This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable with covariates, zero-inflated Poisson/negative binomial regression models are widely used. In this work, we develop a regression model with the fractional binomial distribution that can serve as an additional tool for modeling the count response variable with covariates. The consistency of maximum likelihood estimators of the proposed model is investigated theoretically and empirically with simulations. The practicality of the proposed model is examined through data analysis. The results show that our model is as versatile as or more versatile than the existing zero-inflated models, and especially, it has a better fit with left-skewed discrete data than other models. However, the proposed model faces computational obstacles and will require more work in the future to implement this model on various count data with excess zeros.

翻译：本文提出了一种采用分数二项分布的新型广义线性模型。针对含大量零点的计数数据，通常采用零膨胀泊松/负二项分布。为分析此类计数变量与协变量间的关联性，零膨胀泊松/负二项回归模型已被广泛应用。本研究开发了一种基于分数二项分布的回归模型，可作为对含协变量的计数响应变量进行建模的补充工具。通过理论推导与模拟实验，对所提模型最大似然估计量的一致性进行了探究。通过实际数据分析检验了该模型的实用性。结果表明，本模型具有与现有零膨胀模型相当或更优的适用性，尤其对于左偏离散数据展现出更佳的拟合效果。然而，该模型在计算层面仍存在障碍，未来需进一步研究以实现在各类含过量零点的计数数据中的应用。