Inference in Regression Models with Missing Covariates

描述(申请人提供)：我们将研究以下研究问题： 1.协变量可忽略和不可忽略缺失的广义线性模型的模型可辨识性和后验适定性--我们将进行理论研究，建立协变量可忽略和不可忽略缺失的广义线性模型的后验适定性和极大似然估计存在的充要条件。然后我们的工作将扩展到其他类型的模型，包括i)Cox回归模型和ii)广义线性混合模型。 2.缺失数据问题中的模型评估和敏感性分析-我们将推出模型选择工具，用于评估模型和进行缺失数据问题的敏感性分析。模型评估标准将是非常通用的，并且可用于评估在广义线性模型、纵向数据模型和生存模型中存在不可忽略的缺失协变量和/或响应数据的情况下的拟合优度和敏感性分析。 3.带缺失协变量的Cox回归模型的理论与推断--将对缺失协变量数据的Cox偏似然推断进行理论研究。对于完全数据设置和MAR协变量，将研究存在最大部分似然估计(MPLE)的充要条件。此外，还将研究MAR协变量数据的贝叶斯方法。 4.协变量分布和缺失数据的半参数和非参数规范 机制-我们将研究协变量分布的半参数模型和具有可忽略或不可忽略的丢失协变量和/或响应数据的回归模型的丢失数据机制。

DESCRIPTION (provided by applicant): We will examine the following research problems: 1. Model Identifiability and Posterior Propriety for Generalized Linear Models (GLMs) with Ignorably and Nonignorably Missing Covariates - We will carry out a theoretical investigation for establishing necessary and sufficient conditions for posterior propriety and existence of the maximum likelihood estimator for GLMs with ignorably nor nonignorably missing covariates. Our work will then be extended to other types of models including i) the Cox regression model and ii) generalized linear mixed models. 2. Model Assessment and Sensitivity Analyses in Missing Data Problems - We will derive model selection tools for assessing models and carrying out sensitivity analyses in missing data problems. The model assessment criteria will be quite general, and can be used to assess goodness of fit and sensitivity analyses in the presence of nonignorably missing covariate and/or response data in generalized linear models, models for longitudinal data, and survival models. 3. Theory and Inference for the Cox Regression Model with Missing Covariates - A theoretical investigation for inference with missing covariate data using Cox's partial likelihood will be conducted. Necessary and sufficient conditions for the existence of the maximum partial likelihood estimate (MPLE) will be studied for complete data settings as well as with MAR covariates. In addition, Bayesian methods for MAR covariate data will be studied. 4. Semiparametric and Nonparametric Specification of the Covariate Distribution and Missing Data Mechanism - We will examine semiparametric models for the covariate distribution and missing data mechanism for regression models with ignorably or nonignorably missing covariate and/or response data.