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MRG

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. (2011). Stable classes of graphs containing directed acyclic graphs. Submitted.

Sadeghi, K. and Lauritzen, S.L. (2011). Markov properties for loopless mixed graphs. Submitted. URL http://arxiv.org/abs/1109.5909.

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

Graphical Markov Models with Mixed Graphs

v2.5

GPL-2

Authors

Giovanni M. Marchetti, Mathias Drton, Kayvan Sadeghi

Initial release

2020-02-014

MRG