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Modeling Bounded Count Environmental Data Using a Contaminated Beta‐Binomial Regression Model

Author

Listed:
  • Arnoldus F. Otto
  • Antonio Punzo
  • Johannes T. Ferreira
  • Andriëtte Bekker
  • Salvatore D. Tomarchio
  • Cristina Tortora

Abstract

Bounded count data are commonly encountered in environmental studies. This paper examines two environmental applications illustrating their relevance. The first investigates the effect of winter malnutrition on mule deer (Odocoileus hemionus) fawn mortality. The second application analyzes public perceptions of environmental issues using data from the Eurobarometer 95.1 survey (March–April 2021), which includes a question rating the perceived severity of climate change on a scale from 1 to 10. Together, these studies demonstrate the need for flexible bounded count models in environmental research. In this context, the binomial and beta‐binomial (BB) models are widely used for bounded count data, with the BB model offering the advantage of accounting for overdispersion. However, atypical observations in real‐world applications may hinder the performance of the BB model and lead to biased or misleading inferences. To address this limitation, we propose the contaminated beta‐binomial (cBB) distribution (cBB‐D), which introduces an additional BB component to accommodate atypical observations while preserving the mean and variance structure of the BB model. The cBB‐D thus captures both overdispersion and contamination effects in bounded count data. To incorporate explanatory variables, we further develop the contaminated BB regression model (cBB‐RM), in which none, some, or all cBB parameters may depend on covariates. The proposed models are applied to two environmental datasets, complemented by a sensitivity analysis on simulated data to assess the influence of atypical observations on parameter estimation. The methodology is implemented in the open‐source cBB package for R, available at https://github.com/arnootto/cBB.

Suggested Citation

  • Arnoldus F. Otto & Antonio Punzo & Johannes T. Ferreira & Andriëtte Bekker & Salvatore D. Tomarchio & Cristina Tortora, 2026. "Modeling Bounded Count Environmental Data Using a Contaminated Beta‐Binomial Regression Model," Environmetrics, John Wiley & Sons, Ltd., vol. 37(1), January.
    • Handle: RePEc:wly:envmet:v:37:y:2026:i:1:n:e70067
    DOI: 10.1002/env.70067
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    References listed on IDEAS

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    1. Salvatore D. Tomarchio & Antonio Punzo & Johannes T. Ferreira & Andriette Bekker, 2025. "A New Look at the Dirichlet Distribution: Robustness, Clustering, and Both Together," Journal of Classification, Springer;The Classification Society, vol. 42(1), pages 31-53, March.
    2. Punzo, Antonio & Bagnato, Luca, 2021. "Modeling the cryptocurrency return distribution via Laplace scale mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    3. Antonio Punzo, 2019. "A new look at the inverse Gaussian distribution with applications to insurance and economic data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(7), pages 1260-1287, May.
    4. Francesca Spina, 2015. "Environmental Justice and Patterns of State Inspections," Social Science Quarterly, Southwestern Social Science Association, vol. 96(2), pages 417-429, June.
    5. Yee, Susan Harrell & Santavy, Deborah L. & Barron, Mace G., 2008. "Comparing environmental influences on coral bleaching across and within species using clustered binomial regression," Ecological Modelling, Elsevier, vol. 218(1), pages 162-174.
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