graphID: Identifiability of linear structural equation models.

In Lucaweihs/SEMID: Identifiability of Linear Structural Equation Models

Identifiability of linear structural equation models.

Description

NOTE: graphID has been deprecated, use semID instead.

This function checks global and generic identifiability of linear structural equation models. For generic identifiability the function checks a sufficient criterion as well as a necessary criterion but this check may be inconclusive.

Usage

graphID(
  L,
  O,
  output.type = "matrix",
  file.name = NULL,
  decomp.if.acyclic = TRUE,
  test.globalID = TRUE,
  test.genericID = TRUE,
  test.nonID = TRUE
)

Arguments

L	Adjacency matrix for the directed part of the path diagram/mixed graph; an edge pointing from i to j is encoded as L[i,j]=1 and the lack of an edge between i and j is encoded as L[i,j]=0. There should be no directed self loops, i.e. no i such that L[i,i]=1.
O	Adjacency matrix for the bidirected part of the path diagram/mixed graph. Edges are encoded as for the L parameter. Again there should be no self loops. Also this matrix will be coerced to be symmetric so it is only necessary to specify an edge once, i.e. if O[i,j]=1 you may, but are not required to, also have O[j,i]=1.
output.type	A character string indicating whether output is printed ('matrix'), saved to a file ('file'), or returned as a list ('list') for further processing in R.
file.name	A character string naming the output file.
decomp.if.acyclic	A logical value indicating whether an input graph that is acyclic is to be decomposed before applying identifiability criteria.
test.globalID	A logical value indicating whether or not global identifiability is checked.
test.genericID	A logical value indicating whether or not a sufficient condition for generic identifiability is checked.
test.nonID	A logical value indicating whether or not a condition implying generic non-identifiability is checked.

Value

A list or printed matrix indicating the identifiability status of the linear SEM given by the input graph. Optionally the graph's components are listed.

With output.type = 'list', the function returns a list of components for the graph. Each list entry is again a list that indicates first which nodes form the component and second whether the component forms a mixed graph that is acyclic. The next entries in the list show HTC-identifiable nodes, meaning nodes v for which the coefficients for all the directed edges pointing to v can be identified using the methods from Foygel et al. (2012). The HTC-identifiable nodes are listed in the order in which they are found by the recursive identification algorithm. The last three list entries are logical values that indicate whether or not the graph component is generically identifiable, globally identifiable or not identifiable; compare Drton et al. (2011) and Foygel et al. (2012). In the latter case the Jacobian of the parametrization does not have full rank.

With output.type = 'matrix', a summary of the above information is printed.

References

Drton, M., Foygel, R., and Sullivant, S. (2011) Global identifiability of linear structural equation models. Ann. Statist. 39(2): 865-886.

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.

Examples

## Not run: 
L = t(matrix(
  c(0, 1, 0, 0, 0,
    0, 0, 1, 0, 0,
    0, 0, 0, 1, 0,
    0, 0, 0, 0, 1,
    0, 0, 0, 0, 0), 5, 5))
O = t(matrix(
  c(0, 0, 1, 1, 0,
    0, 0, 0, 1, 1,
    0, 0, 0, 0, 0,
    0, 0, 0, 0, 0,
    0, 0, 0, 0, 0), 5, 5))
O=O+t(O)
graphID(L,O)


## Examples from Foygel, Draisma & Drton (2012)
demo(SEMID)

## End(Not run)

Lucaweihs/SEMID documentation built on July 22, 2023, 7:49 a.m.