Klakattawi Hadeel S, Vinciotti Veronica, Yu Keming
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, UK.
Entropy (Basel). 2018 Feb 22;20(2):142. doi: 10.3390/e20020142.
Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically occurs in count datasets. It is highly desirable to have a unified model that can automatically adapt to the underlying dispersion and that can be easily implemented in practice. In this paper, a discrete Weibull regression model is shown to be able to adapt in a simple way to different types of dispersions relative to Poisson regression: overdispersion, underdispersion and covariate-specific dispersion. Maximum likelihood can be used for efficient parameter estimation. The description of the model, parameter inference and model diagnostics is accompanied by simulated and real data analyses.
计数数据的回归通常由泊松、负二项式（NB）和零膨胀回归等模型来执行。从业者经常面临的一个挑战是选择合适的模型以考虑离散性，离散性通常出现在计数数据集中。非常需要有一个统一的模型，它能够自动适应潜在的离散性并且在实践中易于实现。在本文中，离散韦布尔回归模型被证明能够以一种简单的方式相对于泊松回归适应不同类型的离散性：过度离散、欠离散和协变量特定离散性。最大似然法可用于高效的参数估计。模型描述、参数推断和模型诊断都伴随着模拟数据分析和实际数据分析。
