Editing Factor analysis (section)

{{citations needed|date=August 2023}}
{{Machine learning}}
{{Short description|Statistical method}}
{{About|factor loadings|factorial design|Factorial experiment}}
'''Factor analysis''' is a [[statistics|statistical]] method used to describe [[variance|variability]] among observed, correlated [[Variable (mathematics)|variables]] in terms of a potentially lower number of unobserved variables called '''factors'''. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved [[latent variable]]s. The observed variables are modelled as [[linear combination]]s of the potential factors plus "[[errors and residuals in statistics|error]]" terms, hence factor analysis can be thought of as a special case of [[errors-in-variables models]].<ref>{{cite book |first=Karl G. |last=Jöreskog |authorlink=Karl Gustav Jöreskog |chapter=Factor Analysis as an Errors-in-Variables Model |pages=185–196 |title=Principals of Modern Psychological Measurement |location=Hillsdale |publisher=Erlbaum |year=1983 |isbn=0-89859-277-1 }}</ref>

Simply put, the factor loading of a variable quantifies the extent to which the variable is related to a given factor.<ref>{{cite book |last=Bandalos |first=Deborah L. |year=2017 |title=Measurement Theory and Applications for the Social Sciences |publisher=The Guilford Press |isbn= }}</ref>

A common rationale behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in [[psychometrics]], [[personality]] psychology, biology, [[marketing]], [[product management]], [[operations research]], [[finance]], and [[machine learning]]. It may help to deal with data sets where there are large numbers of observed variables that are thought to reflect a smaller number of underlying/latent variables. It is one of the most commonly used inter-dependency techniques and is used when the relevant set of variables shows a systematic inter-dependence and the objective is to find out the latent factors that create a commonality.