Bayesian Gaussian Copula Graphical Models for Ordinal Survey Data

Thomas M. Menino Convention & Exhibition Center 

It is challenging to assess conditional dependence among a large set of discrete random variables. Bayesian Gaussian copula graphical model is applied to estimate the conditional dependence for ordinal variables. Following the idea of the graphical Lasso prior, graphical spike-and-slab Lasso prior is proposed for the regularization purpose. A block Gibbs sampling scheme is then developed for the posterior computation. We further extend the graphical spike-and-slab Lasso prior to an adaptive version by allowing the parameter of the spike component tying to a prior.
Simulation study is conducted to compare the performance of using different priors.
Simulation results show a good estimation performance of estimating the latent precision matrix when using the graphical Lasso prior and the graphical spike-slab Lasso prior with a relatively large spike parameter. In terms of the graph structure learning, the adaptive graphical Lasso prior and the adaptive graphical spike-slab Lasso prior have a better performance. We then utilize the proposed methods to analyze the survey data about the physiological and psychological health of current Chinese college students.

Conditional independence

Gaussian copula

Graphical Lasso

Partial correlation

Precision matrix

Spike-and-slab 

Section on Bayesian Statistical Science