Abstract

We focus on the development of diagnostic tools and an R package called MNB for a multivariate negative binomial (MNB) regression model for detecting atypical and influential subjects. The MNB model is deduced from a Poisson mixed model in which the random intercept follows the generalized log-gamma (GLG) distribution. The MNB model for correlated count data leads to an MNB regression model that inherits the features of a hierarchical model to accommodate the intraclass correlation and the occurrence of overdispersion simultaneously. The asymptotic consistency of the dispersion parameter estimator depends on the asymmetry of the GLG distribution. Inferential procedures for the MNB regression model are simple, although it can provide inconsistent estimates of the asymptotic variance when the correlation structure is misspecified. We propose the randomized quantile residual for checking the adequacy of the multivariate model and derive global and local influence measures from the multivariate model to assess influential subjects. Finally, two applications are presented in the data analysis section. The code for installing the MNB package and the code used in the two examples is exhibited in the Appendices.

摘要

我们专注于开发诊断工具和名为 MNB 的 R 包，用于检测非典型和有影响力的主题的多元负二项式 (MNB) 回归模型。MNB 模型是从泊松混合模型推导出来的，其中随机截距服从广义对数伽马 (GLG) 分布。相关计数数据的 MNB 模型导致 MNB 回归模型继承了层次模型的特征，以同时适应类内相关性和过度离散的发生。离散参数估计器的渐近一致性取决于 GLG 分布的不对称性。MNB 回归模型的推理过程很简单，尽管在错误指定相关结构时它可能会提供不一致的渐近方差估计。我们提出随机分位数残差来检查多元模型的充分性，并从多元模型中推导出全局和局部影响度量以评估有影响力的主题。最后，数据分析部分介绍了两个应用程序。附录中展示了安装 MNB 包的代码和两个示例中使用的代码。