Impossibility results for equating the Youden Index with average scoring rules and Tjur $R^2$-like metrics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915170904702976 |
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| author | Hoessly, Linard |
| author_facet | Hoessly, Linard |
| contents | We consider the Youden index fas well as measures evaluating predicted probabilities for the maximum-likelihood estimate of a logistic regression model with predictor the classifier. We give impossibility results showing that the Youden index can not equal any average of a real scoring rule nor any metric averaging over binary outcomes (0s and 1s) for any continuous real-valued scoring rule. This shows the obstructions of such potential equivalences and highlights the distinct roles these metrics play in diagnostic assessment. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_05391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Impossibility results for equating the Youden Index with average scoring rules and Tjur $R^2$-like metrics Hoessly, Linard Other Statistics Probability Statistics Theory 62C99, 62H17, 62P10, , 62J12 We consider the Youden index fas well as measures evaluating predicted probabilities for the maximum-likelihood estimate of a logistic regression model with predictor the classifier. We give impossibility results showing that the Youden index can not equal any average of a real scoring rule nor any metric averaging over binary outcomes (0s and 1s) for any continuous real-valued scoring rule. This shows the obstructions of such potential equivalences and highlights the distinct roles these metrics play in diagnostic assessment. |
| title | Impossibility results for equating the Youden Index with average scoring rules and Tjur $R^2$-like metrics |
| topic | Other Statistics Probability Statistics Theory 62C99, 62H17, 62P10, , 62J12 |
| url | https://arxiv.org/abs/2411.05391 |