Outlier-Robust Copula Regression for Bivariate Continuous Proportions: An Application to Cushion Plant Vitality

Abstract Continuous proportions measured on the same experimental unit often pose two challenges: influential interior extremes 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 influential interior extremes 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 two surveys 13 years apart (2003 and 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 reveals 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, indicating good operating characteristics. 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 interior extremes coincide.Supplementary materials accompanying this paper appear online.