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Ties in one block comparison experiments: a generalization of the Mallows–Bradley–Terry ranking model

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  • Amadou Sawadogo
  • Simplice Dossou-Gbété
  • Dominique Lafon

Abstract

This study is concerned with the extension of the Mallows–Bradley–Terry ranking model for one block comparison consisting of all the items of interest to situations which allow an expression of no preference. We consider a modification of the Mallows–Bradley–Terry ranking model by introducing an additional parameter, called an index of discrimination, in the model. This permits ties in the model. The maximum likelihood estimates of the parameters are found using a Maximization–Minimization algorithm: the evaluation of the mathematical expectations involved in the log-likelihood equation is obtained by generating samples of Monte Carlo Markov chain from the stationary distribution. In addition, a simulation study for asymptotic properties assessment has been made. The proposed method is applied to analyze data election.

Suggested Citation

  • Amadou Sawadogo & Simplice Dossou-Gbété & Dominique Lafon, 2017. "Ties in one block comparison experiments: a generalization of the Mallows–Bradley–Terry ranking model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(14), pages 2621-2644, October.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:14:p:2621-2644
    DOI: 10.1080/02664763.2016.1259400
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    References listed on IDEAS

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    1. Dankmar Böhning & Bruce Lindsay, 1988. "Monotonicity of quadratic-approximation algorithms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 641-663, December.
    2. Douglas Critchlow & Michael Fligner, 1991. "Paired comparison, triple comparison, and ranking experiments as generalized linear models, and their implementation on GLIM," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 517-533, September.
    3. Ting Yan & Jinfeng Xu, 2013. "A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices," Biometrika, Biometrika Trust, vol. 100(2), pages 519-524.
    4. 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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