Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of potentially lower number of unobserved variables called factors. It is possible that the variations in three or four observed variables mainly reflect the variations in fewer unobserved variables. Factor analysis searches for such joint variations in response to unobserved latent variables. Factor analysis is related to principal component analysis but the two are not identical.
There are two types of factor analysis, exploratory analysis, EFA, and confirmatory factor analysis, CFA. EFA is used to identify complex interrelationships among items and group items that are part of unified concepts. CFA is a more complex approach that tests the hypothesis that the items are associated with specific factors. CFA uses structural equation modeling to test a measurement model whereby loading on the factors allows for evaluations of relationships between observed variables and unobserved variables. There are also several types of factoring. These include Principal component analysis, canonical factor analysis, common factor analysis, image factoring, alpha factoring and factor regression models.
Factor analysis has been implemented in several statistical analysis programs. It is also implemented in the R programming language and in OpenOpt. Rotations are implemented in the GPArotation R package.