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

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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.