Graphical and numerical diagnostic tools to assess suitability of multiple imputations and imputation models.

Multiple imputation has become a popular approach for analyzing incomplete data. Many software packages are available to multiply impute the missing values and to analyze the resulting completed data sets. However, diagnostic tools to check the validity of the imputations are limited, and the majority of the currently available methods need considerable knowledge of the imputation model. In many practical settings, however, the imputer and the analyst may be different individuals or from different organizations, and the analyst model may or may not be congenial to the model used by the imputer. This article develops and evaluates a set of graphical and numerical diagnostic tools for two practical purposes: (i) for an analyst to determine whether the imputations are reasonable under his/her model assumptions without actually knowing the imputation model assumptions; and (ii) for an imputer to fine tune the imputation model by checking the key characteristics of the observed and imputed values. The tools are based on the numerical and graphical comparisons of the distributions of the observed and imputed values conditional on the propensity of response. The methodology is illustrated using simulated data sets created under a variety of scenarios. The examples focus on continuous and binary variables, but the principles can be used to extend methods for other types of variables.