Fractional Imputation for Missing Data in Social Surveys

DMS-0532413NSF计划：数学、社会和行为科学研究所：爱荷华州立大学首席研究员和合作PI：Larsen，Michael D.，Kang，Shin-soo和Lorentz，Frederick O.标题：社会调查中缺失数据的分数归责摘要对于行为、经济、健康和社会科学中几乎所有大规模调查和研究项目来说，丢失数据都是一个严重的问题。只分析完整的案例会减少样本量，通常会引入偏差，并且会忽略变量之间关系的信息。用单个值替换缺失的观测值将产生完整的数据集，但将完整的数据视为全部真实数据会导致对精度的夸大，并可能导致毫无根据的结论。倍数和分数归因法不是用一个，而是用多个，比方说五个似是而非的值来取代每个缺失的值。使用多个完整的数据集进行的单独分析的结果根据理论推导的规则组合。值得关注的是，当从有限总体中进行抽样时，以及当样本量从中等到小时，多种归算方法的性能。Kim(2004)和Kim和Fuller(2004)最近的理论工作引入了分数补偿(FI)，并阐明了多重补偿方差估计的一个缺陷。对他们工作的一些扩展是可行的，预计将极大地增加行为科学和社会科学研究人员对FI的可用性。缺失数据的模型可以通过利用变量之间的关系来帮助减少或消除偏差，并保持统计能力。FI为研究人员提供了一种计算有效标准误差和由此产生的可信区间和假设检验的方法。为了使行为科学和社会科学的研究人员能够充分利用FI的优势，需要开发用于分类数据、混合连续数据和分类数据以及一般缺失数据模式的FI。对于行为、经济和社会科学中的许多研究来说，数据缺失是一个严重的问题。当受访者没有提供所需数据时，随后的分析可能会有偏见，精确度会降低。通常，研究人员只是忽略了一些观测数据缺失的事实，并根据观测数据来报告结果。虽然这是权宜之计，但这并不是一个推荐的程序。在家庭转变研究中，对男性和女性的缺失反应进行归罪对于保持样本规模和统计能力非常重要。对缺失数据的另一种常见反应是用替换值填充空白处。这些值可以来自观察到的相似个体，可以通过模型预测，也可以通过无响应加权隐式处理。这些方法，如果实施得当，有足够的数据，可以减少偏见。不幸的是，单一的推论如果被视为真实的，可能会导致对不确定性的低估。已经开发了多重和分数补偿方法来反映由于缺少信息而产生的不确定性，目的是使研究人员既可以纠正由于缺少信息而导致的偏差，又可以基于观测数据得出有效的结论。缺失值分数推算理论、方法和程序的发展将极大地提高分数推算在经济、行为和社会科学问题上的适用性。研究丢失的数据、其原因和影响以及可能的补救措施，对于保持家庭过渡项目研究的高质量和梅奥诊所的长期研究至关重要。

DMS - 0532413NSF PROGRAM: Mathematical, Social, and Behavioral SciencesInstitutions: Iowa State UniversityPrincipal Investigators and co-PIs: Larsen, Michael D., Kang, Shin-Soo, and Lorentz, Frederick O.Title: Fractional Imputation for Missing data in Social SurveysABSTRACTMissing data are a serious problem for practically all large-scale surveys and research projects in the behavioral, economic, health, and social sciences. Analyzing only the complete cases reduces sample size, often introduces bias, and ignores information concerning relationships among variables. Substituting single values for the missing observations produces a complete data set, but treating the completed data as if they all were real leads to an overstatement of precision and, potentially, unwarranted conclusions. Multiple and fractional imputation are methods that replace each missing value not with one but with multiple, say five, plausible values. Results from separate analyses using the multiple completed data sets are combined according to theoretically derived rules. Of concern is the performance of multiple imputation methods when sampling from a finite population and when sample sizes are moderate to small. Recent theoretical work by Kim (2004) and Kim and Fuller (2004) ntroduced fractional imputation (FI) and elucidated a shortcoming of multiple imputation variance estimation. A number of extensions to their work are feasible and expected to increase greatly the usability of FI by researchers in the behavioral and social sciences. Models for missing data can help reduce or eliminate bias and maintain statistical power by utilizing relationships among variables. FI provides a way for researchers to calculate valid standard errors and resulting confidence intervals and hypothesis tests. In order for researchers in the behavioral and social sciences to use FI to its full advantage, development of FI for categorical data, mixed continuous and categorical data, and general missing data patterns is needed. Missing data are a serious problem for many research studies in the behavioral, economic, and social sciences. When respondents do not provide the desired data, subsequent analyses can be biased and less precise. Frequently researchers simply ignore the fact that some observations are missing and report results based on those that are observed. Although expedient, this is not a recommended procedure. In the Family Transitions Study, imputation for missing responses from men and women have been very important for maintaining sample size and statistical power. Another common response to missing data is to impute or fill-in the empty space with a substitute value. Values can be donated from observed similar individuals, predicted through a model, or handled implicitly through nonresponse weighting. These methods, if implemented appropriately with adequate data, can reduce bias. Unfortunately, single imputations if treated as real can lead to understatements of uncertainty. Multiple and fractional imputation methods have been developed to reflect uncertainty due to missing information and aim to allow researchers to both correct for bias due to missing information and reach valid conclusions based on the observed data. The development of theory, methods, and procedures for fractional imputation of missing values will greatly enhance the applicability of fractional imputation to problems in economic, behavioral, and social sciences. Study of missing data, its causes and effects and possible remedies, is critical for the maintenance of the high quality of the Family Transitions Project study and for long-term research studies at the Mayo clinic.