Grouped-Poisson hurdle regression for underdispersed ecological counts

Ecological count data often contain structural zeros and positive-count distributions that are more concentrated than the Poisson benchmark. In such settings, standard Poisson and negative-binomial regressions may be too restrictive, especially when underdispersion persists after accounting for covariates and effort. We propose a likelihood-based framework that combines a hurdle specification for structural zeros with a grouped-Poisson mechanism for the positive counts. The positive-count component is modeled by a shared-intensity Poisson–Qm mixture, in which both components depend on the same intensity parameter and a mixing weight controls the contribution of the grouped component. This yields an explicit finite-sum likelihood while preserving a clear intensity interpretation. The grouping index m is treated as a discrete model index and selected over a finite candidate set by information criteria or held-out log-score. We also place the total-count model within a sum–and–split framework for hierarchical taxonomic counts. We establish targeted theoretical properties, including local identifiability for fixed m, aggregation coherence of the split layer, and consistency of BIC-based selection over finite candidate sets. Simulations and a NEON small-mammal illustration show that the proposed extension is conservative in near-Poisson regimes and useful when the positive-count distribution is genuinely underdispersed.