dag2pag function

Convert a DAG with latent variables into a PAG

Convert a DAG with latent variables into its corresponding (unique) Partial Ancestral Graph (PAG).

UTF8

dag2pag(suffStat, indepTest, graph, L, alpha, rules = rep(TRUE,10),
        verbose = FALSE)

Arguments

• suffStat: the sufficient statistics, a list

  containing all necessary elements for the conditional independence decisions in the function indepTest.

• indepTest: a function for testing conditional independence. The function is internally called as indepTest(x,y,S,suffStat), and tests conditional independence of x and y given S. Here, x and y are variables, and S is a (possibly empty) vector of variables (all variables are denoted by their column numbers in the adjacency matrix). suffStat is a list containing all relevant elements for the conditional independence decisions. The return value of indepTest() is the p-value of the test for conditional independence.

• graph: a DAG with p nodes, a graph object. The graph must be topological sorted (for example produced using randomDAG).

• L: array containing the labels of the nodes in the graph

  corresponding to the latent variables.

• alpha: significance level in $(0,1)$ for the individual conditional independence tests.

• rules: logical vector of length 10 indicating which rules should be used when directing edges. The order of the rules is taken from Zhang (2009).

• verbose: logical; if TRUE, detailed output is provided.

Details

This function converts a DAG (graph object) with latent variables into its corresponding (unique) PAG, an fciAlgo class object, using the ancestor information and conditional independence tests entailed in the true DAG. The output of this function is exactly the same as the one using

fci(suffStat, gaussCItest, p, alpha, rules = rep(TRUE, 10))

using the true correlation matrix in gaussCItest() with a large virtual sample size and a large alpha, but it is much faster, see the example.

Returns

An object of class fciAlgo, containing the estimated graph (in the form of an adjacency matrix with various possible edge marks), the conditioning sets that lead to edge removals (sepset) and several other parameters.

References

Richardson, T. and Spirtes, P. (2002). Ancestral graph Markov models. Ann. Statist. 30 , 962--1030; Theorem 4.2., page 983.

Author(s)

Diego Colombo and Markus Kalisch kalisch@stat.math.ethz.ch .

See Also

fci, pc

Examples

## create the graph
set.seed(78)
g <- randomDAG(10, prob = 0.25)
graph::nodes(g) # "1" "2" ... "10" % FIXME: should be kept in result!

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

## compute the true covariance matrix of g
cov.mat <- trueCov(g)
## transform covariance matrix into a correlation matrix
true.corr <- cov2cor(cov.mat)

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

### ---- Find PAG using fci-function --------------------------

## From trueCov(g), delete rows and columns belonging to latent variable L
true.cov1 <- cov.mat[-L,-L]
## transform covariance matrix into a correlation matrix
true.corr1 <- cov2cor(true.cov1)

## Find PAG with FCI algorithm
## as dependence "oracle", we use the true correlation matrix in
## gaussCItest() with a large "virtual sample size" and a large alpha:
system.time(
true.pag1 <- fci(suffStat = list(C = true.corr1, n = 10^9),
                 indepTest = gaussCItest,
                 p = ncol(true.corr1), alpha = 0.9999) )

## confirm that the outputs are equal
stopifnot(true.pag@amat == true.pag1@amat)