Statistical Science

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

Manuela Cattelan

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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.

Article information

Source
Statist. Sci. Volume 27, Number 3 (2012), 412-433.

Dates
First available in Project Euclid: 5 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.ss/1346849947

Digital Object Identifier
doi:10.1214/12-STS396

Mathematical Reviews number (MathSciNet)
MR3012434

Zentralblatt MATH identifier
1331.62368

Keywords
Bradley–Terry model limited information estimation paired comparisons pairwise likelihood Thurstonian models

Citation

Cattelan, Manuela. Models for Paired Comparison Data: A Review with Emphasis on Dependent Data. Statist. Sci. 27 (2012), no. 3, 412--433. doi:10.1214/12-STS396. https://projecteuclid.org/euclid.ss/1346849947


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