network_to_SEset {SEset}

SE-set from precision matrix

Description

Takes a precision matrix and generates the SE-set, a set of statistically equivalent path models. Unless otherwise specified, the SEset will contain one weights matrix for every possible topological ordering of the input precision matrix

Usage

network_to_SEset(
  omega,
  orderings = NULL,
  digits = 20,
  rm_duplicates = FALSE,
  input_type = "precision"
)

Arguments

omega

input p \times p precision matrix

orderings

An optional matrix of n orderings from which to generate the SE-set. Must be in the form of a p \times n matrix with each column a vector of dimension names in the desired order. If unspecified, all p! possible orderings are used

digits

desired rounding of the output weights matrices in the SE-set, in decimal places. Defaults to 20.

rm_duplicates

Logical indicating whether only unique DAGs should be returned

input_type

specifies what type of matrix 'omega' is. default is "precision", other options include a matrix of partial correlations ("parcor") or a model implied covariance or correlation matrix "MIcov"

Value

a p! \times p matrix containing the SE-set (or n \times p matrix if a custom set of n orderings is specified). Each row represents a lower-triangular weights matrix, stacked column-wise.

References

Ryan O, Bringmann LF, Schuurman NK (upcoming). “The challenge of generating causal hypotheses using network models.” in preperation.

Shojaie A, Michailidis G (2010). “Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs.” Biometrika, 97(3), 519–538.

Bollen KA (1989). Structural equations with latent variables. Oxford, England, John Wiley \& Sons.

See Also

network_to_path, reorder_mat, order_gen

Examples

# first estimate the precision matrix
data(riskcor)
omega <- (qgraph::EBICglasso(riskcor, n = 69, returnAllResults = TRUE))$optwi
# qgraph method estimates a non-symmetric omega matrix, but uses forceSymmetric to create
# a symmetric matrix (see qgraph:::EBICglassoCore line 65)
omega <- as.matrix(Matrix::forceSymmetric(omega)) # returns the precision matrix

SE <- network_to_SEset(omega, digits=3)

# each row of SE defines a path-model weights matrix.
# We can extract element 20 by writing it to a matrix
example <- matrix(SE[20,],6,6)

# Example path model can be plotted as a weighted DAG
pos <- matrix(c(2,0,-2,-1,-2,1,0,2,0.5,0,0,-2),6,2,byrow=TRUE)

# qgraph reads matrix elements as "from row to column"
# regression weights matrices are read "from column to row"
# path model weights matrix must be transposed for qgraph

qgraph::qgraph(t(example), labels=rownames(riskcor), layout=pos,
repulsion=.8, vsize=c(10,15), theme="colorblind", fade=FALSE)