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

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.