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We propose a comprehensive Bayesian approach for graphical modeldetermination in observational studies that can accommodate binary, ordinal orcontinuous variables simultaneously. Our new models are called copula Gaussiangraphical models (CGGMs) and embed graphical model selection inside asemiparametric Gaussian copula. The domain of applicability of our methods isvery broad and encompasses many studies from social science and economics. Weillustrate the use of the copula Gaussian graphical models in the analysis of a16-dimensional functional disability contingency table.

Copula Gaussian graphical models and their application to modeling functional disability data