Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.09597 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912054805266432 |
|---|---|
| author | Varin, Cristiano Firth, David |
| author_facet | Varin, Cristiano Firth, David |
| contents | Paired comparison models, such as Bradley-Terry and Thurstone-Mosteller, are commonly used to estimate relative strengths of pairwise compared items in tournament-style data. We discuss estimation of paired comparison models with a ridge penalty. A new approach is derived which combines empirical Bayes and composite likelihoods without any need to re-fit the model, as a convenient alternative to cross-validation of the ridge tuning parameter. Simulation studies demonstrate much better predictive accuracy of the new approach relative to ordinary maximum likelihood. A widely used alternative, the application of a standard bias-reducing penalty, is also found to improve appreciably the performance of maximum likelihood; but the ridge penalty, with tuning as developed here, yields greater accuracy still. The methodology is illustrated through application to 28 seasons of English Premier League football. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tractable Ridge Regression for Paired Comparisons Varin, Cristiano Firth, David Methodology Applications Paired comparison models, such as Bradley-Terry and Thurstone-Mosteller, are commonly used to estimate relative strengths of pairwise compared items in tournament-style data. We discuss estimation of paired comparison models with a ridge penalty. A new approach is derived which combines empirical Bayes and composite likelihoods without any need to re-fit the model, as a convenient alternative to cross-validation of the ridge tuning parameter. Simulation studies demonstrate much better predictive accuracy of the new approach relative to ordinary maximum likelihood. A widely used alternative, the application of a standard bias-reducing penalty, is also found to improve appreciably the performance of maximum likelihood; but the ridge penalty, with tuning as developed here, yields greater accuracy still. The methodology is illustrated through application to 28 seasons of English Premier League football. |
| title | Tractable Ridge Regression for Paired Comparisons |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2406.09597 |