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Weighting Distance Matrices Using Rank Correlations

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  • Ilaria Lucrezia Amerise

    ()

  • Agostino Tarsitano

    ()
    (Dipartimento di Economia e Statistica, Università della Calabria)

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    Abstract

    In a number of applications of multivariate analysis, the data matrix is not fully observed. Instead a set of distance matrices on the same entities is available. A reasonable strategy to construct a global distance matrix is to compute a weighted average of the partial distance matrices, provided that an appropriate system of weights can be defined. The Distatis method developed by Abdi et al. (2005) is a three-step procedure for computing the global distance matrix. An important aspect of that procedure is the computation of the vector correlation coefficient (RV) to measure the similarity between partial distance matrices. The RV coefficient is based on the Pearson product moment correlation coeffcient, which is highly prone to the effects of outliers. We are convinced that, in many measurable phenomena, the relationships between distances are far more likely to be ordinal than interval in nature, and it is therefore preferable to adopt an approach appropriate to ordinal data. The goal of our paper is to revise the system of weights of the Distatis procedure substituting the conventional Pearson coefficient with rank correlations that are less affected by errors of measurement, perturbation or presence of outliers in the data. In the light of our findings on real and simulated data sets, we recommend the use of a speci c coefficient of rank correlation to replace, where necessary, the conventional vector correlation.

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    File URL: http://www.ecostat.unical.it/RePEc/WorkingPapers/WP09_2012.pdf
    File Function: First version, 2012-12
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    Bibliographic Info

    Paper provided by Università della Calabria, Dipartimento di Economia, Statistica e Finanza (Ex Dipartimento di Economia e Statistica) in its series Working Papers with number 201209.

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    Length: 19 pages
    Date of creation: Dec 2012
    Date of revision:
    Handle: RePEc:clb:wpaper:201209

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    Postal: Università della Calabria, Dipartimento di Economia, Statistica e Finanza, Ponte Pietro Bucci, Cubo 0/C, I-87036 Arcavacata di Rende, CS, Italy
    Phone: +39 0984 492413
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    Web page: http://www.unical.it/portale/strutture/dipartimenti_240/disesf/
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    Keywords: Distatis; Ordinal data; Vector rank correlation;

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    1. Francis Cailliez, 1983. "The analytical solution of the additive constant problem," Psychometrika, Springer, vol. 48(2), pages 305-308, June.
    2. Vladimir Batagelj & Matevz Bren, 1995. "Comparing resemblance measures," Journal of Classification, Springer, vol. 12(1), pages 73-90, March.
    3. Véronique Campbell & Pierre Legendre & François-Joseph Lapointe, 2009. "Assessing Congruence Among Ultrametric Distance Matrices," Journal of Classification, Springer, vol. 26(1), pages 103-117, April.
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