Inference in Regression Models with Missing Covariates

在该建议中，我们提出了用于局部影响诊断的贝叶斯和频度方法，并开发了用于完整数据设置以及存在缺失协变量和/或响应数据的各种统计模型的模型评估工具，包括广义线性模型、纵向数据模型和生存模型。在具体目标1中，我们在Cook(1986)的广义局部影响发展的基础上发展了频率局部影响度量和拟合度统计量，并讨论了i)具有随机缺失(MAR)和不可忽略缺失协变量的线性模型和ii)具有MAR和不可忽略缺失协变量的广义线性模型的这些度量。对于特定的目标2，我们针对完全数据集开发了新的贝叶斯案例影响诊断，然后将这些诊断推广到缺失数据框架。AIMS 1-2中提出的方法论主要是基于在国际和平研究所的协作工作中进行的几项研究。

In this proposal, we propose Bayesian and frequentist methodology for local influence diagnostics and develop model assessment tools for complete data settings as well as in the presence of missing covariate and/or response data for a variety of statistical models, including generalized linear models, models for longitudinal data, and survival model. In Specific Aim 1, we develop frequentist local influence measures and goodness of fit statistics based on the general local influence development of Cook (1986), and discuss these measures for i) linear models with missing at random (MAR) and nonignorably missing covariates and ii) generalized linear models with MAR and nonignorably missing covariates. For Specific Aim 2, we develop new classes of Bayesian case influence diagnostics for the complete data setting then generalize these diagnostics to the missing data framework. The proposed methodologies in Aims 1-2 are primarily motivated from several studies in the PI’s collaborative work.