/**
* @return Returns the error covariance matrix of the model. i.e. [a][b] is the covariance of E_a
* and E_b, with [a][a] of course being the variance of E_a. THESE ARE NOT PARAMETERS OF THE
* MODEL; THEY ARE CALCULATED. Note that elements of this matrix may be Double.NaN; this
* indicates that these elements cannot be calculated.
*/
private TetradMatrix errCovar(Map<Node, Double> errorVariances) {
List<Node> variableNodes = getVariableNodes();
List<Node> errorNodes = new ArrayList<Node>();
for (Node node : variableNodes) {
errorNodes.add(semGraph.getExogenous(node));
}
TetradMatrix errorCovar = new TetradMatrix(errorVariances.size(), errorVariances.size());
for (int index = 0; index < errorNodes.size(); index++) {
Node error = errorNodes.get(index);
double variance = getErrorVariance(error);
errorCovar.set(index, index, variance);
}
for (int index1 = 0; index1 < errorNodes.size(); index1++) {
for (int index2 = 0; index2 < errorNodes.size(); index2++) {
Node error1 = errorNodes.get(index1);
Node error2 = errorNodes.get(index2);
Edge edge = semGraph.getEdge(error1, error2);
if (edge != null && Edges.isBidirectedEdge(edge)) {
double covariance = getErrorCovariance(error1, error2);
errorCovar.set(index1, index2, covariance);
}
}
}
return errorCovar;
}
/**
* Calculates the error variance for the given error node, given all of the coefficient values in
* the model.
*
* @param error An error term in the model--i.e. a variable with NodeType.ERROR.
* @return The value of the error variance, or Double.NaN is the value is undefined.
*/
private double calculateErrorVarianceFromParams(Node error) {
error = semGraph.getNode(error.getName());
Node child = semGraph.getChildren(error).get(0);
List<Node> parents = semGraph.getParents(child);
double otherVariance = 0;
for (Node parent : parents) {
if (parent == error) continue;
double coef = getEdgeCoefficient(parent, child);
otherVariance += coef * coef;
}
if (parents.size() >= 2) {
ChoiceGenerator gen = new ChoiceGenerator(parents.size(), 2);
int[] indices;
while ((indices = gen.next()) != null) {
Node node1 = parents.get(indices[0]);
Node node2 = parents.get(indices[1]);
double coef1, coef2;
if (node1.getNodeType() != NodeType.ERROR) {
coef1 = getEdgeCoefficient(node1, child);
} else {
coef1 = 1;
}
if (node2.getNodeType() != NodeType.ERROR) {
coef2 = getEdgeCoefficient(node2, child);
} else {
coef2 = 1;
}
List<List<Node>> treks = GraphUtils.treksIncludingBidirected(semGraph, node1, node2);
double cov = 0.0;
for (List<Node> trek : treks) {
double product = 1.0;
for (int i = 1; i < trek.size(); i++) {
Node _node1 = trek.get(i - 1);
Node _node2 = trek.get(i);
Edge edge = semGraph.getEdge(_node1, _node2);
double factor;
if (Edges.isBidirectedEdge(edge)) {
factor = edgeParameters.get(edge);
} else if (!edgeParameters.containsKey(edge)) {
factor = 1;
} else if (semGraph.isParentOf(_node1, _node2)) {
factor = getEdgeCoefficient(_node1, _node2);
} else {
factor = getEdgeCoefficient(_node2, _node1);
}
product *= factor;
}
cov += product;
}
otherVariance += 2 * coef1 * coef2 * cov;
}
}
return 1.0 - otherVariance <= 0 ? Double.NaN : 1.0 - otherVariance;
}