Department of Statistics, National Taipei University, 151 University Rd., San Shia District New Taipei City, 23741,Taiwan.
Stat Med. 2013 Apr 30;32(9):1572-83. doi: 10.1002/sim.5650. Epub 2012 Oct 11.
Zero-inflated Poisson regression is a popular tool used to analyze data with excessive zeros. Although much work has already been performed to fit zero-inflated data, most models heavily depend on special features of the individual data. To be specific, this means that there is a sizable group of respondents who endorse the same answers making the data have peaks. In this paper, we propose a new model with the flexibility to model excessive counts other than zero, and the model is a mixture of multinomial logistic and Poisson regression, in which the multinomial logistic component models the occurrence of excessive counts, including zeros, K (where K is a positive integer) and all other values. The Poisson regression component models the counts that are assumed to follow a Poisson distribution. Two examples are provided to illustrate our models when the data have counts containing many ones and sixes. As a result, the zero-inflated and K-inflated models exhibit a better fit than the zero-inflated Poisson and standard Poisson regressions.
零膨胀泊松回归是一种常用于分析存在过多零值数据的工具。尽管已经有很多工作用于拟合零膨胀数据，但大多数模型都严重依赖于个别数据的特殊特征。具体来说，这意味着有相当一部分受访者赞成相同的答案，使得数据出现峰值。在本文中，我们提出了一种新模型，该模型具有灵活建模除零以外的过度计数的能力，该模型是多项逻辑回归和泊松回归的混合体，其中多项逻辑回归成分模型化了过度计数的发生，包括零、K（其中 K 是一个正整数）和所有其他值。泊松回归成分模型化了假定服从泊松分布的计数。提供了两个示例来说明我们的模型在数据包含许多 1 和 6 的计数时的应用。结果表明，零膨胀和 K 膨胀模型比零膨胀泊松和标准泊松回归具有更好的拟合度。
