IDEAS home Printed from https://ideas.repec.org/a/spr/qualqt/v51y2017i2d10.1007_s11135-016-0444-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11135-016-0444-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11135-016-0444-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Antonio D’Ambrosio & Carmela Iorio & Michele Staiano & Roberta Siciliano, 2019. "Median constrained bucket order rank aggregation," Computational Statistics, Springer, vol. 34(2), pages 787-802, June.
    3. F. Marta L. Di Lascio & Andrea Menapace & Roberta Pappadà, 2024. "A spatially‐weighted AMH copula‐based dissimilarity measure for clustering variables: An application to urban thermal efficiency," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    4. Christophe Biernacki & Alexandre Lourme, 2019. "Unifying data units and models in (co-)clustering," 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(1), pages 7-31, March.
    5. Kuller, M. & Beutler, P. & Lienert, J., 2023. "Preference change in stakeholder group-decision processes in the public sector: Extent, causes and implications," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1268-1285.
    6. Irurozki, Ekhine & Calvo, Borja & Lozano, Jose A., 2016. "PerMallows: An R Package for Mallows and Generalized Mallows Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i12).
    7. 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.
    8. Xu, Hang & Alvo, Mayer & Yu, Philip L.H., 2018. "Angle-based models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 113-136.
    9. Etumnu, Chinonso & Gray, Allan W., 2020. "A Clustering Approach to Understanding Farmers’ Success Strategies," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 52(3), pages 335-351, August.
    10. Fuchs, Sebastian & Di Lascio, F. Marta L. & Durante, Fabrizio, 2021. "Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    11. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:qualqt:v:51:y:2017:i:2:d:10.1007_s11135-016-0444-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.