Exploratory factor analysis: Difference between revisions

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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}}</ref> EFA is essential to determine underlying factors/constructs for a set of measured variables; while CFA 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.

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===Parallel analysis===

{{Main|Parallel analysis}}

To carry out the PA test, users compute the eigenvalues for the correlation matrix and plot the values from largest to smallest and then plot a set of random eigenvalues. The number of eigenvalues before the intersection points indicates how many factors to include in your model.<ref name=Humphreys>{{cite journal | last1 = Humphreys | first1 = L. G. | last2 = Montanelli | first2 = R. G. Jr | year = 1975 | title = An investigation of the parallel analysis criterion for determining the number of common factors | url = | journal = Multivariate Behavioral Research | volume = 10 | issue = 2| pages = 193–205 | doi = 10.1207/s15327906mbr1002_5 }}</ref><ref>{{cite journal|last=Horn|first=John L.|title=A rationale and test for the number of factors in factor analysis|journal=Psychometrika|date=1 June 1965|volume=30|issue=2|pages=179–185|doi=10.1007/BF02289447|pmid=14306381}}</ref><ref>{{cite journal|last=Humphreys|first=L. G.|author2=Ilgen, D. R.|title=Note On a Criterion for the Number of Common Factors|journal=Educational and Psychological Measurement|date=1 October 1969|volume=29|issue=3|pages=571–578|doi=10.1177/001316446902900303}}</ref> This procedure can be somewhat artbitraryarbitrary (i.e. a factor just meeting the cutoff will be included and one just below will not).<ref name =Fabrigar/> Moreover, the method is very sensitive to sample size, with PA suggesting more factors in datasets with larger sample sizes.<ref>{{cite journal | last1 = Warne | first1 = R. G. | last2 = Larsen | first2 = R. | year = 2014 | title = Evaluating a proposed modification of the Guttman rule for determining the number of factors in an exploratory factor analysis | url = | journal = Psychological Test and Assessment Modeling | volume = 56 | issue = | pages = 104–123 }}</ref> Despite its shortcomings, this procedure performs very well in simulation studies and is one of Courtney's recommended procedures. See Courtney (2013)<ref name="pareonline.net"/> concerning how to perform this procedure from within the SPSS interface.

===Ruscio and Roche's comparison data===