Published

2015-07-01

Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables

Conceptos fundamentales de la clasificación y del análisis estadístico implicativo para variables modales

Keywords:

Classificatory Analysis, Typicality, Contribution, Modal Variables (en)
Análisis clasificatorio, Tipicalidad, Contribución, Variables modales. (es)

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Authors

  • Larisa Zamora-Matamoros University of Oriente, Santiago de Cuba, Cuba
  • Jorge Rey Díaz-Silvera University of Oriente, Santiago de Cuba, Cuba
  • Lariza Portuondo-Mallet University of Oriente, Santiago de Cuba, Cuba
The present work offers some fundamental concepts of the Statistical Implicative Analysis for modal variables and proposes an index to establish the similarity between two modal variables. Expressions to calculate typicality and contribution of the individuals to the classes that are formed in the classification are also presented. This technique is illustrated by two examples, one with binary data, which allows  the coincidence between the formulas presented and the existent for the binary case to be shown, and the other for modal data with more than two modalities.

En el presente trabajo se ofrecen algunos conceptos fundamentales del análisis estadístico implicativo para el caso de variables modales y se propone un índice para establecer la similaridad entre dos variables modales, así como expresiones para el cálculo de la tipicalidad y contribución de los individuos a las clases que se forman en la clasificación. Con el objetivo de ilustrar la técnica presentada, es aplicada a dos juegos de datos, uno binario, el cual permite mostrar numéricamente la coincidencia de las fórmulas presentadas con las existentes para el caso de variables binarias, y otro modal con más de dos modalidades.

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References

Bailleul, M. & Gras, R. (1994), ‘L’implication statistique entre variables modales’, Mathématiques et Sciences Humaines 128, 47–51.

Couturier, R. (2008), ‘CHIC: Cohesive hierarchical implicative classification’, Studies in Computational Intelligence (SCI) 127, 41–53.

Gras, R. (2000), ‘Les fondements de l’analyse statistique implicative’, Quaderni di Ricerca in Didattica 9, 187–208.

Gras, R. & Kuntz, K. (2007), Analyse statistique implicative (ASI), en réponse à des problèmes fondateurs, in ‘Apports Théoriques à l’Analyse Statistique Implicative et Applications’, Université Jaume I, Castellón, pp. 15–40.

Lagrange, J. B. (1998), ‘Analyse implicative d’un ensemble de variables numériques; application au traitement d’un questionnaire à résponses modales ordonnées’, Revue de Statistique Appliquée 46(1), 71–93.

R Core Team (2014), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. *http://CRAN.R-project.org

Ratsimba-Rajohn, H. (1992), Contribution à l’étude de la hiérarchie implicative, application á l’analyse de la gestión didactique des phénomènes d’ostension et de contradiction, Master Thesis, Université de Rennes, France.

Zamora, L., Gregori, P. & Orús, P. (2009), Conceptos Fundamentales del Análisis Estadístico Implicativo (ASI) y su Soporte Computacional CHIC, Departamento de Matemáticas, Universitat Jaume I de Castellón, España.

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Copyright (c) 2015 Revista Colombiana de Estadística

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