R: Identifiability of Linear Structural Equation Models

# Identifiability of Linear Structural Equation Models

## Documentation for package ‘SEMID’ version 0.5.1

- DESCRIPTION file
- Code demos. Use demo() to run them.
- Package NEWS
- Package README

## Help Pages

A B C D E F G H I L M N O P S T U V Z

SEMID-package | SEMID package documentation.

## -- A --

ancestors | All ancestors of a collection of nodes
ancestors.LatentDigraph | All ancestors of a collection of nodes
ancestors.LatentDigraphFixedOrder | All ancestors of a collection of nodes
ancestors.MixedGraph | All ancestors of a collection of nodes
ancestralID | Determines which edges in a mixed graph are ancestralID-identifiable
ancestralIdentifyStep | Perform one iteration of ancestral identification.

## -- B --

bidirectedComponents | Get bidirected components of a mixed graph

## -- C --

checkLocalBBCriterion | Check Local BB-Criterion
checkMatchingCriterion | Check Matching Criterion
children | All children of a collection of nodes.
children.LatentDigraph | All children of a collection of nodes.
children.LatentDigraphFixedOrder | All children of a collection of nodes.
children.MixedGraph | All children of a collection of nodes.
createAncestralIdentifier | Create an ancestral identification function.
createEdgewiseIdentifier | Create an edgewise identification function
createHtcIdentifier | Create an htc identification function.
createIdentifierBaseCase | Create an identifier base case
createLFHtcIdentifier | Create a latent-factor half-trek critierion identification function.
createLFIdentifierBaseCase | Create an latent identifier base case
createSimpleBiDirIdentifier | Identify bidirected edges if all directed edges are identified
createTrekFlowGraph | Helper function to create a flow graph.
createTrekFlowGraph.LatentDigraphFixedOrder | Helper function to create a flow graph.
createTrekSeparationIdentifier | Create an trek separation identification function
createTrGraph | Helper function to create a graph encoding trek reachable relationships.
createTrGraph.LatentDigraphFixedOrder | Helper function to create a graph encoding trek reachable relationships.

## -- D --

descendants | Get descendants of a collection of observed nodes
descendants.LatentDigraph | Get descendants of a collection of observed nodes
descendants.LatentDigraphFixedOrder | Get descendants of a collection of observed nodes
descendants.MixedGraph | Get descendants of a collection of observed nodes

## -- E --

edgewiseID | Determines which edges in a mixed graph are edgewiseID-identifiable
edgewiseIdentifyStep | Perform one iteration of edgewise identification.
edgewiseTSID | Determines which edges in a mixed graph are edgewiseID+TS identifiable
extmID | Check Extended M-Identifiability

## -- F --

findColumnsWithSumOne | A Helper Function for Check ZUTA
flowBetween | Flow from one set of nodes to another.
flowBetween.FlowGraph | Flow from one set of nodes to another.
FlowGraph | Construct FlowGraph object

## -- G --

generalGenericID | A general generic identification algorithm template.
getAncestors | Get getAncestors of nodes in a graph.
getDescendants | Get descendants of nodes in a graph.
getHalfTrekSystem | Determines if a half-trek system exists in the mixed graph.
getHalfTrekSystem.MixedGraph | Determines if a half-trek system exists in the mixed graph.
getMaxFlow | Size of largest HT system Y satisfying the HTC for a node v except perhaps having |getParents(v)| < |Y|.
getMixedCompForNode | Get the mixed component of a node in a mixed subgraph.
getMixedGraph | Get the corresponding mixed graph
getMixedGraph.LatentDigraph | Get the corresponding mixed graph
getParents | Get getParents of nodes in a graph.
getSiblings | Get getSiblings of nodes in a graph.
getTrekSystem | Determines if a trek system exists in the mixed graph.
getTrekSystem.LatentDigraph | Determines if a trek system exists in the mixed graph.
getTrekSystem.LatentDigraphFixedOrder | Determines if a trek system exists in the mixed graph.
getTrekSystem.MixedGraph | Determines if a half-trek system exists in the mixed graph.
globalID | Determines whether a mixed graph is globally identifiable.
graphID | Identifiability of linear structural equation models.
graphID.ancestralID | Determine generic identifiability of an acyclic mixed graph using ancestral decomposition.
graphID.decompose | Determine generic identifiability by Tian Decomposition and HTC
graphID.genericID | Determine generic identifiability of a mixed graph.
graphID.htcID | Determines if a mixed graph is HTC-identifiable.
graphID.main | Helper function to handle a graph component.
graphID.nonHtcID | Check for generic infinite-to-one via the half-trek criterion.

## -- H --

htcID | Determines which edges in a mixed graph are HTC-identifiable.
htcIdentifyStep | Perform one iteration of HTC identification.
htr | Get all HTR nodes from a set of nodes in a graph.
htrFrom | Half trek reachable nodes.
htrFrom.MixedGraph | Half trek reachable nodes.

## -- I --

inducedSubgraph | Get the induced subgraph on a collection of nodes
inducedSubgraph.LatentDigraph | Get the induced subgraph on a collection of nodes
inducedSubgraph.MixedGraph | Get the induced subgraph on a collection of nodes
isSibling | Are two nodes siblings?
isSibling.MixedGraph | Are two nodes siblings?

