Inference in Regression Models with Missing Covariates

在本提案中，我们提出了用于局部影响诊断的贝叶斯和频率方法，并开发了用于完整数据设置的模型评估工具，以及用于各种统计模型（包括广义线性模型、纵向数据模型和生存模型）的协变量和/或响应数据缺失的模型评估工具。在具体目标1中，我们基于Cook（1986）的一般局部影响发展，开发了频率局部影响度量和拟合优度统计，并讨论了i)随机缺失（MAR）和不可忽略缺失协变量的线性模型和ii)随机缺失和不可忽略缺失协变量的广义线性模型的这些度量。对于具体目标2，我们为完整的数据集开发了新的贝叶斯案例影响诊断类，然后将这些诊断推广到缺失的数据框架。目标1-2中提出的方法主要来自PI合作工作中的几项研究。

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.