We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompass many studies from social science and economics. We illustrate the use of the copula Gaussian graphical models in three representative datasets.

Keywords: Bayesian inference, Gaussian graphical models, latent variable model, Markov chain Monte Carlo.