IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i8p2486-2500.html
   My bibliography  Save this article

Mixtures of weighted distance-based models for ranking data with applications in political studies

Author

Listed:
  • Lee, Paul H.
  • Yu, Philip L.H.

Abstract

Analysis of ranking data is often required in various fields of study, for example politics, market research and psychology. Over the years, many statistical models for ranking data have been developed. Among them, distance-based ranking models postulate that the probability of observing a ranking of items depends on the distance between the observed ranking and a modal ranking. The closer to the modal ranking, the higher the ranking probability is. However, such a model assumes a homogeneous population, and the single dispersion parameter in the model may not be able to describe the data well. To overcome these limitations, we formulate more flexible models by considering the recently developed weighted distance-based models which can allow different weights for different ranks. The assumption of a homogeneous population can be relaxed by an extension to mixtures of weighted distance-based models. The properties of weighted distance-based models are also discussed. We carry out simulations to test the performance of our parameter estimation and model selection procedures. Finally, we apply the proposed methodology to analyze synthetic ranking datasets and a real world ranking dataset about political goals priority.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2486-2500
    DOI: 10.1016/j.csda.2012.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000679
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.02.002?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. Lee, Paul H. & Yu, Philip L.H., 2010. "Distance-based tree models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1672-1682, June.
    2. Agostino Tarsitano, 2009. "Comparing The Effectiveness Of Rank Correlation Statistics," Working Papers 200906, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    3. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard & Langrognet, Florent, 2006. "Model-based cluster and discriminant analysis with the MIXMOD software," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 587-600, November.
    4. Gormley, Isobel Claire & Murphy, Thomas Brendan, 2008. "Exploring Voting Blocs Within the Irish Electorate," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1014-1027.
    5. Shieh, Grace S., 1998. "A weighted Kendall's tau statistic," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 17-24, July.
    6. Isobel Claire Gormley & Thomas Brendan Murphy, 2006. "Analysis of Irish third‐level college applications data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 361-379, March.
    7. Murphy, Thomas Brendan & Martin, Donal, 2003. "Mixtures of distance-based models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 645-655, January.
    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. 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.
    2. 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.
    3. 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.
    4. 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).
    5. 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. Antonio D’Ambrosio & Willem J. Heiser, 2016. "A Recursive Partitioning Method for the Prediction of Preference Rankings Based Upon Kemeny Distances," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 774-794, September.
    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. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    4. Lee, Paul H. & Yu, Philip L.H., 2010. "Distance-based tree models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1672-1682, June.
    5. Cascón, J.M. & González-Arteaga, T. & de Andrés Calle, R., 2022. "A new preference classification approach: The λ-dissensus cluster algorithm," Omega, Elsevier, vol. 111(C).
    6. Kung, Yi-Hung & Lin, Chang-Ting & Shih, Yu-Shan, 2012. "Split variable selection for tree modeling on rank data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2830-2836.
    7. 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.
    8. Tahani Coolen-Maturi, 2016. "New weighted rank correlation coefficients sensitive to agreement on top and bottom rankings," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2261-2279, September.
    9. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    10. Ghimire, Ramesh & Green, Gary T. & Paudel, Krishna P. & Poudyal, Neelam C. & Cordell, H. Ken, 2017. "Visitors' Preferences for Freshwater Amenity Characteristics: Implications from the U.S. Household Survey," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 42(1), pages 1-24, January.
    11. Lebret, Rémi & Iovleff, Serge & Langrognet, Florent & Biernacki, Christophe & Celeux, Gilles & Govaert, Gérard, 2015. "Rmixmod: The R Package of the Model-Based Unsupervised, Supervised, and Semi-Supervised Classification Mixmod Library," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i06).
    12. Delaney, Liam & Harmon, Colm & Redmond, Cathy, 2011. "Parental education, grade attainment and earnings expectations among university students," Economics of Education Review, Elsevier, vol. 30(6), pages 1136-1152.
    13. Maugis, C. & Celeux, G. & Martin-Magniette, M.-L., 2011. "Variable selection in model-based discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1374-1387, November.
    14. Cathy Maugis & Gilles Celeux & Marie-Laure Martin-Magniette, 2009. "Variable Selection for Clustering with Gaussian Mixture Models," Biometrics, The International Biometric Society, vol. 65(3), pages 701-709, September.
    15. Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.
    16. Jeffrey Andrews & Paul McNicholas, 2014. "Variable Selection for Clustering and Classification," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 136-153, July.
    17. Fuchs Sebastian & McCord Yann, 2019. "On the lower bound of Spearman’s footrule," Dependence Modeling, De Gruyter, vol. 7(1), pages 126-132, January.
    18. Amaya, Johanna & Arellana, Julian & Delgado-Lindeman, Maira, 2020. "Stakeholders perceptions to sustainable urban freight policies in emerging markets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 329-348.
    19. Isobel Claire Gormley & Thomas Brendan Murphy, 2006. "Analysis of Irish third‐level college applications data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 361-379, March.
    20. Luca Scrucca & Adrian Raftery, 2015. "Improved initialisation of model-based clustering using Gaussian hierarchical partitions," 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. 9(4), pages 447-460, December.

    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:csdana:v:56:y:2012:i:8:p:2486-2500. 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/locate/csda .

    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.