A Bayesian Structural Equations Model for Multilevel Data with Missing Responses and Missing Covariates

Motivated by a large multilevel survey conducted by the US Veterans Health Administration (VHA), we propose a structural equations model which involves a set of latent variables to capture dependence between different responses, a set of facility level random effects to capture facility heterogeneity and dependence between individuals within the same facility, and a set of covariates to account for individual heterogeneity. Identifiability associated with structural equations modeling is addressed and properties of the proposed model are carefully examined. An effective and practically useful modeling strategy is developed to deal with missing responses and to model missing covariates in the structural equations framework. Markov chain Monte Carlo sampling is used to carry out Bayesian posterior computation. Several variations of the proposed model are considered and compared via the deviance information criterion. A detailed analysis of the VHA all employee survey data is presented to illustrate the proposed methodology.