Exploratory Factor Analysis

Exploratory factor analysis (EFA) identifies the latent factor structure that underlies a set of observed variables when no prior structure is imposed. It is used to reduce many indicators to a smaller number of underlying dimensions and to generate hypotheses for subsequent testing with confirmatory factor analysis.

Procedure

EFA proceeds in four decisions. Extraction selects an algorithm — principal axis factoring and maximum likelihood are preferred over principal components analysis when the goal is to recover latent factors rather than summarise variance. Number of factors is judged from a combination of evidence: eigenvalues greater than one (the Kaiser criterion, now considered crude), the scree plot's elbow, parallel analysis (typically the most defensible criterion), and the interpretability of competing solutions. Rotation simplifies the loading matrix: orthogonal rotations such as varimax assume uncorrelated factors, while oblique rotations such as promax or oblimin allow factors to correlate and are usually more realistic for psychological constructs. Interpretation labels each factor from its high-loading indicators.

Application in language assessment

EFA has been used to investigate the dimensionality of vocabulary tests, motivation questionnaires, anxiety scales, and learner-strategy inventories. Schmitt and colleagues' work on vocabulary-knowledge inventories, and Dörnyei's work on the L2 Motivational Self System, both illustrate the EFA-then-CFA sequence: an initial exploratory study identifies candidate factors, and an independent confirmatory study tests whether the structure replicates.

Cautions

EFA is sample-dependent and capitalises on chance covariance; structures that emerge in one dataset routinely fail to replicate in another. Sample-size guidelines vary, but ratios of at least 5–10 respondents per item and absolute samples of 200 or more are common minima. Treating EFA results as confirmatory evidence — testing fit with the same data that generated the structure — is a recurring methodological error and inflates apparent construct support.

References

• 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.
• Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research (2nd ed.). Guilford Press.
• AERA, APA, & NCME (2014). Standards for Educational and Psychological Testing. American Educational Research Association.