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A generalized Mallows model based on ϕ-divergence measures

Author

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  • 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
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    References listed on IDEAS

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    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.
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