On the use of hierarchical models for multiple imputation and synthetic data generation

Abstract

Missing data are often imputed with plausible values when various analyses are performed. One popular approach employed to impute data is multiple imputation, which requires specification of a suitable imputation model. This thesis investigates the impact on multiply imputed hierarchical datasets when the imputation model is misspecified. The first issue studied is the presence of omitted variable bias. The same issue is then studied with a focus on the use of multiple imputation for creating synthetic data to protect data confidentiality. Here, the quality of multiply imputed datasets is studied not only through performance of various analysis models, but also, risks of disclosure for sensitive data. With the help of simulation studies and a longitudinal dataset from establishments in Germany, the detrimental effect of such model misspecification is evaluated, and recommendations are made for users of multiple imputation for both missing and synthetic data. The second issue investigated is model misspecification due to incorrect modelling of the shape of the error term. Existing methods for robust regression and alternatives to the normal distribution are compared within the synthetic data context only. Results from simulation studies and data on household wealth in the UK are used to identify appropriate methods for multiple imputation in such a scenario.

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