Strobl, Carolin and Wickelmaier, Florian and Zeileis, Achim
Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning.
Department of Statistics: Technical Reports, No.54
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 semi-parametric 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.