Bayesian Structural Equations Modeling for Ordinal Response Data with Missing Responses and Missing Covariates

Structural equations models (SEMs) have been extensively used to model survey data arising in the fields of sociology, psychology, health, and economics with increasing applications where self assessment questionnaires are the means to collect the data. We propose the SEM for multilevel ordinal response data from a large multilevel survey conducted by the US Veterans Health Administration (VHA). The proposed model 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. An effective and practically useful modeling strategy is developed to deal with missing responses and to model missing covariates in the structural equations framework. A Markov chain Monte Carlo sampling algorithm is developed for sampling from the posterior distribution. The deviance information criterion measure is used to compare several variations of the proposed model. The proposed methodology is motivated and illustrated by using the VHA All Employee Survey data.