Multiple factor analysis: Difference between revisions

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'''Multiple factor analysis (MFA)''' is a [[Factorial experiment|factorial]] method<ref name="GreenacreBlasius2006">{{cite book|last1=Greenacre|first1=Michael|last2=Blasius|first2=Jorg|author-link2=Jörg Blasius|title=Multiple Correspondence Analysis and Related Methods|url=https://books.google.com/books?id=ZvYV1lfU5zIC&pg=PA352|accessdate=11 June 2014|date=2006-06-23|publisher=CRC Press|isbn=9781420011319|pages=352–}}</ref> devoted to the study of tables in which a group of individuals is described by a set of variables (quantitative and / or qualitative) structured in groups. It is a [[Multivariate statistics|multivariate method]] from the field of [[Ordination (statistics)|ordination]] used to simplify [[Dimensionality reduction|multidimensional data]] structures. MFA treats all involved tables in the same way (symmetrical analysis). It may be seen as an extension of:

* [[Principal component analysis]] (PCA) when variables are quantitative,

* [[Multiple correspondence analysis]] (MCA) when variables are qualitative,

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{| class="wikitable centre" width="60%"

|+ Table 1. MFA. Test data. A etand B (group 1) are uncorrelated. C1 and C2 (group 2) are identical.

|-

! !! <math>A</math> !! <math>B</math> !! <math>C_1</math>!! <math>C_2</math>

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The core of MFA is a weighted factorial analysis: MFA firstly provides the classical results of the factorial analyses.

1. ''Representations of individuals'' in which two individuals are muchclose closerto thaneach other if they haveexhibit similar values for allmany variables in allthe different variable groups; in practice the user particularly studies the first factorial plane.

2.''Representations of quantitative variables'' as in PCA (correlation circle).

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The small size and simplicity of the example allow simple validation of the rules of interpretation. But the method will be more valuable when the data set is large and complex.

Other methods suitable for this type of data are available. [[Procrustes analysis]] is compared to the MFA in.<ref>Pagès Jérôme (2014). Multiple Factor Analysis by Example Using R. Chapman & Hall/CRC The R Series, London. 272p</ref>

== History ==

MFA was developed by Brigitte Escofier and Jérôme Pagès in the 1980s. It is at the heart of two books written by these authors:<ref>''Ibidem''</ref> and.<ref>Escofier Brigitte & Pagès Jérôme (2008). Analyses factorielles simples et multiples ; objectifs, méthodes et interprétation. Dunod, Paris. 318 p. {{ISBN|978-2-10-051932-3}}</ref> The MFA and its extensions (hierarchical MFA, MFA on contingency tables, etc.) are a research topic of applied mathematics laboratory Agrocampus ([http://math.agrocampus-ouest.fr LMA ²]) which published a book presenting basic methods of exploratory multivariate analysis.<ref>Husson F., Lê S. & Pagès J. (2009). Exploratory Multivariate Analysis by Example Using R. Chapman & Hall/CRC The R Series, London. {{ISBN|978-2-7535-0938-2}}</ref>

== Software ==

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== External links ==

* [http://factominer.free.fr/ FactoMineR] A R software devoted to exploratory data analysis.

[[Category:Factor analysis]]