# htcIdentifyStep: Perform one iteration of HTC identification. In Lucaweihs/SEMID: Identifiability of Linear Structural Equation Models

## 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

 `1` ```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 Lambdadenote 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. Omegajust 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

Lucaweihs/SEMID documentation built on June 3, 2019, 2:13 a.m.