Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm

Typical data that arise from surveys, experiments, and observational studies include continuous and discrete variables. In this article, we study the interdependence among a mixed (continuous, count, ordered categorical, and binary) set of variables via graphical models. We propose an (1)-penalized extended rank likelihood with an ascent Monte Carlo expectation maximization approach for the copula Gaussian graphical models and establish near conditional independence relations and zero elements of a precision matrix. In particular, we focus on high-dimensional inference where the number of observations are in the same order or less than the number of variables under consideration. To illustrate how to infer networks for mixed variables through conditional independence, we consider two datasets: one in the area of sports and the other concerning breast cancer