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

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 (BT) model by incorporating a Markovian structure with temporal withincomparison 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. Keywords Bradley-Terry model • log-linear model • longitudinal paired comparison data • Markov chain • temporal change of preference parameters

Modelling changes over time in a multivariate paired comparison: An application to window display design

“…(2006)Dittrich, Francis, Hatzinger, and Katzenbeisser). For many time points and attributes we would suggest modelling short response patterns, containing the responses regarding A attributes, for each PC separately (see Grand et al. (2015)Grand, Dittrich, and Francis), as otherwise the response pattern would become very large.…”

“…In total, there are 23=8 different response patterns for three attributes (A=3) which were modelled through a log-linear MPCC model. The 8 possible response patterns ℓ within one comparison (12) are (see also, e.g., Grand et al. (2015)Grand, Dittrich, and Francis):…”

“…We combined the ideas of the methods of making judgements in PCs between two objects for more than one attribute at a single time point (i.e., multivariate comparisons at one time point, see Dittrich et al. (2006)Dittrich, Francis, Hatzinger, and Katzenbeisser) and the method of comparing repeatedly two objects regarding a single attribute for more than one time point (i.e., univariate comparisons over time , see, e.g., Grand et al. (2015)Grand, Dittrich, and Francis).…”