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<p>Ecological count data often exhibit substantial heterogeneity beyond measured covariates and variable sampling effort. We study negative binomial regression with an additive latent effect on the log-mean and exposure offsets, leaving the random-effects distribution unspecified. Rather than estimating that distribution directly, we develop finite-sample valid one-sided inference for interpretable summaries of latent heterogeneity, with primary focus on heterogeneity quantiles that correspond to multiplicative departures from a covariate-adjusted baseline intensity. Our approach uses sample splitting to separate nuisance estimation from inference, constructs a randomized exceedance statistic on a held-out fold, and calibrates composite null tests through least-favorable mixing configurations. Exact <i>p</i>-values are obtained from Poisson–binomial tail probabilities, and test inversion yields a one-sided lower confidence bound with conditional finite-sample coverage. We also distinguish a sharper bounded calibration, when a scientifically credible upper support bound is available, from a fully distribution-free calibration that remains valid but is more conservative. Simulation experiments under NEON-like designs show conservative coverage and stable behavior across distinct heterogeneity regimes. An application to NEON small mammal live-trapping data illustrates how the proposed lower bound provides a transparent finite-sample statement about residual plot-night heterogeneity after adjusting for seasonality, habitat, site effects, and effort.</p>

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Exact one-sided inference for random-effects quantiles in negative binomial regression for ecological count data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月20日

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  • Abdolnasser Sadeghkhani,
  • Ali Sadeghkhani

摘要

Ecological count data often exhibit substantial heterogeneity beyond measured covariates and variable sampling effort. We study negative binomial regression with an additive latent effect on the log-mean and exposure offsets, leaving the random-effects distribution unspecified. Rather than estimating that distribution directly, we develop finite-sample valid one-sided inference for interpretable summaries of latent heterogeneity, with primary focus on heterogeneity quantiles that correspond to multiplicative departures from a covariate-adjusted baseline intensity. Our approach uses sample splitting to separate nuisance estimation from inference, constructs a randomized exceedance statistic on a held-out fold, and calibrates composite null tests through least-favorable mixing configurations. Exact p-values are obtained from Poisson–binomial tail probabilities, and test inversion yields a one-sided lower confidence bound with conditional finite-sample coverage. We also distinguish a sharper bounded calibration, when a scientifically credible upper support bound is available, from a fully distribution-free calibration that remains valid but is more conservative. Simulation experiments under NEON-like designs show conservative coverage and stable behavior across distinct heterogeneity regimes. An application to NEON small mammal live-trapping data illustrates how the proposed lower bound provides a transparent finite-sample statement about residual plot-night heterogeneity after adjusting for seasonality, habitat, site effects, and effort.