nference in Graphical Gaussian Models with Edge and Vertex Symmetries with the gRc Package for R

Abstract

In this paper we present the R package gRc for statistical inference in graphical Gaussian models in which symmetry restrictions have been imposed on the concentration or partial correlation matrix. The models are represented by coloured graphs where parameters associated with edges or vertices of same colour are restricted to being identical. We describe algorithms for maximum likelihood estimation and discuss model selection issues. The paper illustrates the practical use of the gRc package.

Keywords

• concentration matrix
• conditional independence
• covariance selection
• graphical model
• graph
• graph colouring
• iterative partial maximization
• iterative proportional scaling
• multivariate normal distribution
• partial correlation