Semiparametric Bayesian analysis of structural equation models with fixed covariates.

Latent variables play the most important role in structural equation modeling. In almost all existing structural equation models (SEMs), it is assumed that the distribution of the latent variables is normal. As this assumption is likely to be violated in many biomedical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of SEMs with covariates, we provide a general Bayesian framework in which a semiparametric hierarchical modeling with an approximate truncation Dirichlet process prior distribution is specified for the latent variables. The stick-breaking prior and the blocked Gibbs sampler are used for efficient simulation in the posterior analysis. The developed methodology is applied to a study of kidney disease in diabetes patients. A simulation study is conducted to reveal the empirical performance of the proposed approach. Supplementary electronic material for this paper is available in Wiley InterScience at http://www.mrw.interscience.wiley.com/suppmat/1097-0258/suppmat/. (c) 2007 John Wiley & Sons, Ltd.