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Defining subjects distance in hierarchical cluster analysis by copula approach

Author

Listed:
  • Andrea Bonanomi

    (Università Cattolica del Sacro Cuore di Milano)

  • Marta Nai Ruscone

    (Università Cattaneo LIUC)

  • Silvia Angela Osmetti

    (Università Cattolica del Sacro Cuore di Milano)

Abstract

We propose a new measure to evaluate the distance between subjects expressing their preferences by rankings in order to segment them by hierarchical cluster analysis. The proposed index builds upon the Spearman’s grade correlation coefficient on a transformation, operated by the copula function, of the position/rank denoting the level of the importance assigned by subjects under classification to k objects. In particular, by using the copula functions with tail dependence we obtain an index suitable for emphasizing the agreement on top ranks, when the top ranks are considered more important than the lower ones. We evaluate the performance of our proposal by an example on simulated data, showing that the resulting groups contain subjects whose preferences are more similar on the most important ranks. A further application with real data confirms the pertinence and the importance of our proposal.

Suggested Citation

  • Andrea Bonanomi & Marta Nai Ruscone & Silvia Angela Osmetti, 2017. "Defining subjects distance in hierarchical cluster analysis by copula approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 859-872, March.
    • Handle: RePEc:spr:qualqt:v:51:y:2017:i:2:d:10.1007_s11135-016-0444-9
    DOI: 10.1007/s11135-016-0444-9
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    References listed on IDEAS

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    1. Kojadinovic, Ivan, 2010. "Hierarchical clustering of continuous variables based on the empirical copula process and permutation linkages," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 90-108, January.
    2. Biernacki, Christophe & Jacques, Julien, 2013. "A generative model for rank data based on insertion sort algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 162-176.
    3. Lee, Paul H. & Yu, Philip L.H., 2012. "Mixtures of weighted distance-based models for ranking data with applications in political studies," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2486-2500.
    4. Eugenio Brentari & Livia Dancelli & Marica Manisera, 2016. "Clustering ranking data in market segmentation: a case study on the Italian McDonald's customers’ preferences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 1959-1976, August.
    5. Andrea Bonanomi & Gabriele Cantaluppi & Marta Nai Ruscone & Silvia Osmetti, 2015. "A new estimator of Zumbo’s Ordinal Alpha: a copula approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 941-953, May.
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    Cited by:

    1. Pierpaolo D’Urso & Vincenzina Vitale, 2022. "A Kemeny Distance-Based Robust Fuzzy Clustering for Preference Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 600-647, November.

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