MSG function

Maximal summary graph

MAG generates and plots maximal summary graphs after marginalization and conditioning.

MSG(amat,M=c(),C=c(),showmat=TRUE,plot=FALSE, plotfun = plotGraph, ...)

Arguments

• amat: An adjacency matrix of a MAG, or a graph that can be a graphNEL or an igraph object or a vector of length $3e$, where $e$ is the number of edges of the graph, that is a sequence of triples (type, node1label, node2label). The type of edge can be "a" (arrows from node1 to node2), "b" (arcs), and "l" (lines).

• M: A subset of the node set of a that is going to be marginalized over

• C: Another disjoint subset of the node set of a that is going to be conditioned on.

• showmat: A logical value. TRUE (by default) to print the generated matrix.

• plot: A logical value, FALSE (by default). TRUE to plot the generated graph.

• plotfun: Function to plot the graph when plot == TRUE. Can be plotGraph (the default) or drawGraph.

• ...: Further arguments passed to plotfun.

Details

This function uses the functions SG and Max.

Returns

A matrix that consists 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.

References

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

Sadeghi, K. (2013). Stable mixed graphs. Bernoulli 19(5B), 2330–2358.

Sadeghi, K. and Lauritzen, S.L. (2014). Markov properties for loopless mixed graphs. Bernoulli 20(2), 676-696.

Wermuth, N. (2011). Probability distributions with summary graph structure. Bernoulli, 17(3), 845-879.

Author(s)

Kayvan Sadeghi

See Also

MAG, Max, MRG, SG

Examples

ex<-matrix(c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, ##The adjacency matrix of a DAG
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
             1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
             0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
             0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
             0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,
             0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
             0,0,0,0,1,0,1,0,1,1,0,0,0,0,0,0,
             1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
             0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
             1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
             0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0), 16, 16, byrow=TRUE)
M <- c(3,5,6,15,16)
C <- c(4,7)
MSG(ex,M,C,plot=TRUE)
###################################################
H<-matrix(c(0,100,1,0,100,0,100,0,0,100,0,100,0,1,100,0),4,4)
Max(H)