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


  • Lee, Paul H.
  • Yu, Philip L.H.


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

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    References listed on IDEAS

    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.
    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.
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    Cited by:

    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. repec:jss:jstsof:v:071:i12 is not listed on IDEAS
    3. 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.
    4. repec:eee:csdana:v:121:y:2018:i:c:p:113-136 is not listed on IDEAS
    5. Philip L. H. Yu & Paul H. Lee & S. F. Cheung & Esther Y. Y. Lau & Doris S. Y. Mok & Harry C. Hui, 2016. "Logit tree models for discrete choice data with application to advice-seeking preferences among Chinese Christians," Computational Statistics, Springer, vol. 31(2), pages 799-827, June.


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