Abstract
A simultaneous representation of individuals and variables in a data matrix is called a biplot. When variables are binary, nominal, or ordinal, a classical linear biplot representation is not adequate. Recently, biplots for categorical data-based logistic response models have been proposed. The coordinates of individuals and variables are computed to have logistic responses along the biplot dimensions. The methods are related to logistic regression in the same way as classical biplot analysis (CBA) is related to linear regression, thus are referred as logistic biplot (LB). Most of the estimation methods are developed for matrices in which the number of individuals is much higher than the number of variables. When the number of variables is high, external logistic biplots can be used; row coordinates are obtained by principal coordinates analysis and then logistic regression is fitted to obtain the variables representation. In this work, external logistic biplots for binary data are extended to nominal and ordinal data using parametric and nonparametric logistic fits and then combined in a single representation.
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References
Benzecri, J.P.: L’analyse des donnees, vol. 2, p. l. Dunod, Paris (1973)
De Leeuw, J.: Principal component analysis of binary data by iterated singular value decomposition. Comput. Stat. Data Anal. 50(1), 21–39 (2006)
Demey, J.R., Vicente-Villardón, J.L., Galindo-Villardón, M.P., Zambrano, A.Y.: Identifying molecular markers associated with classification of genotypes by External Logistic Biplots. Bioinformatics 24(24), 2832–2838 (2008)
Gabriel, K.R.: The biplot graphic display of matrices with application to principal component analysis. Biometrika 58(3), 453–467 (1971)
Galindo, M.P.: Una alternativa de representacion simultanea: HJ-Biplot. Questiio 10(1), 13–23 (1986)
Gardner-Lubbe, S., Le Roux, N.J., Gower, J.C.: Measures of fit in principal component and canonical variate analyses. J. Appl. Stat. 35(9), 947–965 (2008)
Gifi, A.: Nonlinear Multivariate Analysis. Wiley, New York (1990)
Gower, J.C.: Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53 (3–4), 325–338 (1966)
Gower, J.C.: Adding a point to vector diagrams in multivariate analysis. Biometrika 55(3), 582–585 (1968)
Gower, J.C.: A general coefficient of similarity and some of its properties. Biometrics 27(4), 857–871 (1971)
Gower, J.C.: Generalized biplots. Biometrika 79(3), 475–493 (1992)
Gower, J.C., Hand, D.J.: Biplots: Monographs on Statistics and Applied Probability, vol. 54. Chapman and Hall, London (1995)
Gower, J.C., Harding, S.A.: Nonlinear biplots. Biometrika 75 (3), 445–455 (1988)
Gower, J.C., Lubbe, S.G., Le Roux, N.J.: Understanding Biplots. Wiley, Hoboken (2011)
Greenacre, M.J.: Theory and Applications of Correspondence Analysis. Academic, Cambridge (1984)
Henderson, H.V., Velleman, P.F.: Building multiple regression models interactively. Biometrics 37(2), 391–411 (1981)
Hernandez-Sanchez, J.C., Vicente-Villardon, J.L.: NominalLogisticBiplot: Nominal Logistic Biplots in R. Salamanca (2014). Available via https://cran.r-project.org/package=NominalLogisticBiplot
Hernandez-Sanchez, J.C., Vicente-Villardon, J.L.: OrdinalLogisticBiplot: Biplot representations of ordinal variables. Salamanca (2014). Available via https://cran.r-project.org/package=OrdinalLogisticBiplot
Hernández-Sánchez, J.C., Vicente-Villardón, J.L.: Logistic biplot for nominal data. Adv. Data Anal. Classif. 11 (2) 307–326 (2017)
Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Probability and Mathematical Statistics. Academic Press, London (1979)
Michailidis, G., de Leeuw, J.: The Gifi system of descriptive multivariate analysis. Stat. Sci. 13, 307–336 (1998)
Podani, J.: Extending Gower’s general coefficient of similarity to ordinal characters. Taxon 48, 331–340 (1999)
R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna (2019). Available via https://www.R-project.org/
Vicente-Villardon, J.L.: Una alternativa a los métodos factoriales clásicos basada en una generalización de los metodos biplot. An alternative to the classical factor methods based on a generalization of biplot methods (Doctoral dissertation, MS Thesis. Universidad de Salamanca. Spain) (1992).
Vicente-Villardon, J.L.: MultBiplotR: Multivariate Analysis using Biplots. R Package Version 19.11.19 (2019). Available via http://biplot.usal.es/multbiplot/multbiplot-in-r/
Vicente-Villardón, J.L., Galindo-Villardón, M.P., Blazquez-Zaballos, A.: Logistic biplots. In: Multiple Correspondence Analysis and Related Methods, pp. 503–521. Chapman and Hall, London (2006)
Vicente-Villardóon, J.L., Henández-Sánchez, J.C.: Logistic Biplots for Ordinal Data with an Application to Job Satisfaction of Doctorate Degree Holders in Spain (2014). Preprint arXiv:1405.0294
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Vicente-Villardón, J.L., Hernández-Sánchez, J.C. (2020). External Logistic Biplots for Mixed Types of Data. In: Imaizumi, T., Okada, A., Miyamoto, S., Sakaori, F., Yamamoto, Y., Vichi, M. (eds) Advanced Studies in Classification and Data Science. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Singapore. https://doi.org/10.1007/978-981-15-3311-2_14
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