Abstract
The similarity of individuals with respect to a number of ordinal variables is the main topic of this work. We consider the application of Multiple Correspondence Analysis (MCA) on k ordinal variables for N subjects. In the context of ordinary MCA, each variable is transformed into a suitable number of binary variables and the derived matrix is analyzed using the \(X^{2}\) metric as the similarity measure. As a consequence, there is a loss of information from the original data, since ordinal variables are treated as nominal. In this paper, we propose a method for transforming the original variables, taking into account their ordinal nature. By applying the proposed method, a variable measured on m categories is transformed into a variable with n categories by assigning a probability to each category, instead of recoding each category into a new binary variable. We argue that the proposed transformation scheme leads to more accurate results than the one used in ordinary MCA.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agresti, A., Kateri, M.: Categorical Data Analysis. Springer, Berlin, Heidelberg (2011)
Becue-Bertaut, M., Pages, J.: Multiple factor analysis and clustering of a mixture of quantitative, categorical and frequency data. Comput. Stat. Data Anal. 52, 3255–3268 (2008)
Benzècri, J.P.: L’analyse des donnees. 2. L’analyse des correspondances. Dunod, Paris (1973)
Gower, J.C.: A General coefficient of similarity and some of its properties. Biometrics 27, 857–871 (1971)
Grabmeier, J., Rudolph, A.: Techniques of cluster algorithms in data mining. Data Min. Knowl. Disc. 6, 303–360 (2002)
Le Roux, B.: Analyse specifique d’un nuage euclidien: application a l’etude des questionnaires. Math. Sci. Hum. 146, 65–83 (1999)
Le Roux, B.: Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis. Springer, New York (2004)
Lombardo, R., Beh, E.J.: Simple and multiple correspondence analysis for ordinal-scale variables using orthogonal polynomials. J. Appl. Stat. 37, 2101–2116 (2010)
McCullagh, P.: Regression models for ordinal data. J. R. Stat. Soc. Ser. B Methodol. 42, 109–142 (1980)
Moschidis, O.E.: A different approach to multiple correspondence analysis (MCA) than that of specific MCA. Math. Sci. Hum. Math. Soc. Sci. 186, 77–88 (2009)
Moschidis, O.: Unified coding of qualitative and quantitative variables and their analysis with ascendant hierarchical classification. Int. J. Data Anal. Tech. Strateg. 7, 114–128 (2015)
Podani, J.: Extending Gower’s general coefficient of similarity to ordinal characters. Taxon 48, 331–340 (1999)
Acknowledgements
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Moschidis, O., Chadjipadelis, T. (2017). A Method for Transforming Ordinal Variables. In: Palumbo, F., Montanari, A., Vichi, M. (eds) Data Science . Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-55723-6_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-55723-6_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-55722-9
Online ISBN: 978-3-319-55723-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)