A Semi-Parametric Multiple Imputation Data Augmentation Procedure

Multiple imputation procedures (MI) are a useful tool to adjust for item non-response but are often based on fully parametric assumptions, such as multivariate normality. For many applications such assumptions may not hold in practice, for example if the data are skewed and affected by rounding and truncation effects. Hot deck imputation methods, however, make less or no assumptions about underlying distributions and may be more appropriate to use in such circumstances. The basic idea is to combine multiple imputation and hot deck approaches with the aim of preserving advantageous properties of MI and at the same time relaxing distributional assumptions. This paper develops a semi-parametric data augmentation method to generate MI under the missing at random assumption and a nonignorable missing data mechanism. The use of predictive mean matching as a form of hot deck imputation is considered as part of the data augmentation procedure to improve the robustness of the multiple imputation method.