| This dissertation presents new computational techniques for multivariate multilevel data with missing values. Current methodology for linear mixed-effects models can accommodate imbalance or missing data in a single response variable, but it cannot handle missing values in multiple responses or additional covariates. In the first part of this dissertation, I develop a new hybrid EM algorithm for parameter estimation and model fitting. This EM algorithm converges more rapidly than traditional EM algorithms because it does not treat the random effects as 'missing data', but integrates them out of the likelihood function analytically. In the second part, I describe a variety of procedures for creating multiple imputations of missing covariates and responses in multivariate multilevel data. These procedures, based on Markov Chain Monte Carlo, are flexible enough to preserve random variation in both means and covariances across individuals or clusters. These techniques are illustrated on two data examples. The first application involves growth-curve modeling of adolescent alcohol use in a large school-based substance-use prevention trial. The second application involves the imputation of missing values in a Seattle crime victimization survey. |
