一般变化、膨胀、截断和收缩回归及其在堆积和渗漏数据中的应用
Generally-Altered, -Inflated, -Truncated and -Deflated Regression, With Application to Heaped and Seeped Data
摘要：
在现代回归分析中，诸如零膨胀和零改变泊松以及零截断二项分布等模型是公认的。我们提出了一个超级模型，共同和最大限度地统一的变更，通货膨胀，截断和通货紧缩的计数，给定一个1或2参数的父（基）分布。七个不相交的特殊值类型的集合被容纳，因为除了截断之外，所有的都有参数和非参数变量。一些亮点包括：（i）混合分布非常灵活，例如，多达7种模式;（ii）可以使用负二项（NB）父项来处理欠分散、等分散和过分散，其中欠分散由新的一般截断扩展方法处理;（iii）可以根据四个算子来整体地研究过分散;（iv）重要的应用：容易处理来自回顾性自报告调查的堆积和渗出数据，例如，峰值和下降，几乎位于任何地方;（v）虽然一般改变回归解释了为什么观察存在，一般膨胀回归解释了为什么它们过量存在，一般收缩回归解释了为什么观察不存在;（vi）VGAM R软件包实现了基于Fisher评分和多项logit模型的方法（实现了Poisson，NB，zeta和对数父母）。GAITD-NB有可能成为计数分布的瑞士军刀。
英文摘要：
Models such as the zero-inflated and zero-altered Poisson and zero-truncated binomial are well-established in modern regression analysis. We propose a super model that jointly and maximally unifies alteration, inflation, truncation and deflation for counts, given a 1- or 2-parameter parent (base) distribution. Seven disjoint sets of special value types are accommodated because all but truncation have parametric and nonparametric variants. Some highlights include: (i) the mixture distribution is exceeding flexible, e.g., up to seven modes; (ii) under-, equi- and over-dispersion can be handled using a negative binomial (NB) parent, with underdispersion handled by a novel Generally-Truncated-Expansion method; (iii) overdispersion can be studied holistically in terms of the four operators; (iv) an important application: heaped and seeped data from retrospective self-reported surveys are readily handled, e.g., spikes and dips which are located virtually anywhere; (v) while generally-altered regression explains why observations are there, generally-inflated regression accounts for why they are there in excess, and generally-deflated regression explains why observations are not there; (vi) the VGAM R package implements the methodology based on Fisher scoring and multinomial logit model (Poisson, NB, zeta and logarithmic parents are implemented.) The GAITD-NB has potential to become the Swiss army knife of count distributions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
