Abstract
(1996) provide a new perspective on the traditional biplot of (1971) by viewing biplots as multivariate analogues of ordinary scatterplots. It is demonstrated by (2001) that extending biplot methodology to discriminant analysis is not only extremely useful for visual displays to accompany discriminant analysis but how the process of classification can be performed using biplot methodology. In particular, a method developed for the inclusion of categorical predictors is discussed. Specific attention is devoted to what is termed a ‘reversal’ when dealing with two binary (categorical) predictor variables. A proposal using biplot methodology is made for dealing with this problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BAHADUR, R.R. (1961): A representation of the joint distribution of responses to n dichotomous items. In: H. Solomon (Ed.): Studies in item analysis and prediction. Stanford University Press, Stanford, California, 158–168.
DILLON, W.R. and GOLDSTEIN, M. (1978): On the performance of some multinomial classification rules. Journal of the American Statistical Association, 73, 305–313.
FLURY, B. (1997): A first course in multivariate statistics. Springer-Verlag, New York.
FLURY, B.D., NEL, D.G. and PIENAAR, I. (1995): Simultaneous detection in shift in means and variances. Journal of the American Statistical Association, 90, 1474–1481.
FLURY, L., BOUKAI, B. and FLURY, B.D. (1997): The discrimination subspace model. Journal of the American Statistical Association, 92, 758–766.
GABRIEL, K.R. (1971): The biplot graphical display of matrices with application to principal component analysis. Biometrika, 58, 453–467.
GARDNER, S. (2001): Extensions of biplot methodology to discriminant analysis with applications of non-parametric principal components. Unpublished PhD thesis. University of Stellenbosch, Stellenbosch.
GILBERT, E.S. (1968): On discrimination using qualitative variables. Journal of the American Statistical Association, 63, 1399–1418.
GOWER, J.C. (1992): Generalized biplots. Biometrika, 79, 475–493.
GOWER, J.C. and HAND, D.J. (1996): Biplots. Chapman & Hall, London.
GRAYBILL, F.A. (1983): Matrices with applications in statistics. 2nd edition. Wadsworth, Belmont, California.
HASTIE, T., TIBSHIRANI, R. and BUJA, A. (1994): Flexible discriminant analysis by optimal scoring. Journal of the American Statistical Association, 89, 12551270.
KRZANOWSKI, W.J. (1977): The performance of Fisher’s linear discriminant function under non-optimal conditions. Technometrics, 19, 191–200.
LACHENBRUCH, P.A. and MICKEY, M.R. (1968): Estimation of error rates in discriminant analysis. Technometrics, 10, 1–11.
McLACHLAN, G.J.(1992): Discriminant analysis and statistical pattern recognition. John Wiley, New York.
MOORE, D.H. (1973): Evaluation of five discrimination procedures for binary variables. Journal of the American Statistical Association, 68, 399–404.
YERUSHALMY, J., VAN DEN BERG, B.J., ERHARDT, C.L. and JACOBZINER, H. (1965): Birth weight and gestation as indices of “immaturity”. American Journal of Diseases of Children, 109, 43–57.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gardner, S., Roux, N.l. (2003). Discriminant Analysis With Categorical Variables: A Biplot Based Approach. In: Schader, M., Gaul, W., Vichi, M. (eds) Between Data Science and Applied Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18991-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-18991-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40354-8
Online ISBN: 978-3-642-18991-3
eBook Packages: Springer Book Archive