The Bradly-Terry Regression Trunk approach for modelling preference data with small trees

TL;DR

This paper proposes the Bradley-Terry Regression Trunk, a tree-based probabilistic model for preference data that captures interactions and individual differences, demonstrated through real data and simulations.

Contribution

It introduces a novel small tree model combining Bradley-Terry and covariate effects for preference analysis with no prior hypotheses.

Findings

Model performance improves with more rankings and objects.

High impact of judge characteristics enhances model accuracy.

The model effectively discovers interaction effects in preference data.

Abstract

This paper introduces the Bradley-Terry Regression Trunk model, a novel probabilistic approach for the analysis of preference data expressed through paired comparison rankings. In some cases, it may be reasonable to assume that the preferences expressed by individuals depend on their characteristics. Within the framework of tree-based partitioning, we specify a tree-based model estimating the joint effects of subject-specific covariates over and above their main effects. We combine a tree-based model and the log-linear Bradley-Terry model using the outcome of the comparisons as response variable. The proposed model provides a solution to discover interaction effects when no a-priori hypotheses are available. It produces a small tree, called trunk, that represents a fair compromise between a simple interpretation of the interaction effects and an easy to read partition of judges based on their characteristics and the preferences they have expressed. We present an application on a real data set following two different approaches, and a simulation study to test the model's performance. Simulations showed that the quality of the model performance increases when the number of rankings and objects increases. In addition, the performance is considerably amplified when the judges' characteristics have a high impact on their choices.