Published

2014-07-01

A Methodology for Biplots Based on Bootstrapping with R

Una metodología para biplots basada en bootstrapping con R

DOI:

https://doi.org/10.15446/rce.v37n2spe.47944

Keywords:

Bootstrap Confidence Interval, Graphical Methods, Multivariate Data, Quantiles, Software (en)
Cuantiles, Datos multivariantes, Intervalos de confianza bootstrap, Métodos gráficos, Software. (es)

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Authors

  • Ana B. Nieto Universidad de Salamanca
  • M. Purificación Galindo Universidad de Salamanca
  • Víctor Leiva Universidad Adolfo Ibáñez - Facultad de Ingeniería y Ciencias Universidad de Valparaíso - Instituto de Estadística
  • Purificación Vicente-Galindo Universidad de Salamanca

A biplot is a graphical representation of two-mode multivariate data based on markers for rows and columns often provided in a two-dimensional space. These markers define parameters that help to interpret goodness of fit, quality of the representation and variability and relationships between variables. However, such parameters are estimated as point values by the biplot, thus no information on the accuracy of the corresponding estimators is obtained. We propose a graphical methodology, that may be considered as an inferential version of a biplot, based on bootstrap confidence intervals for the mentioned parameters. We implement our methodology in an R package and validate it with simulated and real-world data.

Un biplot es una representación gráfica de datos multivariantes de dos vías basada en marcadores para filas y columnas proporcionada usualmente en un espacio bidimensional. Estos marcadores definen parámetros que ayudan a interpretar bondad de ajuste, calidad de representación y variabilidad y relaciones entre variables. Sin embargo, tales parámetros son estimados puntualmente en el biplot, sin proporcionar información acerca de la precisión de los estimadores. Se propone una metodología gráfica, que puede ser considerada como una versión inferencial de un biplot, basada en intervalos de confianza bootstrap para los parámetros mencionados. La metodología es implementada en un paquete R y validada con datos simulados y reales.

https://doi.org/10.15446/rce.v37n2spe.47944

A Methodology for Biplots Based on Bootstrapping with R

Una metodología para biplots basada en bootstrapping con R

ANA B. NIETO1, M. PURIFICACIÓN GALINDO2, VÍCTOR LEIVA3, PURIFICACIÓN VICENTE-GALINDO4

1Universidad de Salamanca, Departamento de Estadística, España. Associate Professor. Email: ananieto@usal.es
2Universidad de Salamanca, Departamento de Estadística, España. Professor. Email: pgalindo@usal.es
3Universidad Adolfo Ibáñez, Facultad de Ingeniería y Ciencias, Chile. Universidad de Valparaíso, Instituto de Estadística, Chile. Professor. Email: victor.leiva@yahoo.com
4Universidad de Salamanca, Departamento de Estadística, España. Professor. Email: purivg@usal.es

Abstract

A biplot is a graphical representation of two-mode multivariate data based on markers for rows and columns often provided in a two-dimensional space. These markers define parameters that help to interpret goodness of fit, quality of the representation and variability and relationships between variables. However, such parameters are estimated as point values by the biplot, thus no information on the accuracy of the corresponding estimators is obtained. We propose a graphical methodology, that may be considered as an inferential version of a biplot, based on bootstrap confidence intervals for the mentioned parameters. We implement our methodology in an \verb"R" package and validate it with simulated and real-world data.

Key words: Bootstrap Confidence Interval, Graphical Methods, Multivariate Data, Quantiles, Software.

Resumen

Un biplot es una representación gráfica de datos multivariantes de dos vías basada en marcadores para filas y columnas proporcionada usualmente en un espacio bidimensional. Estos marcadores definen parámetros que ayudan a interpretar bondad de ajuste, calidad de representación y variabilidad y relaciones entre variables. Sin embargo, tales parámetros son estimados puntualmente en el biplot, sin proporcionar información acerca de la precisión de los estimadores. Se propone una metodología gráfica, que puede ser considerada como una versión inferencial de un biplot, basada en intervalos de confianza bootstrap para los parámetros mencionados. La metodología es implementada en un paquete \verb"R" y validada con datos simulados y reales.

