IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v190y2022ics0047259x22000070.html
   My bibliography  Save this article

A generalized Mallows model based on ϕ-divergence measures

Author

Listed:
  • Kateri, Maria
  • Nikolov, Nikolay I.

Abstract

Rankings occur when a set of items is ordered in agreement with some criteria or personal opinions and can be found in various problems ranging from voting and elections to food preferences. Distances on permutations are commonly used in rank data analysis and are an efficient tool for constructing probability models for rankings. In this paper, we consider the optimal property of the distance-based Mallows model in terms of the Kullback–Leibler divergence and propose a generalization based on the ϕ-divergence. In the sequel, we focus on a special parametric family of models induced by the Cressie–Read power divergence. For the suggested models, we provide parameter estimating algorithms and model fitting methods. Furthermore, we propose a simple approach for the specification of the consensus ranking, based on modal complete or partial rankings modal rankings, that could be used alternatively to complete search algorithms. As an illustration, the described procedures are applied to three examples of rank data.

Suggested Citation

  • Kateri, Maria & Nikolov, Nikolay I., 2022. "A generalized Mallows model based on ϕ-divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000070
    DOI: 10.1016/j.jmva.2022.104958
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22000070
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.104958?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. Forcina, Antonio & Kateri, Maria, 2021. "A new general class of RC association models: Estimation and main properties," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. Kateri, Maria & Agresti, Alan, 2010. "A generalized regression model for a binary response," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 89-95, January.
    3. Ali, Alnur & Meilă, Marina, 2012. "Experiments with Kemeny ranking: What works when?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 28-40.
    4. Kateri, Maria & Agresti, Alan, 2007. "A class of ordinal quasi-symmetry models for square contingency tables," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 598-603, March.
    5. Martin, Nirian & Mata, Raquel & Pardo, Leandro, 2014. "Phi-divergence statistics for the likelihood ratio order: An approach based on log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 387-408.
    6. Han Li & Minxuan Xu & Jun S. Liu & Xiaodan Fan, 2020. "An Extended Mallows Model for Ranked Data Aggregation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 730-746, April.
    7. Nikolay I. Nikolov & Eugenia Stoimenova, 2019. "Asymptotic properties of Lee distance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(3), pages 385-408, April.
    8. Martín, Nirian & Pardo, Leandro, 2008. "New families of estimators and test statistics in log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1590-1609, September.
    Full references (including those not matched with items on IDEAS)

    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. Noelia Rico & Camino R. Vela & Raúl Pérez-Fernández & Irene Díaz, 2021. "Reducing the Computational Time for the Kemeny Method by Exploiting Condorcet Properties," Mathematics, MDPI, vol. 9(12), pages 1-12, June.
    2. Bernard Monjardet, 2013. "Marc Barbut au pays des médianes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00825005, HAL.
    3. Martín, Nirian, 2015. "Diagnostics in a simple correspondence analysis model: An approach based on Cook’s distance for log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 175-189.
    4. Saigusa, Yusuke & Tahata, Kouji & Tomizawa, Sadao, 2015. "Orthogonal decomposition of symmetry model using the ordinal quasi-symmetry model based on f-divergence for square contingency tables," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 33-37.
    5. Kiatsupaibul, Seksan & J. Hayter, Anthony & Liu, Wei, 2017. "Rank constrained distribution and moment computations," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 229-242.
    6. N. Martín & L. Pardo & K. Zografos, 2019. "On divergence tests for composite hypotheses under composite likelihood," Statistical Papers, Springer, vol. 60(6), pages 1883-1919, December.
    7. Kouji Tahata, 2012. "Quasi-asymmetry model for square tables with nominal categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 723-729, August.
    8. Tsagris, Michail, 2015. "A novel, divergence based, regression for compositional data," MPRA Paper 72769, University Library of Munich, Germany.
    9. Azzini, Ivano & Munda, Giuseppe, 2020. "A new approach for identifying the Kemeny median ranking," European Journal of Operational Research, Elsevier, vol. 281(2), pages 388-401.
    10. Rico, Noelia & Vela, Camino R. & Díaz, Irene, 2023. "Reducing the time required to find the Kemeny ranking by exploiting a necessary condition for being a winner," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1323-1336.
    11. 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).
    12. Martin, Nirian & Mata, Raquel & Pardo, Leandro, 2014. "Phi-divergence statistics for the likelihood ratio order: An approach based on log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 387-408.
    13. Martin, Nirian & Mata, Raquel & Pardo, Leandro, 2016. "Wald type and phi-divergence based test-statistics for isotonic binomial proportions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 31-49.
    14. Nikolay I. Nikolov & Eugenia Stoimenova, 2020. "Mallows’ models for imperfect ranking in ranked set sampling," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 459-484, September.
    15. Jansen, C. & Schollmeyer, G. & Augustin, T., 2018. "A probabilistic evaluation framework for preference aggregation reflecting group homogeneity," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 49-62.
    16. (Corresponding author) Gavin Yamey & Kaci Kennedy McDade & Wenhui Mao & Ekene Osakwe, 2022. "Financing Research And Development For New Vaccines In Developing Asia-Pacific Countries," Asia-Pacific Sustainable Development Journal, United Nations Economic and Social Commission for Asia and the Pacific (ESCAP), vol. 29(2), pages 125-153, November.
    17. Yangming Zhou & Jin-Kao Hao & Zhen Li, 2024. "Heuristic Search for Rank Aggregation with Application to Label Ranking," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 308-326, March.
    18. Srikanth Jagabathula & Gustavo Vulcano, 2018. "A Partial-Order-Based Model to Estimate Individual Preferences Using Panel Data," Management Science, INFORMS, vol. 64(4), pages 1609-1628, April.
    19. Aledo, Juan A. & Gámez, Jose A. & Molina, David, 2016. "Using extension sets to aggregate partial rankings in a flexible setting," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 208-223.
    20. Srikanth Jagabathula & Paat Rusmevichientong, 2017. "Nonparametric Joint Assortment and Price Choice Model," Management Science, INFORMS, vol. 63(9), pages 3128-3145, September.

    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:eee:jmvana:v:190:y:2022:i:c:s0047259x22000070. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.