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factor analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in say six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors, plus "error" terms. The information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis originated in psychometrics and is used in behavioral sciences, social sciences, marketing, product management, operations research, and other fields that deal with data sets where there are large numbers of observed variables that are thought to reflect a smaller number of underlying/latent variables.
Factor analysis is related to principal component analysis (PCA), but the two are not identical. There has been significant controversy in the field over differences between the two techniques (see section on exploratory factor analysis versus principal components analysis) below. Clearly though, PCA is a more basic version of exploratory factor analysis (EFA) that was developed in the early days prior to the advent of high-speed computers. From the point of view of exploratory analysis, the eigenvalues of PCA are inflated component loadings, i.e., contaminated with error variance.〔Cattell, R. B. (1952). ''Factor analysis''. New York: Harper.〕〔Fruchter, B. (1954). ''Introduction to Factor Analysis''. Van Nostrand.〕〔Cattell, R. B. (1978). ''Use of Factor Analysis in Behavioral and Life Sciences''. New York: Plenum.〕〔Child, D. (2006). ''The Essentials of Factor Analysis, 3rd edition''. Bloomsbury Academic Press.〕〔Gorsuch, R. L. (1983). ''Factor Analysis, 2nd edition''. Hillsdale, NJ: Erlbaum.〕〔McDonald, R. P. (1985). ''Factor Analysis and Related Methods''. Hillsdale, NJ: Erlbaum.〕
==Statistical model==
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