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

DOI:

https://doi.org/10.15446/rce.v38n2.51664

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.

https://doi.org/10.15446/rce.v38n2.51664

Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables

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

LARISA ZAMORA-MATAMOROS1, JORGE REY DÍAZ-SILVERA2, LARIZA PORTUONDO-MALLET3

1University of Oriente, Faculty of Mathematics and Computer Science, Department of Mathematics, Santiago de Cuba, Cuba. Professor. Email: larisa@csd.uo.edu.cu
2University of Oriente, Faculty of Mathematics and Computer Science, Department of Mathematics, Santiago de Cuba, Cuba. Professor. Email: jdiaz@csd.uo.edu.cu
3University of Oriente, Faculty of Mathematics and Computer Science, Department of Mathematics, Santiago de Cuba, Cuba. Professor. Email: lportuondo@csd.uo.edu.cu

Abstract

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.

Key words: Classificatory Analysis, Typicality, Contribution, Modal\linebreak Variables.

Resumen

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.

Palabras clave: análisis clasificatorio, tipicalidad, contribución, variables modales.

Texto completo disponible en PDF

References

1. Bailleul, M. & Gras, R. (1994), 'L'implication statistique entre variables modales', Mathématiques et Sciences Humaines 128, 47-51.

2. Couturier, R. (2008), 'CHIC: cohesive hierarchical implicative classification', Studies in Computational Intelligence (SCI) 127, 41-53.

3. Gras, R. (2000), 'Les fondements de l'analyse statistique implicative', Quaderni di Ricerca in Didattica 9, 187-208.

4. Gras, R. & Kuntz, K. (2007), Analyse statistique implicative (ASI), en réponse à des problèmes fondateurs, 'Apports Théoriques à l'Analyse Statistique Implicative et Applications', Université Jaume I, Castellón, p. 15-40.

5. 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.

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

7. 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.

8. 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.

[Recibido en junio de 2014. Aceptado en diciembre de 2014]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv38n2a02,
    AUTHOR  = {Zamora-Matamoros, Larisa and Díaz-Silvera, Jorge Rey and Portuondo-Mallet, Lariza},
    TITLE   = {{Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2015},
    volume  = {38},
    number  = {2},
    pages   = {335-351}
}

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.

How to Cite

APA

Zamora-Matamoros, L., Díaz-Silvera, J. R. and Portuondo-Mallet, L. (2015). Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables. Revista Colombiana de Estadística, 38(2), 335–351. https://doi.org/10.15446/rce.v38n2.51664

ACM

[1]
Zamora-Matamoros, L., Díaz-Silvera, J.R. and Portuondo-Mallet, L. 2015. Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables. Revista Colombiana de Estadística. 38, 2 (Jul. 2015), 335–351. DOI:https://doi.org/10.15446/rce.v38n2.51664.

ACS

(1)
Zamora-Matamoros, L.; Díaz-Silvera, J. R.; Portuondo-Mallet, L. Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables. Rev. colomb. estad. 2015, 38, 335-351.

ABNT

ZAMORA-MATAMOROS, L.; DÍAZ-SILVERA, J. R.; PORTUONDO-MALLET, L. Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables. Revista Colombiana de Estadística, [S. l.], v. 38, n. 2, p. 335–351, 2015. DOI: 10.15446/rce.v38n2.51664. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/51664. Acesso em: 22 jan. 2025.

Chicago

Zamora-Matamoros, Larisa, Jorge Rey Díaz-Silvera, and Lariza Portuondo-Mallet. 2015. “Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables”. Revista Colombiana De Estadística 38 (2):335-51. https://doi.org/10.15446/rce.v38n2.51664.

Harvard

Zamora-Matamoros, L., Díaz-Silvera, J. R. and Portuondo-Mallet, L. (2015) “Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables”, Revista Colombiana de Estadística, 38(2), pp. 335–351. doi: 10.15446/rce.v38n2.51664.

IEEE

[1]
L. Zamora-Matamoros, J. R. Díaz-Silvera, and L. Portuondo-Mallet, “Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables”, Rev. colomb. estad., vol. 38, no. 2, pp. 335–351, Jul. 2015.

MLA

Zamora-Matamoros, L., J. R. Díaz-Silvera, and L. Portuondo-Mallet. “Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables”. Revista Colombiana de Estadística, vol. 38, no. 2, July 2015, pp. 335-51, doi:10.15446/rce.v38n2.51664.

Turabian

Zamora-Matamoros, Larisa, Jorge Rey Díaz-Silvera, and Lariza Portuondo-Mallet. “Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables”. Revista Colombiana de Estadística 38, no. 2 (July 1, 2015): 335–351. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/51664.

Vancouver

1.
Zamora-Matamoros L, Díaz-Silvera JR, Portuondo-Mallet L. Fundamental Concepts on Classification and Statistical Implicative Analysis for Modal Variables. Rev. colomb. estad. [Internet]. 2015 Jul. 1 [cited 2025 Jan. 22];38(2):335-51. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/51664

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