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Markov models of dependence in longitudinal paired comparisons: an application to course design

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  • Alexandra Grand
  • Regina Dittrich
  • Brian Francis

Abstract

This article suggests a new approach for modelling longitudinal paired comparison data. As individual preferences may change from one time point to another, we propose extending the basic log-linear Bradley–Terry model by incorporating a Markovian structure with temporal within-comparison dependence parameters and parameters indicating the amount of change of the unknown preference parameters of the objects. We illustrate this approach by analysing a student survey relating to statistics course design with three time points. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Alexandra Grand & Regina Dittrich & Brian Francis, 2015. "Markov models of dependence in longitudinal paired comparisons: an application to course design," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 237-257, April.
  • Handle: RePEc:spr:alstar:v:99:y:2015:i:2:p:237-257
    DOI: 10.1007/s10182-014-0239-z
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    References listed on IDEAS

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    3. Mark E. Glickman, 1999. "Parameter Estimation in Large Dynamic Paired Comparison Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 377-394.
    4. Dittrich, R. & Hatzinger, R. & Katzenbeisser, W., 2002. "Modelling dependencies in paired comparison data: A log-linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 39-57, July.
    5. Jackson, Christopher, 2011. "Multi-State Models for Panel Data: The msm Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i08).
    6. Manuela Cattelan & Cristiano Varin & David Firth, 2013. "Dynamic Bradley–Terry modelling of sports tournaments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(1), pages 135-150, January.
    7. Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
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