Palabras clave: cuantiles, datos multivariantes, intervalos de confianza bootstrap, métodos gráficos, software.

Texto completo disponible en PDF

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[Recibido en mayo de 2014. Aceptado en octubre de 2014]

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

@ARTICLE{RCEv37n2a07,
    AUTHOR  = {Nieto, Ana B. and Galindo, M. Purificación and Leiva, Víctor and Vicente-Galindo, Purificación},
    TITLE   = {{A Methodology for Biplots Based on Bootstrapping with R}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {2},
    pages   = {367-397}
}

References

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Bickel, P. & Krieger, A. (1989), 'Confidence bands for a distribution function using the bootstrap', Journal of the American Statistical Association 84, 95-100.

Bradu, D. & Gabriel, K. (1974), 'Simultaneous statistical inference on interactions in two-way analysis of variance', Journal of the American Statistical Association 29, 428-436.

Bradu, D. & Gabriel, K. (1978), 'The biplot as a diagnostic tool for models of two-way tables', Technometrics 20, 47-68.

Cárdenas, O. & Galindo, M. P. (2003), Biplot with External Information based on Generalized Bilinear Models, Council of Scientific and Humanistic Development of the Central University of Venezuela, Caracas url bit.ly/14BARON.

Cárdenas, O., Galindo, M. & Vicente-Villardón, J. (2007), 'Biplot methods: Evolution and applications', Revista Venezolana de Análisis de Coyuntura 13, 279-303.

Carlier, A. & Kroonenberg, P. (1996), 'Decompositions and biplots in three-way correspondence analysis', Psychometrika 61, 355-373.

Caro-Lopera, F., Leiva, V. & Balakrishnan, N. (2012), 'Connection between the Hadamard and matrix products with an application to a matrix-variate Birnbaum-Saunders distribution', Journal of Multivariate Analysis 104, 126-139.

Chatterjee, S. (1984), 'Variance estimation in factor analysis: An application of the bootstrap', British Journal of Mathematical and Statistical Psychology 37, 252-262.

Chernick, M. (1999), Bootstrap Methods: A Practitioner's Guide, Wiley & Sons, New York, US..

Chessel, D., Dufour, A., Dray, S., Jombart, T., Lobry, J., Ollier, S. & Thioulouse, J. (2013), The ADE4 R package version 1.5-2: Analysis of ecological data: Exploratory and Euclidean methods in environmental sciences, R project. *cran.r-project.org/packageade4

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Díaz-García, J., Galea, M. & Leiva, V. (2003), 'Influence diagnostics for multivariate elliptic regression linear models', Communications in Statistics: Theory and Methods 32, 625-641.

Díaz-García, J. & Leiva, V. (2003), 'Doubly non-central t and F distribution obtained under singular and non-singular elliptic distributions', Communications in Statistics: Theory and Methods 32, 11-32.

Díaz-García, J., Leiva, V. & Galea, M. (2002), 'Singular elliptic distribution: Density and applications', Communications in Statistics: Theory and Methods 31, 665-681.

Daudin, J., Duby, C. & Trécourt, P. (1988), 'Stability of principal components studied by the bootstrap method', Statistics 19, 241-258.

Del Ferraro, M., Kiers, H. & Giordani, P. (2013), The ThreeWay R package version 1.1.1: Three-way component analysis, R project. *cran.r-project.org/packageThreeWay

Demey, J., Vicente-Villardón, J., Galindo, M. & Zambrano, A. (2008), 'Identifying molecular markers associated with classifications of genotypes by external logistic biplot', Bioinformatics 24, 28-32.

Denis, J. (1991), 'Ajustements de modelles lineaires et bilineaires sous constraintes lineaires avec donnes manquantes', Statistique Applique 39, 5-24.

Dray, S. & Dufour, A. (2007), 'The ADE4 package: Implementing the duality diagram for ecologists', Journal of Statistical Software 22, 1-20.

