Graphical Markov Models with Mixed Graphs in R

Abstract

In this paper we provide a short tuto- rial illustrating the new functions in the package ggm that deal with ancestral, summary and rib- bonless graphs. These are mixed graphs (con- taining three types of edges) that are impor- tant because they capture the modified inde- pendence structure after marginalisation over, and conditioning on, nodes of directed acyclic graphs. We provide functions to verify whether a mixed graph implies that A is independent of B given C for any disjoint sets of nodes and to generate maximal graphs inducing the same independence structure of non-maximal graphs. Finally, we provide functions to decide on the Markov equivalence of two graphs with the same node set but different types of edges. Introduction and background Graphical Markov models have become a part of the mainstream of statistical theory and application in recent years. These models use graphs to represent conditional independencies among sets of random variables. Nodes of the graph correspond to random variables and edges to some type of conditional de- pendency.