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Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning

Author

Listed:
  • Carolin Strobl

    (Ludwig-Maximilians-Universität München)

  • Florian Wickelmaier

    (Eberhard Karls Universität Tübingen)

  • Achim Zeileis

    (Universität Innsbruck)

Abstract

The preference scaling of a group of subjects may not be homogeneous, but different groups of subjects with certain characteristics may show different preference scalings, each of which can be derived from paired comparisons by means of the Bradley-Terry model. Usually, either different models are fit in predefined subsets of the sample or the effects of subject covariates are explicitly specified in a parametric model. In both cases, categorical covariates can be employed directly to distinguish between the different groups, while numeric covariates are typically discretized prior to modeling. Here, a semiparametric approach for recursive partitioning of Bradley-Terry models is introduced as a means for identifying groups of subjects with homogeneous preference scalings in a data-driven way. In this approach, the covariates that—in main effects or interactions—distinguish between groups of subjects with different preference orderings, are detected automatically from the set of candidate covariates. One main advantage of this approach is that sensible partitions in numeric covariates are also detected automatically.

Suggested Citation

  • Carolin Strobl & Florian Wickelmaier & Achim Zeileis, 2011. "Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning," Journal of Educational and Behavioral Statistics, , vol. 36(2), pages 135-153, April.
    • Handle: RePEc:sae:jedbes:v:36:y:2011:i:2:p:135-153
    DOI: 10.3102/1076998609359791
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    References listed on IDEAS

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    1. J. N. S. Matthews & K. P. Morris, 1995. "An Application of Bradley‐Terry‐Type Models to the Measurement of Pain," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(2), pages 243-255, June.
    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. Achim Zeileis & Kurt Hornik, 2007. "Generalized M‐fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508, November.
    4. Dittrich, Regina & Francis, Brian & Hatzinger, Reinhold & Katzenbeisser, Walter, 2006. "Modelling dependency in multivariate paired comparisons: A log-linear approach," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 197-209, September.
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    Cited by:

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    2. Jones, Payton J. & Mair, Patrick & Simon, Thorsten & Zeileis, Achim, 2019. "Network Model Trees," OSF Preprints ha4cw, Center for Open Science.
    3. Weichen Wu & Nynke Niezink & Brian Junker, 2022. "A diagnostic framework for the Bradley–Terry model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 461-484, December.
    4. Mousa, Gehan A. & Elamir, Elsayed A.H. & Hussainey, Khaled, 2022. "The effect of annual report narratives on the cost of capital in the Middle East and North Africa: A machine learning approach," Research in International Business and Finance, Elsevier, vol. 62(C).
    5. Anna Gottard & Giorgio Calzolari, 2014. "Alternative estimating procedures for multiple membership logit models with mixed effects: indirect inference and data cloning," Econometrics Working Papers Archive 2014_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    6. 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.
    7. Daniel Wochner, 2020. "Dynamic Factor Trees and Forests – A Theory-led Machine Learning Framework for Non-Linear and State-Dependent Short-Term U.S. GDP Growth Predictions," KOF Working papers 20-472, KOF Swiss Economic Institute, ETH Zurich.

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