ABSTRACT
In the final chapter of the book we briefly touch on some advanced topics of multiple imputation analysis. We use simulation examples to illustrate the idea of imputation uncongeniality, where the assumptions behind the imputation model and completed-data analysis procedure are different. This frequently happens in practice. Some interesting phenomenon such as superefficiency could happen. However, there should be less concern about the inference if the imputation model has a rather general assumption and follows the inclusive imputation strategy. We also discuss about possible extensions of multiple imputation combining rules. When the normality assumption of estimands is violated, it is possible that some variance-stabilizing transformation can be used in the combining process. There are other alternative options for combining estimates including mixing the posterior distributions of parameters or bootstrap distributions of estimates from multiply imputed datasets. When completed-data analysis is more than just an estimate, such as variable selection, the combining process can become less straightforward, and we provide some brief literature review on that topic. Finally, in the era of big data and data science, practitioners often have to face a large volume of data or variables that cannot be handled well by traditional statistical models. We cite some examples from the literature regarding imputation for high-dimensional data. The models and techniques used in these examples include applying ridge-prior distributions, factor analysis models, latent-class models and their extensions, all of which effectively reduce the dimension of variables. New missing data problems and analysis needs keep calling for new ideas of multiple imputation analysis!
