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Type I multivariate zero-inflated generalized Poisson distribution with applications

机译：I型多元零膨胀广义泊松分布及其应用

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摘要

Excessive zeros in multivariate count data are often encountered in practice. Since the Poisson distribution only possesses the property of equi-dispersion, the existing Type I multivariate zero-inflated Poisson distribution (Liu and Tian, 2015, CSDA) cannot be used to model multivariate zero-inflated count data with over-dispersion or under-dispersion. In this paper, we extend the univariate zero-inflated generalized Poisson (ZIGP) distribution to Type I multivariate ZIGP distribution via stochastic representation aiming to model positively correlated multivariate zero-inflated count data with over-dispersion or underdispersion. Its distributional theories and associated properties are derived. Due to the complexity of the ZIGP model, we provide four useful algorithms (a very fast Fisher-scoring algorithm, an expectation/conditional-maximization algorithm, a simple EM algorithm and an explicit majorization– minimization algorithm) for finding maximum likelihood estimates of parameters of interest and develop efficient statistical inference methods for the proposed model. Simulation studies for investigating the accuracy of point estimates and confidence interval estimates and comparing the likelihood ratio test with the score test are conducted. Under both AIC and BIC, our analyses of the two data sets show that Type I multivariate ZIGP model is superior over Type I multivariate zero-inflated Poisson model.
机译：在实践中经常会遇到多元计数数据中的零。由于Poisson分布仅具有等分散性，因此现有的I型多元零膨胀Poisson分布（Liu和Tian，2015，CSDA）不能用于对离散度过高或不足的多元零膨胀计数数据进行建模。分散。在本文中，我们通过随机表示将单变量零膨胀广义泊松（ZIGP）分布扩展到I型多变量ZIGP分布，旨在对正相关的多元零膨胀计数数据进行过度分散或分散不足建模。推导了其分布理论和相关属性。由于ZIGP模型的复杂性，我们提供了四个有用的算法（一个非常快速的Fisher评分算法，一个期望/条件最大化算法，一个简单的EM算法以及一个显式的主化最小化算法）来查找参数的最大似然估计感兴趣并为该模型开发有效的统计推断方法。进行了模拟研究，以调查点估计和置信区间估计的准确性，并将似然比测试与得分测试进行比较。在AIC和BIC的情况下，我们对这两个数据集的分析表明，I型多元ZIGP模型优于I型多元零膨胀Poisson模型。

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