Exploratory Factor Analysis is rightly described as both an art and a science, where researchers follow a series of analytic steps involving judgments more reminiscent of qualitative inquiry, an interesting irony given the mathematical sophistication underlying EFA models.
EFA is a widely utilized and broadly applied statistical technique in the social sciences. When we surveyed a recent two-year period in PsycINFO we found over 1700 studies that used some form of EFA. The widespread nature of EFA is both gratifying and problematic. On one hand, it is a powerful tool that can help researchers explore complex data efficiently. On the other hand, EFA is a complex procedure with few absolute guidelines, no inferential statistics for hypothesis testing (although some procedures provide inferential statistics (e.g., maximum likelihood extraction), they are unevenly implemented and are heavily influenced by sample size, limiting their effectiveness substantially), and many (often ill-defined) options. To make matters worse, terminology can vary significantly across software packages.
EFA is open to abuse by researchers ill-informed as to the limitations of the procedure. For example, using EFA to “confirm” or “validate” a measure is most likely a mis-application of the procedure, since EFA does not have inferential statistics available to test goodness of fit (as Confirmatory Factor Analysis does), yet one sees studies that claim to do just that.
Even when EFA is the correct choice, researchers must deal with issues such as: (a) factor extraction methods, (b) rules for retaining factors, (c) factor rotation strategies, and (d) sample size issues. Perusing the EFA literature, one will quickly discover that most researchers utilize principal components analysis (PCA) with varimax rotation, utilizing the Kaiser (1970) criterion (retaining factors with eigenvalues greater than one) as the decision rule for deciding how many factors to interpret. Readers will also find analyses reported where the sample size is woefully inadequate to ensure even marginal generalizability.
So, while this state of affairs represents the norm in the literature (and often the defaults in popular statistical software packages), it will not always yield the best results for a particular data set. This chapter will: review standard practice in the social sciences, review and propose best practices for researchers wishing to utilize EFA, and examine how sample size affects the “goodness” of EFA results in detail. Aside from sample size, we will discuss: 1) component vs. factor extraction, 2) number of factors to retain for rotation, and 3) orthogonal vs. oblique rotation. Finally, we will briefly discuss FACTOR, freely available software that implements EFA options nicely
Thanks to Paul Ginns: A relatively new and comprehensive Factor Analysis package FACTOR developed by Urbano Lorenzo-Seva & Pere J. Ferrando. Its authors have included a wide range of analysis options, includes Velicer's (1976) MAP test and Horn's (1965) parallel analysis - these provide much better methods for deciding on the number of factors to extract than the commonly used scree test or eigenvalues greater than 1 rule.
The authors describe FACTOR in the following article:
Lorenzo-Seva, U., & Ferrando, P.J. (2006). FACTOR: a computer program to fit the exploratory factor analysis model. Behavior Research Methods, 38, 88-91.