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Extended Poisson Models for Count Data with Inflated Frequencies

机译：具有膨胀频率的扩展Poisson模型用于计数数据

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摘要

Count data often exhibits inflated counts for zero. There are numerous papers in the literature that show how to fit Poisson regression models that account for the zero inflation. However, in many situations the frequencies of zero and of some other value k tends to be higher than the Poisson model can fit appropriately. Recently, Sheth-Chandra (2011), Lin and Tsai (2012) introduced a mixture model to account for the inflated frequencies of zero and k. In this dissertation, we study basic properties of this mixture model and parameter estimation for grouped and ungrouped data. Using stochastic representation we show how the EM algorithm can be adapted to obtain maximum likelihood estimates of the parameters. We derive the observed information matrix which yields standard errors of the EM estimates using ideas from Louis (1982). We also derive asymptotic distributions to test significance of the inflation points. We use real life examples to illustrate the procedure of fitting our model via EM algorithm.;The second part of this dissertation deals with a generalization of this mixture model where the one parameter Poisson distribution is replaced by a two parameter Conway-Maxwell-Poisson (CMP) distribution, which unlike the Poisson distribution accounts for both over and underdispersion in the count data. The CMP distribution has recently gained popularity, and a CMP model for zero inflated count data was introduced by Sellers and Raim (2016). We discuss properties of the CMP distribution and propose a new mixture distribution, namely zero and k inflated Conway-Maxwell-Poisson (ZkICMP) to address inflated counts with over and underdispersions. We develop regression models based on ZkICMP and discuss parameter estimation using analytical and numerical methods. Finally, we compare goodness of fit of inflated and standard models on simulated and real life data examples.
机译：计数数据通常显示为零的虚高计数。文献中有大量论文表明如何拟合解释零通胀的泊松回归模型。但是，在许多情况下，零频率和其他值k的频率往往高于泊松模型可以适当拟合的频率。最近，Sheth-Chandra（2011），Lin和Tsai（2012）引入了一种混合模型来说明零和k的膨胀频率。本文研究了混合模型的基本性质以及分组和非分组数据的参数估计。使用随机表示，我们展示了如何将EM算法调整为获得参数的最大似然估计。我们使用Louis（1982）的思想得出观测到的信息矩阵，该矩阵产生EM估计值的标准误差。我们还导出了渐近分布，以检验通货膨胀点的显着性。我们用现实生活中的例子来说明通过EM算法拟合模型的过程。;本文的第二部分是对混合模型的推广，其中一个参数泊松分布被两个参数Conway-Maxwell-Poisson（ CMP）分布，这与Poisson分布不同，是计数数据的过度分散和欠分散。 CMP分布最近变得越来越流行，Sellers和Raim（2016）引入了用于零膨胀计数数据的CMP模型。我们讨论了CMP分布的属性，并提出了一种新的混合分布，即零和k膨胀的Conway-Maxwell-Poisson（ZkICMP），以解决过度分散和分散不足的膨胀计数。我们基于ZkICMP开发回归模型，并讨论使用解析和数值方法进行参数估计。最后，我们在模拟和现实数据示例中比较了膨胀模型和标准模型的拟合优度。

著录项

  • 作者

    Arora, Monika.;

  • 作者单位

    Old Dominion University.;

  • 授予单位 Old Dominion University.;
  • 学科 Statistics.;Applied mathematics.
  • 学位 Ph.D.
  • 年度 2018
  • 页码 101 p.
  • 总页数 101
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 古生物学;
  • 关键词

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