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

This paper investigates two environmental applications related to climate change, where observations consist of bounded counts. The binomial and beta-binomial (BB) models are commonly used for bounded count data, with the BB model offering the advantage of accounting for potential overdispersion. However, extreme observations in real-world applications may hinder the performance of the BB model and lead to misleading inferences. To address this issue, we propose the contaminated beta-binomial (cBB) distribution (cBB-D), which provides the necessary flexibility to accommodate extreme observations. The cBB model accounts for overdispersion and extreme values while maintaining the mean and variance properties of the BB distribution. The availability of covariates that improve inference about the mean of the bounded count variable motivates the further proposal of the cBB regression model (cBB-RM). Different versions of the cBB-RM model - where none, some, or all of the cBB parameters are regressed on available covariates - are fitted to the datasets.