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Angle-based models for ranking data

Author

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  • Xu, Hang
  • Alvo, Mayer
  • Yu, Philip L.H.

Abstract

A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of the relative preference of the items. The probability of observing a ranking is modeled to be proportional to its cosine of the angle from the consensus vector. Bayesian variational inference is employed to determine the corresponding predictive density. It can be seen from simulation experiments that the Bayesian variational inference approach not only has great computational advantage compared to the traditional MCMC, but also avoids the problem of overfitting inherent when using maximum likelihood methods. The model also works when a large number of items are ranked which is usually an NP-hard problem to find the estimate of parameters for other classes of ranking models. Model extensions to incomplete rankings and mixture models are also developed. Real data applications demonstrate that the model and extensions can handle different tasks for the analysis of ranking data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:113-136
    DOI: 10.1016/j.csda.2017.12.004
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    References listed on IDEAS

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    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Hornik, Kurt & Grün, Bettina, 2014. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i10).
    3. 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.
    4. Philip L. H. Yu & K. F. Lam & S. M. Lo, 2005. "Factor analysis for ranked data with application to a job selection attitude survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(3), pages 583-597, July.
    5. Suvrit Sra, 2012. "A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of I s (x)," Computational Statistics, Springer, vol. 27(1), pages 177-190, March.
    6. Philip Yu, 2000. "Bayesian analysis of order-statistics models for ranking data," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 281-299, September.
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