A function that does one step through all the nodes in a mixed graph and tries to determine if directed edge coefficients are generically identifiable by leveraging decomposition by ancestral subsets. See algorithm 1 of Drton and Weihs (2015); this version of the algorithm is somewhat different from Drton and Weihs (2015) in that it also works on cyclic graphs.
ancestralIdentifyStep(mixedGraph, unsolvedParents, solvedParents, identifier)a list
a MixedGraph object representing
the mixed graph.
a list whose ith index is a vector of all the parents j of i in G which for which the edge j->i is not yet known to be generically identifiable.
the complement of unsolvedParents, a list whose
ith index is a vector of all parents j of i for which the edge i->j
is known to be generically identifiable (perhaps by other algorithms).
an identification function that must produce the
identifications corresponding to those in solved parents. That is
identifier should be a function taking a single argument Sigma
(any generically generated covariance matrix corresponding
to the mixed graph) and returns a list with two named arguments
denote the number of nodes in mixedGraph as n. Then
Lambda is an nxn matrix whose i,jth entry
equals 0 if i is not a parent of j,
equals NA if i is a parent of j but identifier cannot
identify it generically,
equals the (generically) unique value corresponding to the weight along the edge i->j that was used to produce Sigma.
just as Lambda but for the bidirected edges in the mixed graph
such that if j is in solvedParents[[i]] we must have that
Lambda[j,i] is not NA.
Drton, M. and Weihs, L. (2015) Generic Identifiability of Linear Structural Equation Models by Ancestor Decomposition. arXiv 1504.02992