In this article, we consider the problem of reconstructing networks for
continuous, binary, count and discrete ordinal variables by estimating sparse
precision matrix in Gaussian copula graphical models. We propose two
approaches: β1β penalized extended rank likelihood with Monte Carlo
Expectation-Maximization algorithm (copula EM glasso) and copula skeptic with
pair-wise copula estimation for copula Gaussian graphical models. The proposed
approaches help to infer networks arising from nonnormal and mixed variables.
We demonstrate the performance of our methods through simulation studies and
analysis of breast cancer genomic and clinical data and maize genetics data