Exploratory factor analysis: Difference between revisions

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When selecting how many factors to include in a model, researchers must try to balance [[Occam's razor|parsimony]] (a model with relatively few factors) and plausibility (that there are enough factors to adequately account for correlations among measured variables).<ref>{{cite book|last=Fabrigar|first=Leandre R.|title=Exploratory factor analysis|publisher=Oxford University Press|___location=Oxford|isbn=978-0-19-973417-7|author2=Wegener, Duane T.|date=2012-01-12}}</ref> It is better to include too many factors (overfactoring) than too few factors (underfactoring){{Citation needed|date=June 2018}}.

''Overfactoring'' occurs when too many factors are included in a model. It is not as bad as underfactoring because major factors will usually be accurately represented and extra factors will have no measured variables load onto them. Still, it should be avoided because overfactoring may lead researchers to put forward constructs with little theoretical value.

''Underfactoring'' occurs when too few factors are included in a model. This is considered to be a greater error than overfactoring. If not enough factors are included in a model, there is likely to be substantial error. Measured variables that load onto a factor not included in the model can falsely load on factors that are included, altering true factor loadings. This can result in rotated solutions in which two factors are combined into a single factor, obscuring the true factor structure.

There are a number of procedures designed to determine the optimal number of factors to retain in EFA. These include Kaiser's (1960) eigenvalue-greater-than-one rule (or K1 rule),<ref>{{cite journal|last=Kaiser|first=H.F.|title=The application of electronic computers to factor analysis|journal=Educational and Psychological Measurement|year=1960|volume=20|pages=141–151|doi=10.1177/001316446002000116}}</ref> Cattell's (1966) [[scree plot]],<ref name="Cattell, R. B. 1966">Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, I, 245-276.</ref> Revelle and Rocklin's (1979) very simple structure criterion,<ref>{{cite journal | last1 = Revelle | first1 = W. | last2 = Rocklin | first2 = T. | year = 1979 | title = Very simple structure-alternative procedure for estimating the optimal number of interpretable factors | url = | journal = Multivariate Behavioral Research | volume = 14 | issue = 4| pages = 403–414 | doi = 10.1207/s15327906mbr1404_2 | pmid = 26804437 }}</ref> model comparison techniques,<ref>{{cite journal | last1 = Fabrigar | first1 = Leandre R. | last2 = Wegener | first2 = Duane T. | last3 = MacCallum | first3 = Robert C. | last4 = Strahan | first4 = Erin J. | year = 1999 | title = Evaluating the use of exploratory factor analysis in psychological research. | url = | journal = Psychological Methods | volume = 4 | issue = 3| pages = 272–299 | doi = 10.1037/1082-989X.4.3.272 }}</ref> Raiche, Roipel, and Blais's (2006) acceleration factor and optimal coordinates,<ref>Raiche, G., Roipel, M., & Blais, J. G.|Non graphical solutions for the Cattell’s scree test. Paper presented at The International Annual Meeting of the Psychometric Society, Montreal|date=2006|Retrieved December 10, 2012 from {{cite web |url=https://ppw.kuleuven.be/okp/_pdf/Raiche2013NGSFC.pdf |title=Archived copy |accessdate=2013-05-03 |url-status=live |archiveurl=https://web.archive.org/web/20131021052759/https://ppw.kuleuven.be/okp/_pdf/Raiche2013NGSFC.pdf |archivedate=2013-10-21 }}</ref> Velicer's (1976) minimum average partial,<ref name=Velicer>{{cite journal|last=Velicer|first=W.F.|title=Determining the number of components from the matrix of partial correlations|journal=Psychometrika|year=1976|volume=41|issue=3|pages=321–327|doi=10.1007/bf02293557}}</ref> Horn's (1965) [[parallel analysis]], and Ruscio and Roche's (2012) comparison data.<ref name =Ruscio>{{cite journal|last=Ruscio|first=J.|author2=Roche, B.|title=Determining the number of factors to retain in an exploratory factor analysis using comparison data of a known factorial structure|journal=Psychological Assessment|year=2012|volume=24|issue=2|pages=282–292|doi=10.1037/a0025697|pmid=21966933}}</ref> Recent simulation studies assessing the robustness of such techniques suggest that the latter five can better assist practitioners to judiciously model data.<ref name =Ruscio/> These five modern techniques are now easily accessible through integrated use of IBM SPSS Statistics software (SPSS) and R (R Development Core Team, 2011). See Courtney (2013)<ref name="pareonline.net">Courtney, M. G. R. (2013). Determining the number of factors to retain in EFA: Using the SPSS R-Menu v2.0 to make more judicious estimations. ''Practical Assessment, Research and Evaluation'', 18(8). Available online: