Bayesian Poisson-Lognormal Regression With Compositional Effect Shares for Multivariate Count Data

Multivariate count data are central in community ecology and related fields, where interest lies in how environmental gradients and management actions jointly shape the abundances of many taxa. The Poisson-lognormal (PLN) model is a natural workhorse in this setting, accommodating overdispersion and cross-taxon dependence via a latent Gaussian layer. Standard PLN regressions, however, treat species-specific slopes as unconstrained, which obscures situations where a covariate represents a finite resource or “budget” that is implicitly shared across taxa. We introduce a Bayesian multivariate count regression model in which the effects of selected covariates are modeled via an estimated overall effect magnitude together with compositional effect shares on a simplex. For a focal covariate, the vector of slopes across taxa is parameterized through a signed magnitude-share decomposition and endowed with a logistic-normal prior on additive logratio coordinates, so that each component can be interpreted as a species' share of the total increasing and/or decreasing effect. This construction is embedded in a multigroup PLN framework with a hierarchical prior, allowing effect shares to vary across groups while borrowing strength. Simulation studies show that the constrained Bayesian estimator improves on constrained maximum likelihood in terms of estimation error and predictive Kullback-Leibler risk, and produces more stable, interpretable effect allocations, particularly at small sample sizes. In an ecological application to dune meadow vegetation, the proposed model quantifies how a moisture gradient redistributes abundance among native grasses by allowing taxa to increase or decrease along the gradient within the same community and yields posterior predictive fits consistent with observed count patterns. The approach provides a principled way to encode and interpret effect-sharing structure in multivariate count regression, and is readily extensible to additional covariates, priors, and likelihoods.