/10.1080/00273170903504810.Google Scholar
Schmitt, T. A. (2011). Current methodological considerations in exploratory and confirmatory factor analysis. Journal of Psychoeducational Assessment, 29(4), 304–321.Google Scholar
Schmitt, T. A., Sass, D. A., Chappelle, W., & Thompson, W. (2018). Selecting the “best” factor structure and moving measurement validation forward: An illustration. Journal of Personality Assessment, 100(4), 345–362.Google Scholar
Schoedel, R., Au, J. Q., Völkel, S. T., et al. (2018) Digital footprints of sensation seeking. Zeitschrift Für Psychologie, 226(4), 232–245.Google Scholar
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464.CrossRefGoogle Scholar
Sellbom, M. & Tellegen, A. (2019). Factor analysis in psychological assessment research: Common pitfalls and recommendations. Psychological Assessment, 31(12), 1428–1441. https://doi.org/10.1037/pas0000623Google Scholar
Spearman, C. (1904). “General intelligence,” objectively determined and measured. American Journal of Psychology, 15, 201–293.Google Scholar
Thurstone, L. L. (1938). Primary Mental Abilities. University of Chicago Press.Google Scholar
Thurstone, L. L. (1947). Multiple Factor Analysis. University of Chicago Press.Google Scholar
Thurstone, L. L. & Thurstone, T. G. (1941). Factorial studies of intelligence. Psychometric Monographs, 2, 94.Google Scholar
Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321–327. https://doi.org/10.1007/BF02293557Google Scholar
Wedel, M. & Kamakura, W. A. (2001). Factor analysis with (mixed) observed and latent variables in the exponential family. Psychometrika, 66(4), 515–530.Google Scholar
Widaman, K.F. (1993). Common factor analysis versus principal component analysis: Differential bias in representing model parameters? Multivariate Behavioral Research, 28, 263–311.Google Scholar
Yates, A. (1987). Multivariate Exploratory Data Analysis: A Perspective on Exploratory Factor Analysis. State University of New York Press.Google Scholar
Yuan, K. H. & Bentler, P. M. (1998). Normal theory based test statistics in structural equation modelling. British Journal of Mathematical and Statistical Psychology, 51, 289–309.Google Scholar

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