A zero-inflated overdispersed hierarchical Poisson model
A zero-inflated overdispersed hierarchical Poisson model
复制标题
DOI：
10.1177/1471082x14524676
复制
发表时间：
2014-10-01
影响因子：
1
通讯作者：
Verbeke, Geert
中科院分区：
文献类型：
--
作者：
Kassahun, Wondwosen;Neyens, Thomas;Verbeke, Geert
计数数据最常用泊松模型或其众多扩展之一来建模。需要这种扩展的原因有很多：(1)数据中的层次结构，例如，由于聚类，收集重复测量的结果等；(2)出现过分散（或欠分散），即数据中遇到的变异性不等于泊松分布规定的平均值；(3)超出泊松模型允许范围的额外零的出现。第一个问题通常是通过包含随机的特定主题效应来解决的。尽管并非总是如此，但人们通常认为这种随机效应是正态分布的。过度分散通常通过为此目的开发的模型来处理，例如计数数据的负二项模型。这可以通过一个随机泊松参数来理解。通常使用所谓的零膨胀模型来解释多余的零，该模型将泊松模型或负二项模型与处于零的原子相结合。本文的新颖之处在于它结合了所有这些特性。这项工作建立在Molenberghs等人（2010）定义的建模框架的基础上，该框架通过广义线性模型中的两组独立的随机效应来容纳聚类和过度分散。
Count data are most commonly modeled using the Poisson model, or by one of its many extensions. Such extensions are needed for a variety of reasons: (1) a hierarchical structure in the data, e.g., due to clustering, the collection of repeated measurements of the outcome, etc.; (2) the occurrence of overdispersion (or underdispersion), meaning that the variability encountered in the data is not equal to the mean, as prescribed by the Poisson distribution; and (3) the occurrence of extra zeros beyond what a Poisson model allows. The first issue is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. Overdispersion is often dealt with through a model developed for this purpose, such as, for example, the negative-binomial model for count data. This can be conceived through a random Poisson parameter. Excess zeros are regularly accounted for using so-called zero-inflated models, which combine either a Poisson or negative-binomial model with an atom at zero. The novelty of this article is that it combines all these features. The work builds upon the modelling framework defined by Molenberghs et al. (2010) in which clustering and overdispersion are accommodated for through two separate sets of random effects in a generalized linear model.