Posterior Predictive Checking of Imputation Models
We explore use of posterior predictive checks to assess the adequacy of imputation models. One strategy applies analyses of substantive interest to both the completed data with imputations and replicated copies of the completed data under the imputation model and compares the results. Posterior predictive p-values for the differences of these estimates quantify the evidence of misfit of the imputation model. A variant of this strategy integrates out the missing data and their replicates using multiple imputation, yielding posterior predictive p-values that are generally more powerful than those estimated using the completed data. The checking procedure can be easily implemented in many cases using standard imputation software by treating re-imputations under the model as posterior predictive replicates, and thus can be applied for methods that are not fully Bayesian.