Dray, S., Dufour, A. & Chessel, D. (2007), 'The ADE4 package-II: Two-table and K-table methods', R Journal 7, 47-52.

Edelman, A. (1988), 'Eigenvalues and condition numbers of random matrices', SIAM Journal on Matrix Analysis and Applications 9, 543-560.

Efron, B. (1979), 'Bootstrap methods: Another look at the jackknife', The Annals of Statistics 7, 1-26.

Efron, B. (1987), 'Better bootstrap confidence intervals', Journal of the American Statistical Association 82, 171-185.

Efron, B. (1993), An Introduction into the Bootstrap, Chapman and Hall, New York, US..

Egido, J. (2014), The dynBiplotGUI R package version 1.0.1: full interactive GUI for dynamic biplot, R project. *cran.r-project.org/web/packages/dynBiplotGUI

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How to Cite

APA

Nieto, A. B., Galindo, M. P., Leiva, V. and Vicente-Galindo, P. (2014). A Methodology for Biplots Based on Bootstrapping with R. Revista Colombiana de Estadística, 37(2Spe), 367–397. https://doi.org/10.15446/rce.v37n2spe.47944

ACM

[1]
Nieto, A.B., Galindo, M.P., Leiva, V. and Vicente-Galindo, P. 2014. A Methodology for Biplots Based on Bootstrapping with R. Revista Colombiana de Estadística. 37, 2Spe (Jul. 2014), 367–397. DOI:https://doi.org/10.15446/rce.v37n2spe.47944.

ACS

(1)
Nieto, A. B.; Galindo, M. P.; Leiva, V.; Vicente-Galindo, P. A Methodology for Biplots Based on Bootstrapping with R. Rev. colomb. estad. 2014, 37, 367-397.

ABNT

NIETO, A. B.; GALINDO, M. P.; LEIVA, V.; VICENTE-GALINDO, P. A Methodology for Biplots Based on Bootstrapping with R. Revista Colombiana de Estadística, [S. l.], v. 37, n. 2Spe, p. 367–397, 2014. DOI: 10.15446/rce.v37n2spe.47944. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/47944. Acesso em: 27 jul. 2024.

Chicago

Nieto, Ana B., M. Purificación Galindo, Víctor Leiva, and Purificación Vicente-Galindo. 2014. “A Methodology for Biplots Based on Bootstrapping with R”. Revista Colombiana De Estadística 37 (2Spe):367-97. https://doi.org/10.15446/rce.v37n2spe.47944.

Harvard

Nieto, A. B., Galindo, M. P., Leiva, V. and Vicente-Galindo, P. (2014) “A Methodology for Biplots Based on Bootstrapping with R”, Revista Colombiana de Estadística, 37(2Spe), pp. 367–397. doi: 10.15446/rce.v37n2spe.47944.

IEEE

[1]
A. B. Nieto, M. P. Galindo, V. Leiva, and P. Vicente-Galindo, “A Methodology for Biplots Based on Bootstrapping with R”, Rev. colomb. estad., vol. 37, no. 2Spe, pp. 367–397, Jul. 2014.

MLA

Nieto, A. B., M. P. Galindo, V. Leiva, and P. Vicente-Galindo. “A Methodology for Biplots Based on Bootstrapping with R”. Revista Colombiana de Estadística, vol. 37, no. 2Spe, July 2014, pp. 367-9, doi:10.15446/rce.v37n2spe.47944.

Turabian

Nieto, Ana B., M. Purificación Galindo, Víctor Leiva, and Purificación Vicente-Galindo. “A Methodology for Biplots Based on Bootstrapping with R”. Revista Colombiana de Estadística 37, no. 2Spe (July 1, 2014): 367–397. Accessed July 27, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/47944.

Vancouver

1.
Nieto AB, Galindo MP, Leiva V, Vicente-Galindo P. A Methodology for Biplots Based on Bootstrapping with R. Rev. colomb. estad. [Internet]. 2014 Jul. 1 [cited 2024 Jul. 27];37(2Spe):367-9. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/47944

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