ggm (version 2.5.1)

makeMG: Mixed Graphs

Description

Defines a loopless mixed graph from the directed, undirected and undirected components.

Usage

makeMG(dg = NULL, ug = NULL, bg = NULL)

Value

a square matrix obtained by combining the three graph components into an adjacency matrix of a mixed graph. The matrix consists of 4 different integers as an \(ij\)-element: 0 for a missing edge between \(i\) and \(j\), 1 for an arrow from \(i\) to \(j\), 10 for a full line between

\(i\) and \(j\), and 100 for a bi-directed arrow between \(i\) and \(j\). These numbers are added to be associated with multiple edges of different types. The matrix is symmetric w.r.t full lines and bi-directed arrows.

Arguments

dg

the adjacency matrix of a directed graph specifying the arrows of the mixed graph.

ug

the adjacency matrix of an undirected graph specifying the lines of the mixed graph.

bg

the adjacency matrix of an undirected graph specifying the bidirected edges of the mixed graph.

Author

Giovanni M. Marchetti, Mathias Drton

Details

A loopless mixed graph is a mixed graph with three types of edges: undirected, directed and bi-directed edges. Note that the three adjacency matrices must have labels and may be defined using the functions DG, DAG or UG. The adjacency matrices of the undirected graphs may be just symmetric Boolean matrices.

References

Richardson, T. S. and Spirtes, P. (2002). Ancestral Graph Markov Models. Annals of Statistics, 30(4), 962--1030.

See Also

UG, DAG

Examples

## Examples from Richardson and Spirtes (2002)
a1 <- makeMG(dg=DAG(a~b, b~d, d~c), bg=UG(~a*c))  
isAG(a1)    # Not an AG. (a2) p.969    
a2 <- makeMG(dg=DAG(b ~ a, d~c), bg=UG(~a*c+c*b+b*d))           # Fig. 3 (b1) p.969  
isAG(a1)
a3 <- makeMG(ug = UG(~ a*c), dg=DAG(b ~ a, d~c), bg=UG(~ b*d)) # Fig. 3 (b2) p.969
a5 <- makeMG(bg=UG(~alpha*beta+gamma*delta), dg=DAG(alpha~gamma,
delta~beta))  # Fig. 6 p. 973
## Another Example
a4 <- makeMG(ug=UG(~y0*y1), dg=DAG(y4~y2, y2~y1), bg=UG(~y2*y3+y3*y4))  
## A mixed graphs with double edges. 
mg <- makeMG(dg = DG(Y ~ X, Z~W, W~Z, Q~X), ug = UG(~X*Q), 
bg = UG(~ Y*X+X*Q+Q*W + Y*Z) )
## Chronic pain data: a regression graph
chronic.pain <- makeMG(dg = DAG(Y ~ Za, Za ~ Zb + A, Xa ~ Xb, 
Xb ~ U+V, U ~ A + V, Zb ~ B, A ~ B), bg = UG(~Za*Xa + Zb*Xb))