Multilevel multiple imputation: A review and evaluation of joint modeling and chained equations imputation.

Although missing data methods have advanced in recent years, methodologists have devoted less attention to multilevel data structures where observations at level-1 are nested within higher-order organizational units at level-2 (e.g., individuals within neighborhoods; repeated measures nested within individuals; students nested within classrooms). Joint modeling and chained equations imputation are the principal imputation frameworks for single-level data, and both have multilevel counterparts. These approaches differ algorithmically and in their functionality; both are appropriate for simple random intercept analyses with normally distributed data, but they differ beyond that. The purpose of this paper is to describe multilevel imputation strategies and evaluate their performance in a variety of common analysis models. Using multiple imputation theory and computer simulations, we derive 4 major conclusions: (a) joint modeling and chained equations imputation are appropriate for random intercept analyses; (b) the joint model is superior for analyses that posit different within- and between-cluster associations (e.g., a multilevel regression model that includes a level-1 predictor and its cluster means, a multilevel structural equation model with different path values at level-1 and level-2); (c) chained equations imputation provides a dramatic improvement over joint modeling in random slope analyses; and (d) a latent variable formulation for categorical variables is quite effective. We use a real data analysis to demonstrate multilevel imputation, and we suggest a number of avenues for future research. (PsycINFO Database Record (c) 2016 APA, all rights reserved).