Outlier-robust copula regression for bivariate continuous proportions: an application to cushion plant vitality

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.