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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. Brian Francis & Regina Dittrich & Reinhold Hatzinger & Roger Penn, 2002. "Analysing partial ranks by using smoothed paired comparison methods: an investigation of value orientation in Europe," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(3), pages 319-336, July.
    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. Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
    7. 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.
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