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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 variables. EFA is a technique within Factor Analysis whose overarching goal is to identify the underlying relationships between measured variables<ref>{{cite journal|last=Norris|first=Megan|coauthors=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}}</ref> . It is commonly used by researchers when developing a scale{{clarify|reason=undefined technical term|date=April 2012}} and serves to identify a set of [[Latent variable|latent constructs]] underlying a battery of measured variables.<ref>Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). "Evaluating the use of exploratory factor analysis in psychological research". ''Psychological Methods'', 4(3), 272-299.</ref> It should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables.<ref>Finch, J. F., & West, S. G. (1997). "The investigation of personality structure: Statistical models". ''Journal of Research in Personality'', 31 (4), 439-485.</ref> ''Measured variables'' are any one of several attributes of people that may be observed and measured. An example of a measured variable would be one item on a scale. Researchers must{{cn|date=April 2012}} carefully consider the number of measured variables to include in the analysis. EFA procedures are more accurate when each factor is represented by multiple measured variables in the analysis. There should be at least 3 to 5 measured variables per factor.<ref>Maccallum, R. C. (1990). "The need for alternative measures of fit in covariance structure modeling". ''Multivariate Behavioral Research'', 25(2), 157-162.</ref>
EFA is based on the common factor model. Within the common factor model, measured variables are
expressed as a function of common factors, unique factors, and errors of measurement. Common factors influence two or more measured variables, while each unique factor influences only one measured variable and does not explain correlations among measured variables.<ref>{{cite journal|last=Norris|first=Megan|coauthors=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}}</ref>
The researcher's assumption when conducting EFA is 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). EFA requires the researcher to make a number of important decisions about how to conduct the analysis because there is no one set method.
==Fitting procedures==
Fitting procedures are used to estimate the factor loadings and unique variances of the model. (''Factor loadings'' are the regression coefficients between items and factors and measure the influence of a common factor on a measured variable). There are several factor analysis fitting methods to choose from, however there is little information on all of their strengths and weaknesses and many don’t even have an exact name that is used consistently. Principal axis factoring (PAF) and [[maximum likelihood]] (ML) are two extraction methods that are generally recommended.{{cn|date=April 2012}} In general, ML or PAF give the best results, depending on whether data are normally-distributed or if the assumption of normality has been violated.
===Maximum likelihood (ML)===
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