createIdentifierBaseCase: Create an identifier base case

In SEMID: Identifiability of Linear Structural Equation Models

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.

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