Diagnostic checking of multiple imputation models

Model checking in multiple imputation (MI, Rubin in Multiple imputation for nonresponse in surveys, Wiley, New York, 1987) becomes increasingly important with the recent developments in MI and its widespread use in statistical analysis with missing data (e.g. van Buuren et al. in J Stat Comput Simul 76(12):1049–1064, 2006; van Buuren and Groothuis-Oudshoorn in J Stat Soft 45(3):1–67, 2011; Chen et al. in Biometrics 67:799–809, 2011; Nguyen et al. in Emerg Themes Epidemiol 14(8):1–12, 2017). The currently recommended posterior predictive checking method (He and Zaslavsky in Stat Med 31:1–18, 2012; Nguyen et al. in Biom J 4:676–694, 2015) is less effective when the proportion of missing values increases and its produced posterior predictive p value is not supported by a null distribution as a standard p value (Meng in Annu Stat 22:1142–1160, 1994). This research develops a new diagnostic method for checking MI models and proposes a test statistic with a standard p value. The new diagnostic checking method is effective and flexible. It does not depend on the proportion of missing values and can deal with data sets with arbitrary nonmonotone missing data patterns. We examine the performance of the proposed method in a simulation study and illustrate the method in a study of coronary disease and associated factors.