Abstract

Zero-inflated models have become a popular tool for assessing relationships between explanatory variables and a zero-inflated count outcome. In these models, regression coefficients have latent class interpretations, where latent classes correspond to a susceptible subpopulation with observations generated from a count distribution and a non susceptible subpopulation that provides only zeros. However, it is often of interest to evaluate covariates effects in the overall mixture population, that is, on the marginal mean of the zero-inflated count. Marginal zero-inflated models, such as the marginal zero-inflated Poisson models, have been developed for that purpose. They specify independent submodels for the susceptibility probability and the marginal mean of the count response. When the count outcome is bounded, it is tempting to formulate a marginal zero-inflated binomial model in the same fashion. This, however, is not possible, due to inherent constraints that relate, in the zero-inflated binomial model, the susceptibility probability and the latent and marginal means of the count outcome. In this paper, we propose a new marginal zero-inflated binomial regression model that accommodates these constraints. We investigate the maximum likelihood estimator in this model, both theoretically and by simulations. An application to the analysis of health-care demand is provided for illustration.

摘要

零膨胀模型已成为评估解释变量与零膨胀计数结果之间关系的流行工具。在这些模型中，回归系数具有潜在类别解释，其中潜在类别对应于具有从计数分布生成的观察值的易感亚群和仅提供零的非易感亚群。然而，评估总体混合总体中的协变量效应通常是有意义的，即在零膨胀计数的边际均值上。为此目的开发了边际零膨胀模型，例如边际零膨胀泊松模型。他们为敏感性概率和计数响应的边际均值指定了独立的子模型。当计数结果有界时，以同样的方式制定边际零膨胀二项式模型是很诱人的。然而，这是不可能的，因为在零膨胀二项式模型中，与敏感性概率以及计数结果的潜在和边际均值相关的固有约束。在本文中，我们提出了一种适应这些约束的新边际零膨胀二项式回归模型。我们从理论上和通过模拟研究了该模型中的最大似然估计量。提供了一个用于分析医疗保健需求的应用程序以进行说明。我们提出了一种新的边际零膨胀二项式回归模型来适应这些约束。我们从理论上和通过模拟研究了该模型中的最大似然估计量。提供了一个用于分析医疗保健需求的应用程序以进行说明。我们提出了一种新的边际零膨胀二项式回归模型来适应这些约束。我们从理论上和通过模拟研究了该模型中的最大似然估计量。提供了一个用于分析医疗保健需求的应用程序以进行说明。