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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.10016 |
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| _version_ | 1866917078243475456 |
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| author | Burger, Divan A. van Niekerk, Janet Roux, Peter C. le Raath-Krüger, Morgan J. |
| author_facet | Burger, Divan A. van Niekerk, Janet Roux, Peter C. le Raath-Krüger, Morgan J. |
| contents | Continuous proportions measured on the same experimental unit often pose two challenges: interior outliers that inflate variance beyond the beta ceiling and residual dependence that invalidates independent-margin models. We introduce a Bayesian copula modeling approach that combines rectangular-beta margins, which temper interior outliers by reallocating mass from the peak to a uniform component, with a single-parameter copula to capture concordance. Gaussian, Gumbel, and Clayton copula families are fitted, and log marginal likelihoods are obtained via bridge sampling to guide model selection. Applied to a 13-year survey (2003-2016) of Azorella selago cushion plants on sub-Antarctic Marion Island, the copula models outperform independence baselines in explaining percent dead stem cover. Accounting for between-year dependence uncovers a positive west-slope effect and weakens the cushion size effect. Simulation results show negligible bias and near-nominal 95% highest posterior density coverage across a range of tail weight and dependence scenarios, confirming good frequentist properties. The method integrates readily with JAGS and provides a robust default for paired proportion data in ecology and other disciplines where bounded outcomes and occasional outliers coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10016 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Outlier-robust copula regression for bivariate continuous proportions: an application to cushion plant vitality Burger, Divan A. van Niekerk, Janet Roux, Peter C. le Raath-Krüger, Morgan J. Methodology Continuous proportions measured on the same experimental unit often pose two challenges: interior outliers that inflate variance beyond the beta ceiling and residual dependence that invalidates independent-margin models. We introduce a Bayesian copula modeling approach that combines rectangular-beta margins, which temper interior outliers by reallocating mass from the peak to a uniform component, with a single-parameter copula to capture concordance. Gaussian, Gumbel, and Clayton copula families are fitted, and log marginal likelihoods are obtained via bridge sampling to guide model selection. Applied to a 13-year survey (2003-2016) of Azorella selago cushion plants on sub-Antarctic Marion Island, the copula models outperform independence baselines in explaining percent dead stem cover. Accounting for between-year dependence uncovers a positive west-slope effect and weakens the cushion size effect. Simulation results show negligible bias and near-nominal 95% highest posterior density coverage across a range of tail weight and dependence scenarios, confirming good frequentist properties. The method integrates readily with JAGS and provides a robust default for paired proportion data in ecology and other disciplines where bounded outcomes and occasional outliers coincide. |
| title | Outlier-robust copula regression for bivariate continuous proportions: an application to cushion plant vitality |
| topic | Methodology |
| url | https://arxiv.org/abs/2511.10016 |