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Copula-Based Non-Metric Unfolding on Augmented Data Matrix

Author

Listed:
  • Marta Nai Ruscone

    (University of Genoa)

  • Daniel Fernández

    (Universitat Politècnica de Catalunya, BarcelonaTech (UPC))

  • Antonio D’Ambrosio

    (University of Naples Federico II)

Abstract

A multidimensional unfolding technique that is not prone to degenerate solutions and is based on multidimensional scaling of a complete data matrix is proposed. We adopt the strategy of augmenting the data matrix, trying to build a complete dissimilarity matrix, by using copula-based association measures among rankings (the individuals), and between rankings and objects (namely, a rank-order representation of the objects through tied rankings). The proposed technique leads to acceptable recovery of given preference structures.

Suggested Citation

  • Marta Nai Ruscone & Daniel Fernández & Antonio D’Ambrosio, 2024. "Copula-Based Non-Metric Unfolding on Augmented Data Matrix," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 678-697, November.
    • Handle: RePEc:spr:jclass:v:41:y:2024:i:3:d:10.1007_s00357-024-09495-x
    DOI: 10.1007/s00357-024-09495-x
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    References listed on IDEAS

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    1. Gregory Bonn & Romin Tafarodi, 2013. "Visualizing the Good Life: A Cross-Cultural Analysis," Journal of Happiness Studies, Springer, vol. 14(6), pages 1839-1856, December.
    2. Willem Heiser & Patrick Groenen, 1997. "Cluster differences scaling with a within-clusters loss component and a fuzzy successive approximation strategy to avoid local minima," Psychometrika, Springer;The Psychometric Society, vol. 62(1), pages 63-83, March.
    3. Carter, Nathan T. & Lake, Christopher J. & Zickar, Michael J., 2010. "Toward Understanding the Psychology of Unfolding," Industrial and Organizational Psychology, Cambridge University Press, vol. 3(4), pages 511-514, December.
    4. John Ross & Norman Cliff, 1964. "A generalization of the interpoint distance model," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 167-176, June.
    5. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    6. Ian Spence & Dennis Domoney, 1974. "Single subject incomplete designs for nonmetric multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 469-490, December.
    7. 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.
    8. K. Deun & P. Groenen & W. Heiser & F. Busing & L. Delbeke, 2005. "Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 45-69, March.
    9. Frank Busing & Patrick Groenen & Willem Heiser, 2005. "Avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 71-98, March.
    10. 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.
    11. Amodio, S. & D’Ambrosio, A. & Siciliano, R., 2016. "Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 667-676.
    12. 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.
    13. de Leeuw, Jan & Mair, Patrick, 2009. "Multidimensional Scaling Using Majorization: SMACOF in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i03).
    14. Rust, Roland T., 2020. "The future of marketing," International Journal of Research in Marketing, Elsevier, vol. 37(1), pages 15-26.
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