The premise of independence among subjects in the same cluster/group often fails in practice, and models that rely on such untenable assumption can produce misleading results. To overcome this severe deficiency, we introduce a new regression model to handle overdispersed and correlated clustered counts. To account for correlation within clusters, we propose a Poisson regression model where the observations within the same cluster are driven by the same latent random effect that follows the Birnbaum-Saunders distribution with a parameter that controls the strength of dependence among the individuals. This novel multivariate count model is called Clustered Poisson Birnbaum-Saunders (CPBS) regression. As illustrated in this paper, the CPBS model is analytically tractable, and its moment structure can be explicitly obtained. Estimation of parameters is performed through the maximum likelihood method, and an Expectation-Maximization (EM) algorithm is also developed. Simulation results to evaluate the finite-sample performance of our proposed estimators are presented. We also discuss diagnostic tools for checking model adequacy. An empirical application concerning the number of inpatient admissions by individuals to hospital emergency rooms, from the Medical Expenditure Panel Survey (MEPS) conducted by the United States Agency for Health Research and Quality, illustrates the usefulness of our proposed methodology.
翻译:为了克服这一严重缺陷,我们引入了新的回归模式,以处理过于分散和相互关联的集群计数。为了说明集群内部的相关性,我们提议了一个 Poisson 回归模式,在同一集群内进行观测的动力与Birnbaum-Saunders分布后的潜在随机效应相同,并有一个参数来控制个人依赖力的参数。这个新的多变量计数模型称为Crouped Poisson Birnbaum-Saunds(CPBS)回归模型。如本文件所示,CPBS模型具有分析性可动性,其目前的结构可以明确获得。参数的动画通过最大可能性方法进行,还开发了期望-最大化算法。模拟结果用来评估我们拟议估算者有限的性能。我们还介绍了用于检查模型是否充分的诊断工具。关于个人住院入院入院人数的实际应用情况,从“医疗调查”中展示了美国用于医院质量研究的“研究”方法。