Fractional Imputation for Incomplete Data Analysis

由于无响应、测量不准确、两阶段抽样等原因，调查数据中经常会遇到不完整的数据。任何形式的不完整数据都会损害样本的代表性，而对不完整数据的天真分析可能会导致估计偏差。补偿是为缺失的项目赋值的过程，目的是减少偏差并提高得到的估计器的效率。该项目将开发分数分配方法，作为处理不完整数据的工具，用于一般用途的估计。这些方法将作为建立完整的统计包的重要组成部分，用于分析不完整的数据，最终可应用于各种学科的问题，包括社会、行为和经济科学。特别是，该项目将开发分数推算，以解决数据不完整的几个重要问题，包括(1)基于似然的推断，(2)使用分数热甲板推算的稳健估计，(3)用于调查整合的综合推算，以及(4)统计匹配技术。由于分数补偿是处理不完整数据的一种相对较新的方法，因此迫切需要理论和方法的发展。分数阶梯度法的优点在于计算简单、适用范围广和统计有效性。通过使用分数权重，分数补偿避免了迭代计算的负担，例如马尔可夫链蒙特卡罗，用于评估与缺失数据相关联的条件期望。该方法具有参数估计的一致性和高效性。分数归因法可以应用于非标准情况，如测量误差模型、结合两个不同调查的回归分析以及来自观察性研究的因果推断。因此，拟议研究的影响是巨大的，因为拟议的方法可用作不完整数据的一般方法。由于分数补偿方法的计算简单性和统计有效性，所提出的研究结果应该具有广泛的适用性。它还应在为分析提供完整的数据集和结合来自不同调查的信息的新数据产品方面产生重大影响。

Incomplete data frequently are encountered in survey data due to nonresponse, inaccurate measurement, and two-phase sampling, among other things. Any form of incomplete data can damage the representativeness of a sample, and a naive analysis with incomplete data can lead to biased estimation. Imputation is a process of assigning values to the missing items with the objective of reducing bias and improving the efficiency of the resulting estimators. This project will develop fractional imputation methods as a tool for handling incomplete data for general-purpose estimation. These methods will serve as important building blocks for the establishment of a complete statistical package for analysis of incomplete data that ultimately can be applied to problems in a variety of disciplines, including the social, behavioral, and economic sciences. In particular, the project will develop fractional imputation to address several important problems with incomplete data, including (1) likelihood-based inference, (2) robust estimation using fractional hot deck imputation, (3) synthetic imputation for survey integration, and (4) statistical matching technique. Because fractional imputation is a relatively new approach for handling incomplete data, there is a critical need for theoretical and methodological development. The advantages of the fractional imputation approach lie in its computational simplicity, wide applicability, and its statistical validity. By using fractional weights, fractional imputation avoids the burden of iterative computation, such as Markov Chain Monte Carlo, for the evaluation of conditional expectation associated with missing data. The proposed approach can be used to estimate parameters consistently and efficiently. The fractional imputation approach can be applied to nonstandard situations such as measurement error models, regression analysis combining two different surveys, and causal inference from observational studies. The impact of the proposed research is therefore substantial because the proposed approach can be used as a general methodology for incomplete data. Because of the computational simplicity and statistical validity of the fractional imputation approach, the results of the proposed research should have wide applicability. It also should have a major impact in providing complete data sets for analysis and new data products combining information from different surveys.