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On the connection between the distribution of eigenvalues in multiple correspondence analysis and log-linear analysis

Salwa Benammou 1 Gilbert Saporta 2
2 CEDRIC - MSDMA - CEDRIC. Méthodes statistiques de data-mining et apprentissage
CEDRIC - Centre d'études et de recherche en informatique et communications
Abstract : Multiple Correspondence Analysis (MCA) and Log-Linear modelling are two techniques of multi-way contingency table analysis having different problematics and fields of applications. Log-Linear models are profitably when applied to a small number of variables. Multiple Correspondence Analysis is useful in large tables. This efficiency is balanced by the fact that MCA is not able to explicit relations between more than two variables, as can be done by Log-Linear modelling. The two approaches are complementary. We present in this paper the distribution of eigenvalues in MCA when data fit a known Log-Linear model, then we induct this model by successive utilisation of MCA. We demonstrates that, in MCA, under independence hypothesis each observed eigenvalue is asymptotically normally distributed. The eigenvalues diagram takes a very particular shape. This shape changes if there is one or more interaction between variables, and we can recognize the model fitted by data in some particular cases.
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https://hal.archives-ouvertes.fr/hal-01124808
Contributor : Laboratoire Cedric <>
Submitted on : Friday, March 6, 2015 - 10:48:50 AM
Last modification on : Monday, March 30, 2020 - 2:58:59 PM

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  • HAL Id : hal-01124808, version 1

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Salwa Benammou, Gilbert Saporta. On the connection between the distribution of eigenvalues in multiple correspondence analysis and log-linear analysis. CARME2003: Correspondence Analysis and Related Methods, Jun 2003, Barcelone, Spain. ⟨hal-01124808⟩

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