A generalized Mahalanobis distance for mixed data

A. R. de Leon and K. C. Carrière

Journal of Multivariate Analysis, 2005, vol. 92, issue 1, 174-185

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.

Keywords: Latent; variable; models; Maximum; likelihood; Measurement; level; Multivariate; normal; distribution; Polychoric; and; polyserial; correlations; Probit; models (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (4)

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