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

Abstract

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.

Keywords:

• DIC
• Latent variable
• Markov chain Monte Carlo
• Missing at random
• Ordinal response data
• Random effects
• VHA all employee survey data

Mathematics Subject Classification:

• 62F15
• 91C99
• 65C05

Acknowledgments

The authors wish to thank the Guest Editor and a referee for helpful comments which have led to an improvement of this article. The authors also wish to acknowledge and thank the Veterans Health Administration and the National Center for Organizational Development for access to the All Employee Survey (AES) 2001 data and their substantial efforts to insure the quality and integrity of these data. Dr. Kim's research is supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development; National Institutes of Health. Dr. Chen's research was partially supported by NIH grants \#GM 70335 and \#CA 74015 and a Faculty Large Research Grant from University of Connecticut. Dr. Warren's research was funded by the VHA National Center for Organizational Development.