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EFA is based on the common factor model.<ref name =Norris/> In this model, manifest variables are expressed as a function of common factors, unique factors, and errors of measurement. Each unique factor influences only one manifest variable, and does not explain correlations between manifest variables. Common factors influence more than one manifest variable and "factor loadings" are measures of the influence of a common factor on a manifest variable.<ref name =Norris/> For the EFA procedure, we are more interested in identifying the common factors and the related manifest variables.
EFA assumes that any indicator/measured variable may be associated with any factor. When developing a scale, researchers should use EFA first before moving on to [[confirmatory factor analysis]] (CFA).<ref name=worthington>{{cite journal|last=Worthington|first=Roger L.|author2= Whittaker, Tiffany A J. |title=Scale development research: A content analysis and recommendations for best practices.|journal=The Counseling Psychologist|date=1 January 2006|volume=34|issue=6|pages=806–838|doi=10.1177/0011000006288127|s2cid=146284440 }}</ref> EFA is essential to determine underlying factors/constructs for a set of measured variables; while CFAconfirmatory factor analysis allows the researcher to test the hypothesis that a relationship between the observed variables and their underlying latent {{Not a typo|factor(s)/construct(s)}} exists.<ref>Suhr, D. D. (2006). Exploratory or confirmatory factor analysis? (pp. 1-17). Cary: SAS Institute.</ref>
EFA requires the researcher to make a number of important decisions about how to conduct the analysis because there is no one set method.
''Underfactoring'' occurs when too few factors are included in a model. 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. Broadly speaking, most of the existing procedures approach the determination of the appropriate number of factors (1) by inspecting patterns of eigenvalues of the covariance matrix, or (2) treating it as a model selection problem.<ref name=":0">{{Cite journal |last=Haslbeck |first=Jonas M. B. |last2=van Bork |first2=Riet |date=February 2024-02 |title=Estimating the number of factors in exploratory factor analysis via out-of-sample prediction errors. |url=https://doi.apa.org/doi/10.1037/met0000528 |journal=Psychological Methods |language=en |volume=29 |issue=1 |pages=48–64 |doi=10.1037/met0000528 |issn=1939-1463}}</ref> Existing approaches 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|s2cid=146138712 }}</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 | 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. | 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 |access-date=2013-05-03 |url-status=live |archive-url=https://web.archive.org/web/20131021052759/https://ppw.kuleuven.be/okp/_pdf/Raiche2013NGSFC.pdf |archive-date=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|s2cid=122907389 }}</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:
{{cite web |url=http://pareonline.net/getvn.asp?v=18&n=8 |title=Archived copy |access-date=2014-06-08 |url-status=live |archive-url=https://web.archive.org/web/20150317145450/http://pareonline.net/getvn.asp?v=18&n=8 |archive-date=2015-03-17 }}</ref> for guidance on how to carry out these procedures for continuous, ordinal, and heterogenous (continuous and ordinal) data.
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