ROC Analysis for Paired Comparison Data

TL;DR

This paper introduces two novel methods for applying ROC analysis to paired comparison data, overcoming previous interpretability issues, and demonstrates their effectiveness on sports competition data.

Contribution

The paper develops and validates two new ROC curve construction methods specifically designed for paired comparison models, addressing a key gap in the analysis of such data.

Findings

The proposed methods produce interpretable ROC curves for paired comparison data.

Application to sports data demonstrates the methods' practical utility.

The methods maintain desirable asymptotic properties.

Abstract

Paired comparison models are used for analyzing data that involves pairwise comparisons among a set of objects. When the outcomes of the pairwise comparisons have no ties, the paired comparison models can be generalized as a class of binary response models. Receiver operating characteristic (ROC) curves and their corresponding areas under the curves are commonly used as performance metrics to evaluate the discriminating ability of binary response models. Despite their individual wide range of usage and their close connection to binary response models, ROC analysis to our knowledge has never been extended to paired comparison models since the problem of using different objects as the reference in paired comparison models prevents traditional ROC approach from generating unambiguous and interpretable curves. We focus on addressing this problem by proposing two novel methods to construct ROC curves for paired comparison data which provide interpretable statistics and maintain desired asymptotic properties. The methods are then applied and analyzed on head-to-head professional sports competition data.