/**
* @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;
}
public boolean containsParameter(Edge edge) {
if (Edges.isBidirectedEdge(edge)) {
edge =
Edges.bidirectedEdge(
semGraph.getExogenous(edge.getNode1()), semGraph.getExogenous(edge.getNode2()));
}
return edgeParameters.keySet().contains(edge);
}
public void setParameterValue(Edge edge, double value) {
if (Edges.isDirectedEdge(edge)) {
setEdgeCoefficient(edge.getNode1(), edge.getNode2(), value);
} else if (Edges.isBidirectedEdge(edge)) {
setErrorCovariance(edge.getNode1(), edge.getNode2(), value);
} else {
throw new IllegalArgumentException(
"Only directed and bidirected edges are supported: " + edge);
}
}
private void uncorrelationExogenousVariables() {
Graph graph = getWorkbench().getGraph();
Set<Edge> edges = graph.getEdges();
for (Edge edge : edges) {
if (Edges.isBidirectedEdge(edge)) {
try {
graph.removeEdge(edge);
} catch (Exception e) {
// Ignore.
}
}
}
}
private void correlateExogenousVariables() {
Graph graph = getWorkbench().getGraph();
if (graph instanceof Dag) {
JOptionPane.showMessageDialog(
JOptionUtils.centeringComp(), "Cannot add bidirected edges to DAG's.");
return;
}
List<Node> nodes = graph.getNodes();
List<Node> exoNodes = new LinkedList<Node>();
for (int i = 0; i < nodes.size(); i++) {
Node node = nodes.get(i);
if (graph.isExogenous(node)) {
exoNodes.add(node);
}
}
for (int i = 0; i < exoNodes.size(); i++) {
loop:
for (int j = i + 1; j < exoNodes.size(); j++) {
Node node1 = exoNodes.get(i);
Node node2 = exoNodes.get(j);
List<Edge> edges = graph.getEdges(node1, node2);
for (int k = 0; k < edges.size(); k++) {
Edge edge = edges.get(k);
if (Edges.isBidirectedEdge(edge)) {
continue loop;
}
}
graph.addBidirectedEdge(node1, node2);
}
}
}
/**
* @return The edge coefficient matrix of the model, a la SemIm. Note that this will normally need
* to be transposed, since [a][b] is the edge coefficient for a-->b, not b-->a. Sorry.
* History. THESE ARE PARAMETERS OF THE MODEL--THE ONLY PARAMETERS.
*/
public TetradMatrix edgeCoef() {
List<Node> variableNodes = getVariableNodes();
TetradMatrix edgeCoef = new TetradMatrix(variableNodes.size(), variableNodes.size());
for (Edge edge : edgeParameters.keySet()) {
if (Edges.isBidirectedEdge(edge)) {
continue;
}
Node a = edge.getNode1();
Node b = edge.getNode2();
int aindex = variableNodes.indexOf(a);
int bindex = variableNodes.indexOf(b);
double coef = edgeParameters.get(edge);
edgeCoef.set(aindex, bindex, coef);
}
return edgeCoef;
}
/** @return a string representation of the coefficients and variances of the model. */
public String toString() {
StringBuilder buf = new StringBuilder();
NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
buf.append("\nStandardized SEM:");
buf.append("\n\nEdge coefficients (parameters):\n");
for (Edge edge : edgeParameters.keySet()) {
if (!Edges.isDirectedEdge(edge)) {
continue;
}
buf.append("\n" + edge + " " + nf.format(edgeParameters.get(edge)));
}
buf.append("\n\nError covariances (parameters):\n");
for (Edge edge : edgeParameters.keySet()) {
if (!Edges.isBidirectedEdge(edge)) {
continue;
}
buf.append("\n" + edge + " " + nf.format(edgeParameters.get(edge)));
}
buf.append("\n\nError variances (calculated):\n");
for (Node error : getErrorNodes()) {
double variance = getErrorVariance(error);
buf.append("\n" + error + " " + (Double.isNaN(variance) ? "Undefined" : nf.format(variance)));
}
buf.append("\n");
return buf.toString();
}
/** Constructs a new SemPm from the given SemGraph. */
public GeneralizedSemPm(SemGraph graph) {
if (graph == null) {
throw new NullPointerException("Graph must not be null.");
}
// if (graph.existsDirectedCycle()) {
// throw new IllegalArgumentExcneption("Cycles are not supported.");
// }
// Cannot afford to allow error terms on this graph to be shown or hidden from the outside; must
// make a
// hidden copy of it and make sure error terms are shown.
