Multiple imputation inference for multivariate multilevel continuous data with ignorable non-response

Methods specifically targeting missing values in a wide spectrum of statistical analyses are now part of serious statistical thinking due to many advances in computational statistics and increased awareness among sophisticated consumers of statistics. Despite many advances in both theory and applied methods for missing data, missing-data methods in multilevel applications lack equal development. In this paper, I consider a popular inferential tool via multiple imputation in multilevel applications with missing values. I specifically consider missing values occurring arbitrarily at any level of observational units. I use Bayesian arguments for drawing multiple imputations from the underlying (posterior) predictive distribution of missing data. Multivariate extensions of well-known mixed-effects models form the basis for simulating the posterior predictive distribution, hence creating the multiple imputations. The discussion of these topics is demonstrated in an application assessing correlates to unmet need for mental health care among children with special health care needs.