Moderated paired comparisons: A generalized Bradley-Terry model for continuous data using a discontinuous penalized likelihood function

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

Standard paired comparison models are widely used in circumstances where a measure of preference is available on a sequence or collection of pairwise comparisons between a group of objects or treatments. Typically, the measure of preference observations takes the form of simple binary outcomes, indicating which of the two objects or treatments in a particular comparison is preferred. Common examples of such situations include models of choice behaviour in politics or marketing, comparisons of medical treatments or in the realm of sports rankings. We investigate situations where the observed measure of preference for the paired comparisons is instead a continuous outcome indicating not simply the direction of preference but the degree of preference as well; in particular, we present, as a motivating example, a ranking analysis of the top 12 international limited overs cricket teams, with an appropriately defined margin of victory in individual matches playing the role of the measure of preference. We propose a new method, which is termed moderated paired comparisons, that is based on fitting a penalized likelihood model to the observed margins of victory. Importantly, the structure of the penalty function chosen allows for the model to assign differential importance to the information that is contained solely in the dichotomous win-loss outcome of a match as against that contained in the actual margin of the victory.

Original languageEnglish
Pages (from-to)397-415
Number of pages19
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Volume60
Issue number3
DOIs
Publication statusPublished - May 2011
Externally publishedYes

Fingerprint

Bradley-Terry Model
Paired Comparisons
Penalized Likelihood
Likelihood Function
Margin
Ranking
Binary Outcomes
Pairwise Comparisons
Penalty Function
Model
Assign
Paired comparisons

Cite this

@article{35453de4b33340b0b2f719632c24bae0,
title = "Moderated paired comparisons: A generalized Bradley-Terry model for continuous data using a discontinuous penalized likelihood function",
abstract = "Standard paired comparison models are widely used in circumstances where a measure of preference is available on a sequence or collection of pairwise comparisons between a group of objects or treatments. Typically, the measure of preference observations takes the form of simple binary outcomes, indicating which of the two objects or treatments in a particular comparison is preferred. Common examples of such situations include models of choice behaviour in politics or marketing, comparisons of medical treatments or in the realm of sports rankings. We investigate situations where the observed measure of preference for the paired comparisons is instead a continuous outcome indicating not simply the direction of preference but the degree of preference as well; in particular, we present, as a motivating example, a ranking analysis of the top 12 international limited overs cricket teams, with an appropriately defined margin of victory in individual matches playing the role of the measure of preference. We propose a new method, which is termed moderated paired comparisons, that is based on fitting a penalized likelihood model to the observed margins of victory. Importantly, the structure of the penalty function chosen allows for the model to assign differential importance to the information that is contained solely in the dichotomous win-loss outcome of a match as against that contained in the actual margin of the victory.",
author = "Stern, {Steven E.}",
year = "2011",
month = "5",
doi = "10.1111/j.1467-9876.2010.00751.x",
language = "English",
volume = "60",
pages = "397--415",
journal = "Journal of the Royal Statistical Society. Series C: Applied Statistics",
issn = "0035-9254",
publisher = "Wiley-Blackwell",
number = "3",

}

TY - JOUR

T1 - Moderated paired comparisons

T2 - A generalized Bradley-Terry model for continuous data using a discontinuous penalized likelihood function

AU - Stern, Steven E.

PY - 2011/5

Y1 - 2011/5

N2 - Standard paired comparison models are widely used in circumstances where a measure of preference is available on a sequence or collection of pairwise comparisons between a group of objects or treatments. Typically, the measure of preference observations takes the form of simple binary outcomes, indicating which of the two objects or treatments in a particular comparison is preferred. Common examples of such situations include models of choice behaviour in politics or marketing, comparisons of medical treatments or in the realm of sports rankings. We investigate situations where the observed measure of preference for the paired comparisons is instead a continuous outcome indicating not simply the direction of preference but the degree of preference as well; in particular, we present, as a motivating example, a ranking analysis of the top 12 international limited overs cricket teams, with an appropriately defined margin of victory in individual matches playing the role of the measure of preference. We propose a new method, which is termed moderated paired comparisons, that is based on fitting a penalized likelihood model to the observed margins of victory. Importantly, the structure of the penalty function chosen allows for the model to assign differential importance to the information that is contained solely in the dichotomous win-loss outcome of a match as against that contained in the actual margin of the victory.

AB - Standard paired comparison models are widely used in circumstances where a measure of preference is available on a sequence or collection of pairwise comparisons between a group of objects or treatments. Typically, the measure of preference observations takes the form of simple binary outcomes, indicating which of the two objects or treatments in a particular comparison is preferred. Common examples of such situations include models of choice behaviour in politics or marketing, comparisons of medical treatments or in the realm of sports rankings. We investigate situations where the observed measure of preference for the paired comparisons is instead a continuous outcome indicating not simply the direction of preference but the degree of preference as well; in particular, we present, as a motivating example, a ranking analysis of the top 12 international limited overs cricket teams, with an appropriately defined margin of victory in individual matches playing the role of the measure of preference. We propose a new method, which is termed moderated paired comparisons, that is based on fitting a penalized likelihood model to the observed margins of victory. Importantly, the structure of the penalty function chosen allows for the model to assign differential importance to the information that is contained solely in the dichotomous win-loss outcome of a match as against that contained in the actual margin of the victory.

UR - http://www.scopus.com/inward/record.url?scp=79954585132&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9876.2010.00751.x

DO - 10.1111/j.1467-9876.2010.00751.x

M3 - Article

VL - 60

SP - 397

EP - 415

JO - Journal of the Royal Statistical Society. Series C: Applied Statistics

JF - Journal of the Royal Statistical Society. Series C: Applied Statistics

SN - 0035-9254

IS - 3

ER -