零截断及零调整离散模型的计数数据分析方法的新进展之综述研究

Advances of the Zero Truncated and Zero Inflated/Adjusted Discrete Models in Count Data Analyses

在社会学、心理学、生态学、保险学、医学、流行病学等领域,人们经常收集到各种各样的计数资料以研究它们的规律和特征.往往会出现计数数据不包含零观测值或零观测值过多的情形.一系列零截断和零膨胀离散模型也由此提出用于分析这一类数据,如零截断/零膨胀泊松分布、零截断/零膨胀负二项分布等.在利用这一类模型进行拟合时,对未知参数进行统计推断是必要的.已有的文献仅局限于解决单一模型的参数推断问题.本文基于近几年提出的零截断分布和零膨胀分布的随机表示,在统一的模型框架下,建立了计算参数极大似然估计的一般方法并应用于常见的离散型分布.进一步提出更一般的零调整模型,扩大了模型的适用范围,为研究人员进行零调整计数数据分析提供合适和便捷的方法与选择.我们通过随机模拟和两个实例分析来说明这些方法的实用性.

In fields of sociology,psychology,ecology,insurance,medicine and epidemiology,count data are often collected for specific studies.While count data without zero-category or with excess zeros arise quite frequently,a series of zero-truncated and zero-inflated models were soon developed to analyze these kinds of data,such as zero-truncated/inflated Poisson distribution and zero-truncated/inflated negative binomial distribution.It is necessary to make statistical inferences on unknown parameters when fitting data by these models.Existing studies merely focus on one of these models.In this paper,based on the stochastic representations of zero-truncated and zero-inflated distributions proposed in recent years,we construct a general method to obtain the maximum likelihood estimates of parameters under a unified framework,and make a review on familiar discrete distributions.Moreover,zero-adjusted models are further proposed to extend the applications,aiming to provide researchers appropriate and convenient methods in count data analyses.All methods are demonstrated by simulation studies and two real data analyses.