createIdentifierBaseCase {SEMID}

Create an identifier base case

Description

Identifiers are functions that take as input a covariance matrix Sigma corresponding to some mixed graph G and, from that covariance matrix, identify some subset of the coefficients in the mixed graph G. This function takes as input the matrices, L and O, defining G and creates an identifier that does not identify any of the coefficients of G. This is useful as a base case when building more complex identification functions.

Usage

createIdentifierBaseCase(L, O)

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.

Value

a function that takes as input a covariance matrix compatible with the mixed graph defined by L/O and returns a list with two named components:

Lambda

a matrix equal to L but with NA values instead of 1s

Omega

a matrix equal to O but with NA values instead of 1s

When building more complex identifiers these NAs will be replaced by the value that can be identified from Sigma.