Table 2.

Summary of the imputation approaches for handling incomplete three-level data

MI approach	Paradigm	Model	Softwarea	How the two sources of clustering are handled
				Clustering due to higher level clusters	Clustering due to repeated measures
JM-1L-DI-wide	JM	Standard (single-level)	SAS [64], SPSS [36], Stata [35], Mplus [24], R [46]	DI	Repeated measures arranged in wide format
FCS-1L-DI-wide	FCS	Standard (single-level)	SAS, SPSS, Stata, Mplus, R, Blimp [26]	DI	Repeated measures arranged in wide format
JM-2L-wide	JM	Two-level MLMM	SAS [28], Mplus, Realcom-impute [23], Stat-JR [29], R	RE	Repeated measures arranged in wide format
JM-2L-wide				DI	RE
FCS-2L-wide	FCS	Two-level LMM	Mplus, R, Blimp	RE	Repeated measures arranged in wide format
FCS-2L-DI				DI	RE
JM-3L	JM	Three-level MLMM	Stat-JR, Mplus	RE	RE
CS-3L	FCS	Three-level LMM	R, Blimp	RE	RE

DI dummy indicators, FCS fully conditional specification, JM joint modelling, LMM linear mixed model, MLMM multivariate linear mixed model, RE random effects

^aR and Blimp are the only freely available, open-source software implementations