Models for Paired Comparison Data: A Review with Emphasis on Dependent Data

TL;DR

This paper reviews models for paired comparison data, focusing on dependent data, discussing extensions, implementation challenges, and comparing estimation methods using simulations and real university comparison data.

Contribution

It provides an updated overview of models for dependent paired comparison data, including covariate incorporation and pairwise likelihood implementation.

Findings

Pairwise likelihood performs well compared to other methods.

Dependent models are more realistic but computationally challenging.

Simulation results highlight estimation accuracy and efficiency.

Abstract

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specific covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In particular, a pairwise likelihood approach is explored for models for dependent paired comparison data, and a simulation study is carried out to compare the performance of maximum pairwise likelihood with other limited information estimation methods. The methodology is illustrated throughout using a real data set about university paired comparisons performed by students.