Exploratory factor analysis: Difference between revisions

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In [[multivariate statistics]], '''exploratory factor analysis''' ('''EFA''') is a statistical method used to uncover the underlying structure of a relatively large set of [[Variable (research)|variables]]. EFA is a technique within [[factor analysis]] whose overarching goal is to identify the underlying relationships between measured variables.<ref name=Norris>{{cite journal|last=Norris|first=Megan|author2=Lecavalier, Luc|title=Evaluating the Use of Exploratory Factor Analysis in Developmental Disability Psychological Research|journal=Journal of Autism and Developmental Disorders|date=17 July 2009|volume=40|issue=1|pages=8–20|doi=10.1007/s10803-009-0816-2|pmid=19609833}}</ref> It is commonly used by researchers when developing a scale (a ''scale'' is a collection of questions used to measure a particular research topic) and serves to identify a set of [[Latent variable|latent constructs]] underlying a battery of measured variables.<ref name=Fabrigar>{{cite journal|last=Fabrigar|first=Leandre R.|author2=Wegener, Duane T. |author3=MacCallum, Robert C. |author4=Strahan, Erin J. |title=Evaluating the use of exploratory factor analysis in psychological research.|journal=Psychological Methods|date=1 January 1999|volume=4|issue=3|pages=272–299|doi=10.1037/1082-989X.4.3.272|url=http://www.statpower.net/Content/312/Handout/Fabrigar1999.pdf}}</ref> It should be used when the researcher has no ''a priori'' hypothesis about factors or patterns of measured variables.<ref name=Finch>{{cite journal | last1 = Finch | first1 = J. F. | last2 = West | first2 = S. G. | year = 1997 | title = The investigation of personality structure: Statistical models | url = | journal = Journal of Research in Personality | volume = 31 | issue = 4| pages = 439–485 | doi=10.1006/jrpe.1997.2194}}</ref> ''Measured variables'' are any one of several attributes of people that may be observed and measured. Examples of measured variables could be the physical height, weight, and pulse rate of a human being. Usually, researchers would have a large number of measured variables, which are assumed to be related to a smaller number of "unobserved" factors. Researchers must carefully consider the number of measured variables to include in the analysis.<ref name =Fabrigar/> EFA procedures are more accurate when each factor is represented by multiple measured variables in the analysis.

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.