MRG: Maximal ribbonless graph

In ggm: Graphical Markov Models with Mixed Graphs

Maximal ribbonless graph

Description

MRG generates and plots maximal ribbonless graphs (a modification of MC graph to use m-separation) after marginalisation and conditioning.

Usage

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

Arguments

amat	An adjacency matrix, 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 RG and Max.

Value

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.

Author(s)

Kayvan Sadeghi

References

Koster, J.T.A. (2002). Marginalizing and conditioning in graphical models. Bernoulli, 8(6), 817-840.

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.

See Also

MAG, Max, MSG, RG

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)
MRG(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)

ggm documentation built on May 29, 2024, 7:27 a.m.