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

TL;DR

This paper introduces a Bayesian copula regression method with robust beta margins for analyzing bivariate proportions, effectively handling outliers and dependence, demonstrated on ecological cushion plant data.

Contribution

The paper presents a novel Bayesian copula approach combining rectangular-beta margins with various copula families for robust modeling of bounded proportion data.

Findings

Copula models outperform independence models in explaining plant cover.

Accounting for dependence reveals new ecological effects.

Simulation confirms good frequentist properties of the method.

Abstract

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.