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We present and compare multiple imputation methods for multilevel continuousand binary data where variables are systematically and sporadically missing.  The methods are compared from a theoretical point of view and through anextensive simulation study motivated by a real dataset comprising multiplestudies. Simulations are reproducible. The comparisons show why these multipleimputation methods are the most appropriate to handle missing values in amultilevel setting and why their relative performances can vary according tothe missing data pattern, the multilevel structure and the type of missingvariables.  This study shows that valid inferences can only be obtained if the datasetgathers a large number of clusters. In addition, it highlights thatheteroscedastic MI methods provide more accurate inferences than homoscedasticmethods, which should be reserved for data with few individuals per cluster.Finally, the method of Quartagno and Carpenter (2016a) appears generallyaccurate for binary variables, the method of Resche-Rigon and White (2016) withlarge clusters, and the approach of Jolani et al. (2015) with small clusters.

Multiple imputation for multilevel data with continuous and binary variables