htcIdentifyStep: Perform one iteration of HTC identification.

In SEMID: Identifiability of Linear Structural Equation Models

Perform one iteration of HTC identification.

Description

A function that does one step through all the nodes in a mixed graph and tries to identify new edge coefficients using the existence of half-trek systems as described in Foygel, Draisma, Drton (2012).

Usage

htcIdentifyStep(mixedGraph, unsolvedParents, solvedParents, identifier)

Arguments

mixedGraph	a MixedGraph object representing the mixed graph.
unsolvedParents	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.
solvedParents	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).
identifier	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 Lambda 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. Omega 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.

Value

a list with four components:

identifiedEdges

a matrix rx2 matrix where r is the number of edges that where identified by this function call and identifiedEdges[i,1] -> identifiedEdges[i,2] was the ith edge identified

unsolvedParents

as the input argument but updated with any newly identified edges

solvedParents

as the input argument but updated with any newly identified edges

identifier

as the input argument but updated with any newly identified edges

References

Foygel, R., Draisma, J., and Drton, M. (2012) Half-trek criterion for generic identifiability of linear structural equation models. Ann. Statist. 40(3): 1682-1713

SEMID documentation built on July 26, 2023, 5:40 p.m.