Graphical and numerical diagnostic tools to assess multiple imputation models by posterior predictive checking

Abstract

Problem: The congenial of the imputation model is crucial for valid statistical inferences. Hence, it is important to develop methodologies for diagnosing imputation models. Aim: We propose and evaluate a new diagnostic method based on posterior predictive checking to diagnose the congeniality of fully conditional imputation models. Our method applies to multiple imputation by chained equations, which is widely used in statistical software. Methods: The proposed method compares the observed data with their replicates generated under the corresponding posterior predictive distributions to diagnose the performance of imputation models. The method applies to various imputation models, including parametric and semi-parametric approaches and continuous and discrete incomplete variables. We studied the validity of the method through simulation and application. Results: The proposed diagnostic method based on posterior predictive checking demonstrates its validity in assessing the performance of imputation models. The method can diagnose the consistency of imputation models with the substantive model and can be applied to a broad range of research contexts. Conclusion: The diagnostic method based on posterior predictive checking provides a valuable tool for researchers who use fully conditional specification to handle missing data. By assessing the performance of imputation models, our method can help researchers improve the accuracy and reliability of their analyzes. Furthermore, our method applies to different imputation models. Hence, it is a versatile and valuable tool for researchers identifying plausible imputation models.