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A generalized Mahalanobis distance for mixed data

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  • de Leon, A. R.
  • Carrière, K. C.

Abstract

A distance for mixed nominal, ordinal and continuous data is developed by applying the Kullback-Leibler divergence to the general mixed-data model, an extension of the general location model that allows for ordinal variables to be incorporated in the model. The distance obtained can be considered as a generalization of the Mahalanobis distance to data with a mixture of nominal, ordinal and continuous variables. Moreover, it includes as special cases previous Mahalanobis-type distances developed by Bedrick et al. (Biometrics 56 (2000) 394) and Bar-Hen and Daudin (J. Multivariate Anal. 53 (1995) 332). Asymptotic results regarding the maximum likelihood estimator of the distance are discussed. The results of a simulation study on the level and power of the tests are reported and a real-data example illustrates the method.

Suggested Citation

  • de Leon, A. R. & Carrière, K. C., 2005. "A generalized Mahalanobis distance for mixed data," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 174-185, January.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:174-185
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    References listed on IDEAS

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    1. Barhen, A. & Daudin, J. J., 1995. "Generalization of the Mahalanobis Distance in the Mixed Case," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 332-342, May.
    2. Sik-Yum Lee & Wai-Yin Poon & P. Bentler, 1989. "Simultaneous analysis of multivariate polytomous variates in several groups," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 63-73, March.
    3. W. Krzanowski, 1984. "On the null distribution of distance between two groups, using mixed continuous and categorical variables," Journal of Classification, Springer;The Classification Society, vol. 1(1), pages 243-253, December.
    4. Edward J. Bedrick & Jodi Lapidus & Joseph F. Powell, 2000. "Estimating the Mahalanobis Distance from Mixed Continuous and Discrete Data," Biometrics, The International Biometric Society, vol. 56(2), pages 394-401, June.
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    Cited by:

    1. Cheng, Tsung-Chi & Biswas, Atanu, 2008. "Maximum trimmed likelihood estimator for multivariate mixed continuous and categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2042-2065, January.
    2. Alban Mbina Mbina & Guy Martial Nkiet & Fulgence Eyi Obiang, 2019. "Variable selection in discriminant analysis for mixed continuous-binary variables and several groups," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 773-795, September.
    3. Mortier, F. & Robin, S. & Lassalvy, S. & Baril, C.P. & Bar-Hen, A., 2006. "Prediction of Euclidean distances with discrete and continuous outcomes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1799-1814, September.
    4. A. R. de Leon & A. Soo & T. Williamson, 2011. "Classification with discrete and continuous variables via general mixed-data models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1021-1032, February.

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