Fractional Imputation for Missing Data in Social Surveys

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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.