Bayesian generalized structural equation modeling

Structural equation models (SEMs) provide a very general framework for modeling relationships among multivariate variables. The main goal of this study is to develop a Bayesian generalized SEMs framework that could accommodate a broader class of (mixed) observed variables and (mixed) latent variables in the exponential family. Incorporating the generalized linear latent variable model into the measurement model and the generalized linear model in the structural model, our Bayesian generalized SEMs framework could accommodate a great variety of (mixed) data from the exponential family distributions, including categorical, count and continuous data. We also extend the parametric relationships between latent variables to the semiparametric relationship, where the relationship is not predetermined, but suggested from the data. Fixed covariates and multilevel structure of the data will be incorporate into our modeling framework also. Using simulation studies, we found that our generalized modeling framework is satisfactory in estimating the model parameters of SEMs with mixed count, binary or normal observed variables and in uncovering the true relationship between latent variables. The proposed modeling framework was then applied to study the multivariate relationship between dietary factors and multivariate metabolic syndrome.