Substantive model compatible multilevel multiple imputation: A joint modeling approach.

Abstract

Substantive model compatible multiple imputation (SMC-MI) is a relatively novel imputation method that is particularly useful when the analyst's model includes interactions, non-linearities, and/or partially observed random slope variables. Here we thoroughly investigate a SMC-MI strategy based on joint modeling of the covariates of the analysis model. We provide code to apply the proposed strategy and we perform an extensive simulation work to test it in various circumstances. We explore the impact on the results of various factors, including whether the missing data are at the individual or cluster level, whether there are non-linearities and whether the imputation model is correctly specified. Finally, we apply the imputation methods to the motivating example data. SMC-JM appears to be superior to standard JM imputation, particularly in presence of large variation in random slopes, non-linearities, and interactions. Results seem to be robust to slight mis-specification of the imputation model for the covariates. When imputing level 2 data, enough clusters have to be observed in order to obtain unbiased estimates of the level 2 parameters. SMC-JM is preferable to standard JM imputation in presence of complexities in the analysis model of interest, such as non-linearities or random slopes.