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

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 .