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 Appendix.
翻译:我们的重点是开发诊断工具和一个称为MNB的R包,用于检测非典型和有影响力的主体的多变量负二元回归模型。MNB模型来自一个Poisson混合模型,随机拦截遵循通用log-gamma(GLG)分布法。MNB相关计数数据模型导致一个MNB回归模型,该模型继承了等级模型的特征,以同时适应同级关系和过度扩散的发生。分散参数估计器的不协调性取决于GLG分布的不对称性。MNB回归模型的推断程序很简单,尽管当相关结构被错误地描述时,它可以提供不一致的对同源差异的估算。我们提出了用于检查多变量模型是否充分性的随机量化残余值,并从多变量模型中得出全球和地方影响计量,以评估有影响力的课题。最后,数据分析部分介绍了两种应用。在附录中展示了安装MNB软件包的代码和两个示例中使用的代码。