pag2mag: Transform a PAG into a MAG in the Corresponding Markov Equivalence Class

Description

Transform a Partial Ancestral Graph (PAG) into a valid Maximal Ancestral Graph (MAG) that belongs to the Markov equivalence class represented by the given PAG, with no additional edges into node x.

Usage

pag2magAM(amat.pag, x, max.chordal = 10, verbose = FALSE)

Arguments

amat.pag

Adjacency matrix (coding 0,1,2,3 for no edge, circle, arrowhead, tail; e.g., amat[a,b] = 2 and amat[b,a] = 3 implies a -> b)

Node in the PAG into which no additional edges are oriented.

max.chordal

Positive integer: graph paths larger than max.chordal are considered to be too large to be checked for chordality.

verbose

Logical; if true, some output is produced during computation.

Value

The output is an adjacency matrix M of a valid MAG with edge marks. The edge marks are coded in the following way: M[i,j]=M[j,i]=0: no edge; M[i,j]=2, M[j,i]=3: i -> j; M[i,j]=2, M[j,i]=2: i <-> j.

Details

This function converts a PAG (adjacency matrix) to a valid MAG (adjacency matrix) that belongs to the Markov equivalence class represented by the given PAG. Note that we assume that there are no selection variables, meaning that the edges in the PAG can be of the following types: ->, <->, o->, and o-o. In a first step, it uses the Arrowhead Augmentation of Zhang (2006), i.e., any o-> edge is oriented into ->. Afterwards, it orients each chordal component into a valid DAG without orienting any additional edges into x.

This function is used in the Generalized Backdoor Criterion backdoor with type="pag", see Maathuis and Colombo (2013) for details.

References

M.H. Maathuis and D. Colombo (2013). A generalized backdoor criterion. arXiv preprint arXiv:1307.5636.

Zhang, J. (2006). Causal Inference and Reasoning in Causally Insufficient Systems. Ph. D. thesis, Carnegie Mellon University.

Examples

Run this code

## create the graph
set.seed(78)
p <- 12
g <- randomDAG(p, prob = 0.4)
## Compute the true covariance and then correlation matrix of g:
true.corr <- cov2cor(trueCov(g))

## define nodes 2 and 6 to be latent variables
L <- c(2,6)

## Find PAG
## As dependence "oracle", we use the true correlation matrix in
## gaussCItest() with a large "virtual sample size" and a large alpha:
true.pag <- dag2pag(suffStat = list(C= true.corr, n= 10^9),
                    indepTest= gaussCItest, graph=g, L=L, alpha= 0.9999)

## find a valid MAG such that no additional edges are directed into
(amat.mag <- pag2magAM(true.pag@amat, 4)) # -> the adj.matrix of the MAG

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