Multiple Imputation Inferences with Public-Use Data Files and Frequentist Properties of Bayesian Procedures

使用公共使用数据文件和贝叶斯过程的频率属性进行多重插补推理

• 批准号: 9626691
• 负责人: Xiao-Li Meng
• 金额: $ 16.7万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626691&HistoricalAwards=false
• 关键词: Multiple; Imputation; Inferences; Public; Use

DMS 9626691 Meng This is a comprehensive research program on multiple imputation methodology. Multiple imputation methodology is the most effective inferential method available for handling the common and complex problem of nonresponse in sample surveys, especially those that produce public-use data files shared by many users. The multiple imputation framework was established under the Bayesian perspective, mainly because the Bayesian approach provides a coherent and flexible general framework for constructing sophisticated imputation models that incorporate all available information. However, the fact that the public-use data files are designed to be shared by many users requires that the procedures used for creating multiple imputations, and for analyzing the multiply-imputed data sets, must have good frequentist properties. Thus, the study and use of multiple imputation highlights and requires the melding of the Bayesian and frequentist perspectives, thus posing many challenging and intriguing research problems at the intersection of these two perspectives. To effectively tackle these problems, this research is conducted simultaneously at two levels. At the general level, the research examines new robust frequentist properties of Bayesian procedures. At the specific level, the research studies the use of these properties in multiple imputation, with a focus on constructing new procedures as well as justifying existing ones under more general conditions. Specific topics include confidence validity under uncongenial multiple imputation inferences, frequentist properties of posterior predictive p-values, and unbiased imputations with single observation unbiased priors. This research studies the important and complicated problem of nonresponse, a problem inherent to all sample surveys. The most serious problem caused by nonresponse is nonresponse bias, that is, those people who do not respond are systematically different from those who do respond. Su ch systematic differences have been repeatedly documented in the social, economic, and statistical literature, for example, on self-reporting of income. If the bias is not corrected and only the answers from respondents are used, a very distorted picture of the characteristics (e.g., average annual income of households) of the underlying population is likely to be obtained. Correcting for such systematic distortion, especially for large public-data files, is a very complex and demanding task. The basic task is to reduce the nonresponse bias by using available information (e.g., demographic information) on the nonrespondents to predict their missing values. Since we have uncertainty in our prediction, we need more than one prediction, i.e. imputation, to honestly display the uncertainty. With more than one imputation, it becomes straightforward for an individual user to estimate the loss of information due to nonresponse and thus obtain valid statistical inference using only standard complete-data analysis procedures. It is obvious that the quality of the imputation model has direct impact on the quality of the subsequent statistical analyses. A main aim of this research is to provide better and more flexible methodologies for constructing imputation models; the significance of such a research is highlighted by the fact that the analyses of public-use data files typically have a profound impact on our society because the conclusions from these analyses are typically used to answer questions in economics, education, demographic studies, public health and policy, sociology, political science, among others. Another aim of this research is to explore the possible use of the methodologies developed for multiple imputation to missing-data problems in other content areas, such as the problem of handling the missing observations in ultraviolet radiation measurements, which are crucial for accessing global atmospheric changes due to ozone depletion.

DMS 9626691 孟 这是一个关于多重插补方法的综合研究项目。 多重插补方法是处理抽样调查中常见且复杂的无答复问题的最有效的推断方法，特别是那些产生许多用户共享的公共数据文件的调查。 多重插补框架是在贝叶斯视角下建立的，主要是因为贝叶斯方法为构建包含所有可用信息的复杂插补模型提供了连贯且灵活的通用框架。 然而，公共使用数据文件被设计为由许多用户共享的事实要求用于创建多重插补和分析多重插补数据集的过程必须具有良好的频率属性。 因此，多重插补的研究和使用强调并需要贝叶斯和频率论观点的融合，从而在这两种观点的交叉点提出了许多具有挑战性和有趣的研究问题。 为了有效解决这些问题，本研究分两个层面同时进行。在一般层面上，该研究检查了贝叶斯过程的新的稳健频率特性。 在具体层面上，该研究研究了这些属性在多重插补中的使用，重点是构建新程序以及在更一般的条件下证明现有程序的合理性。 具体主题包括不一致的多重插补推论下的置信有效性、后验预测 p 值的频率属性以及单次观察无偏先验的无偏插补。 这项研究研究了重要而复杂的无答复问题，这是所有抽样调查所固有的问题。不回应造成的最严重的问题是不回应偏差，即那些不回应的人与那些回应的人存在系统性差异。 这种系统性差异已在社会、经济和统计文献中多次被记录，例如在自我报告收入方面。 如果不纠正偏差而仅使用受访者的答案，则可能会获得非常扭曲的基础人口特征（例如家庭平均年收入）。纠正这种系统性失真，特别是对于大型公共数据文件，是一项非常复杂且艰巨的任务。 基本任务是通过使用无应答者的可用信息（例如人口统计信息）来预测其缺失值，从而减少无应答偏差。 由于我们的预测存在不确定性，因此我们需要不止一种预测（即插补）来诚实地显示不确定性。通过不止一种插补，单个用户可以直接估计由于无响应而导致的信息丢失，从而仅使用标准的完整数据分析程序即可获得有效的统计推断。 显然，插补模型的质量直接影响后续统计分析的质量。这项研究的主要目的是为构建插补模型提供更好、更灵活的方法；这种研究的意义在于，对公用数据文件的分析通常会对我们的社会产生深远的影响，因为这些分析的结论通常用于回答经济学、教育、人口研究、公共卫生和政策、社会学、政治学等领域的问题。 这项研究的另一个目的是探索为其他内容领域的缺失数据问题进行多重插补而开发的方法的可能用途，例如处理紫外线辐射测量中缺失观测值的问题，这对于了解臭氧消耗造成的全球大气变化至关重要。