L’analyse des multitableaux (ou multiblocs) peut être abordée à l’aide d’un certain nombre de méthodologies plus ou moins diffusées, selon les disciplines et les pratiques. Par contre, il existe très peu de méthodes généralisant la discrimination à des multiblocs. Nous allons proposer une nouvelle approche, et son algorithme associé, pour résoudre ce problème de discrimination (dans le cas, bien sûr, où les groupes d’observations sont identiques pour tous les tableaux) qui utilise l’Analyse Factorielle Discriminante usuelle (au sens de Fisher) et l’approche STATIS. La méthode proposée, appelée STATIS-LDA, utilise la décomposition inter/intra de chaque bloc et permet de quantifier l’importance de chaque bloc pour la discrimination. De plus, sa robustesse est démontrée à partir de deux exemples d’applications.
Multiblock tables analysis can be performed thanks to several methodologies, more or less widely known according to disciplines and customs. Conversely, there exist very few methods allowing to generalize classification to multiblocks. We propose a new approach and its associated algorithm to solve this classification task (when groups of individuals are the same ones in all tables) which uses usual linear discriminant analysis (Fisher’s linear discriminant) and STATIS approach. The proposed method, called STATIS-LDA, uses the between-within decomposition of variance from each block and allows to quantify the importance of each block with regards to the classification. Moreover, its robustness is shown thanks to two applications.
Keywords: Multiway tables, Linear discriminant analysis (LDA), STATIS, Compromize
@article{JSFS_2013__154_3_31_0,
author = {Sabatier, Robert and Vivien, Myrtille and Reyn\`es, Christelle},
title = {Une nouvelle proposition, {l{\textquoteright}Analyse} {Discriminante} {Multitableaux~:} {STATIS-LDA}},
journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
pages = {31--43},
publisher = {Soci\'et\'e fran\c{c}aise de statistique},
volume = {154},
number = {3},
year = {2013},
mrnumber = {3147064},
zbl = {1316.62093},
language = {fr},
url = {http://www.numdam.org/item/JSFS_2013__154_3_31_0/}
}
TY - JOUR AU - Sabatier, Robert AU - Vivien, Myrtille AU - Reynès, Christelle TI - Une nouvelle proposition, l’Analyse Discriminante Multitableaux : STATIS-LDA JO - Journal de la société française de statistique PY - 2013 SP - 31 EP - 43 VL - 154 IS - 3 PB - Société française de statistique UR - http://www.numdam.org/item/JSFS_2013__154_3_31_0/ LA - fr ID - JSFS_2013__154_3_31_0 ER -
%0 Journal Article %A Sabatier, Robert %A Vivien, Myrtille %A Reynès, Christelle %T Une nouvelle proposition, l’Analyse Discriminante Multitableaux : STATIS-LDA %J Journal de la société française de statistique %D 2013 %P 31-43 %V 154 %N 3 %I Société française de statistique %U http://www.numdam.org/item/JSFS_2013__154_3_31_0/ %G fr %F JSFS_2013__154_3_31_0
Sabatier, Robert; Vivien, Myrtille; Reynès, Christelle. Une nouvelle proposition, l’Analyse Discriminante Multitableaux : STATIS-LDA. Journal de la société française de statistique, Tome 154 (2013) no. 3, pp. 31-43. http://www.numdam.org/item/JSFS_2013__154_3_31_0/
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