## -- L --

L | Get directed adjacency matrix.
L.LatentDigraph | Get directed adjacency matrix.
L.LatentDigraphFixedOrder | Get directed adjacency matrix.
L.MixedGraph | Get directed adjacency matrix.
LatentDigraph | Construct a LatentDigraph object
LatentDigraphFixedOrder | Construct LatentDigraphFixedOrder object
latentDigraphHasSimpleNumbering | Checks that a LatentDigraph has appropriate node numbering
latentNodes | Get all latent nodes in the graph.
latentNodes.LatentDigraph | Get all latent nodes in the graph.
lfhtcID | Determines which edges in a latent digraph are LF-HTC-identifiable.
lfhtcIdentifyStep | Perform one iteration of latent-factor HTC identification.

## -- M --

mID | Check M-Identifiability.
MixedGraph | Construct MixedGraph object
mixedGraphHasSimpleNumbering | Checks that a MixedGraph has appropriate node numbering

## -- N --

nodes | Get all nodes in the graph.
nodes.MixedGraph | Get all nodes in the graph.
numLatents | Number of latent nodes in the graph.
numLatents.LatentDigraph | Number of latent nodes in the graph.
numLatents.LatentDigraphFixedOrder | Number of latent nodes in the graph.
numNodes | Number of nodes in the graph.
numNodes.LatentDigraph | Number of nodes in the graph.
numNodes.LatentDigraphFixedOrder | Number of nodes in the graph.
numNodes.MixedGraph | Number of nodes in the graph.
numObserved | Number of observed nodes in the graph.
numObserved.LatentDigraph | Number of observed nodes in the graph.
numObserved.LatentDigraphFixedOrder | Number of observed nodes in the graph.

## -- O --

O | Get adjacency matrix for bidirected part.
O.MixedGraph | Get adjacency matrix for bidirected part.
observedNodes | Get all observed nodes in the graph.
observedNodes.LatentDigraph | Get all observed nodes in the graph.
observedParents | Get the observed parents on a collection of nodes
observedParents.LatentDigraph | Get the observed parents on a collection of nodes

## -- P --

parents | All parents of a collection of nodes.
parents.LatentDigraph | All parents of a collection of nodes.
parents.LatentDigraphFixedOrder | All parents of a collection of nodes.
parents.MixedGraph | All parents of a collection of nodes.
plot.LatentDigraph | Plots the latent digraph
plot.MixedGraph | Plots the latent digraph
plotLatentDigraph | Plot a latent factor graph
plotMixedGraph | Plot a mixed graph
print.extmIDresult | Prints a extmIDresult object
print.GenericIDResult | Prints a GenericIDResult object
print.LfhtcIDResult | Prints a LfhtcIDResult object
print.mIDresult | Prints a mIDresult object
print.SEMIDResult | Prints a SEMIDResult object
print.ZUTAresult | Prints a ZUTAresult object

## -- S --

SEMID | SEMID package documentation.
semID | Identifiability of linear structural equation models.
siblings | All siblings of a collection of nodes
siblings.MixedGraph | All siblings of a collection of nodes
stronglyConnectedComponent | Strongly connected component
stronglyConnectedComponent.LatentDigraph | Strongly connected component
stronglyConnectedComponent.LatentDigraphFixedOrder | Strongly connected component
stronglyConnectedComponent.MixedGraph | Strongly connected component
subsetsOfSize | Returns all subsets of a certain size

## -- T --

tianComponent | Returns the Tian c-component of a node
tianComponent.MixedGraph | Returns the Tian c-component of a node
tianDecompose | Performs the tian decomposition on the mixed graph
tianDecompose.MixedGraph | Performs the tian decomposition on the mixed graph
tianIdentifier | Identifies components in a tian decomposition
tianSigmaForComponent | Globally identify the covariance matrix of a C-component
toEx | Transforms a vector of node indices in the internal rep. into external numbering
toEx.LatentDigraph | Transforms a vector of node indices in the internal rep. into external numbering
toEx.MixedGraph | Transforms a vector of node indices in the internal rep. into external numbering
toIn | Transforms a vector of given node indices into their internal numbering
toIn.LatentDigraph | Transforms a vector of given node indices into their internal numbering
toIn.MixedGraph | Transforms a vector of given node indices into their internal numbering
trekSeparationIdentifyStep | Perform one iteration of trek separation identification.
trFrom | Trek reachable nodes.
trFrom.LatentDigraph | Trek reachable nodes.
trFrom.LatentDigraphFixedOrder | Trek reachable nodes.
trFrom.MixedGraph | Trek reachable nodes.

## -- U --

updateEdgeCapacities | Update edge capacities.
updateEdgeCapacities.FlowGraph | Update edge capacities.
updateVertexCapacities | Update vertex capacities.
updateVertexCapacities.FlowGraph | Update vertex capacities.

## -- V --

validateLatentNodesAreSources | A helper function to validate that latent nodes in a LatentDigraph are sources.
validateMatrices | A helper function to validate input matrices.
validateMatrix | A helper function to validate an input matrix.
validateNodes | A helper function to validate if input nodes are valid.
validateVarArgsEmpty | A helper function to validate that there are no variable arguments

## -- Z --

ZUTA | Check the Zero Upper Triangular Assumption