R/factor_analysis_graphFunctions.R

In SEMID: Identifiability of Linear Structural Equation Models

# functions to find specific sets of nodes in a graph

# compute joint parents of a set of nodes
jointParents <- function(adjMatrix, nodes, latentNodes){
  jointParents <- c()
  remainingSet <- nodes
  remainingLatentNodes <- latentNodes
  for(u in nodes){
    remainingSet <- setdiff(remainingSet, u)
    for(v in remainingSet){
      for(parent in remainingLatentNodes){
        if(!is.na(adjMatrix[parent, u]) && !is.na(adjMatrix[parent, v]) && adjMatrix[parent, u]== 1 && adjMatrix[parent, v]== 1){
          jointParents <- append(jointParents, parent)
          remainingLatentNodes <- setdiff(remainingLatentNodes, parent)
        }
      }
    }
  }
  return(jointParents)
}

# compute set of children of a set of nodes
childrenOfNodes <- function(adjMatrix, nodes, possibleChildren){
  setOfChildren <- c()
  for(node in nodes) {
    for (child in possibleChildren){
      if (!is.na(adjMatrix[node, child]) && adjMatrix[node, child] ==1 && !(child %in% setOfChildren)){
        setOfChildren <- append(setOfChildren, child)
      }
    }
  }
  return(setOfChildren)
}

# compute the parents of a set of nodes
parentsOfNodes <- function(adjMatrix, nodes, possibleParents){
  setOfParents <- c()
  for (node in nodes) {
    for (parent in possibleParents){
      if (!is.na(adjMatrix[parent, node]) && (adjMatrix[parent, node] == 1) && !(parent %in% setOfParents)){
        setOfParents <- append(setOfParents, parent)
      }
    }
  }
  return(setOfParents)
}

# transform the Lambda matrix into a "large" adjacency matrix and also return
# the latent and observed nodes
transformLambda <- function(lambda){
  columns <- ncol(lambda)
  rows <- nrow(lambda)
  zeroMatrix1 <- matrix(0,columns,columns)
  zeroMatrix2 <- matrix(0,rows,columns+rows)
  transposeOfLambda <- t(lambda)
  upperPartMatrix <- cbind(zeroMatrix1,transposeOfLambda)
  adjMatrix <- rbind(upperPartMatrix,zeroMatrix2)
  latentNodes <- c(1:columns)
  observedNodes <- c((columns+1):(columns+rows))
  return(list(adjMatrix,latentNodes,observedNodes))
}