Herschtal Alan
School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia.
Stat Med. 2025 Aug;44(18-19):e70217. doi: 10.1002/sim.70217.
There has been growing awareness recently that conventional models for count data, such as the Negative Binomial model and zero inflated models, often yield poor fit and sub-optimal performance when applied to real-world count data problems. In response, a new, more flexible model for count data, the Poisson-Beta model, has started to attract attention. The Poisson-Beta model is a Poisson mixture where the underlying mixing distribution is a scaled Beta density. However, because its density function cannot be expressed in closed form, its use has been limited to very simple applications such as parameter estimation. This work presents a method of overcoming the computational complexity issues associated with the Poisson-Beta density to allow its application to problems of far greater complexity, enabling it to be used to model response variables in multivariate regression. This work additionally demonstrates that Poisson-Beta regression compares favorably to a range of commonly used regression models for count response data, achieving narrower confidence intervals and superior power.
最近，人们越来越意识到，传统的计数数据模型，如负二项式模型和零膨胀模型，在应用于实际计数数据问题时，往往拟合效果不佳且性能次优。作为回应，一种新的、更灵活的计数数据模型——泊松 - 贝塔模型开始受到关注。泊松 - 贝塔模型是一种泊松混合模型，其潜在的混合分布是一个缩放后的贝塔密度。然而，由于其密度函数无法以封闭形式表示，它的应用仅限于非常简单的情况，如参数估计。这项工作提出了一种克服与泊松 - 贝塔密度相关的计算复杂性问题的方法，使其能够应用于更复杂得多的问题，从而能够用于多元回归中对响应变量进行建模。这项工作还表明，泊松 - 贝塔回归与一系列常用于计数响应数据的回归模型相比具有优势，能实现更窄的置信区间和更高的功效。