this.graph = new SemGraph(graph);
this.graph.setShowErrorTerms(true);
for (Edge edge : this.graph.getEdges()) {
if (Edges.isBidirectedEdge(edge)) {
throw new IllegalArgumentException(
"The generalized SEM PM cannot currently deal with bidirected " + "edges. Sorry.");
}
}
this.nodes = Collections.unmodifiableList(this.graph.getNodes());
for (Node node : nodes) {
namesToNodes.put(node.getName(), node);
}
this.variableNodes = new ArrayList<>();
this.measuredNodes = new ArrayList<>();
for (Node variable : this.nodes) {
if (variable.getNodeType() == NodeType.MEASURED
|| variable.getNodeType() == NodeType.LATENT) {
variableNodes.add(variable);
}
if (variable.getNodeType() == NodeType.MEASURED) {
measuredNodes.add(variable);
}
}
this.errorNodes = new ArrayList<>();
for (Node variable : this.variableNodes) {
List<Node> parents = this.graph.getParents(variable);
boolean added = false;
for (Node _node : parents) {
if (_node.getNodeType() == NodeType.ERROR) {
errorNodes.add(_node);
added = true;
break;
}
}
if (!added) {
errorNodes.add(null);
}
}
this.referencedParameters = new HashMap<>();
this.referencedNodes = new HashMap<>();
this.nodeExpressions = new HashMap<>();
this.nodeExpressionStrings = new HashMap<>();
this.parameterExpressions = new HashMap<>();
this.parameterExpressionStrings = new HashMap<>();
this.parameterEstimationInitializationExpressions = new HashMap<>();
this.parameterEstimationInitializationExpressionStrings = new HashMap<>();
this.startsWithParametersTemplates = new HashMap<>();
this.startsWithParametersEstimationInitializationTemplates = new HashMap<>();
this.variableNames = new ArrayList<>();
for (Node _node : variableNodes) variableNames.add(_node.getName());
for (Node _node : errorNodes) variableNames.add(_node.getName());
try {
List<Node> variableNodes = getVariableNodes();
for (Node node : variableNodes) {
if (!this.graph.isParameterizable(node)) continue;
if (nodeExpressions.get(node) != null) {
continue;
}
String variablestemplate = getVariablesTemplate();
String formula =
TemplateExpander.getInstance().expandTemplate(variablestemplate, this, node);
setNodeExpression(node, formula);
Set<String> parameters = getReferencedParameters(node);
String parametersTemplate = getParametersTemplate();
for (String parameter : parameters) {
if (parameterExpressions.get(parameter) == null) {
if (parametersTemplate != null) {
setParameterExpression(parameter, parametersTemplate);
} else if (this.graph.isTimeLagModel()) {
String expressionString = "Split(-0.9, -.1, .1, 0.9)";
setParameterExpression(parameter, expressionString);
setParametersTemplate(expressionString);
} else {
String expressionString = "Split(-1.5, -.5, .5, 1.5)";
setParameterExpression(parameter, expressionString);
setParametersTemplate(expressionString);
}
}
}
for (String parameter : parameters) {
if (parameterEstimationInitializationExpressions.get(parameter) == null) {
if (parametersTemplate != null) {
setParameterEstimationInitializationExpression(parameter, parametersTemplate);
} else if (this.graph.isTimeLagModel()) {
String expressionString = "Split(-0.9, -.1, .1, 0.9)";
setParameterEstimationInitializationExpression(parameter, expressionString);
} else {
String expressionString = "Split(-1.5, -.5, .5, 1.5)";
setParameterEstimationInitializationExpression(parameter, expressionString);
}
}
setStartsWithParametersTemplate("s", "Split(-1.5, -.5, .5, 1.5)");
setStartsWithParametersEstimationInitializaationTemplate(
"s", "Split(-1.5, -.5, .5, 1.5)");
}
}
for (Node node : errorNodes) {
if (node == null) continue;
String template = getErrorsTemplate();
String formula = TemplateExpander.getInstance().expandTemplate(template, this, node);
setNodeExpression(node, formula);
Set<String> parameters = getReferencedParameters(node);
setStartsWithParametersTemplate("s", "U(1, 3)");
setStartsWithParametersEstimationInitializaationTemplate("s", "U(1, 3)");
for (String parameter : parameters) {
setParameterExpression(parameter, "U(1, 3)");
}
}
} catch (ParseException e) {
throw new IllegalStateException("Parse error in constructing initial model.", e);
}
}
/**
* 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;
}
/**
* @param edge a->b or a<->b.
* @return the range of the covariance parameter for a->b or a<->b.
*/
public ParameterRange getParameterRange(Edge edge) {
if (Edges.isBidirectedEdge(edge)) {
edge =
Edges.bidirectedEdge(
semGraph.getExogenous(edge.getNode1()), semGraph.getExogenous(edge.getNode2()));
}
if (!(edgeParameters.keySet().contains(edge))) {
throw new IllegalArgumentException("Not an edge in this model: " + edge);
}
double initial = edgeParameters.get(edge);
if (initial == Double.NEGATIVE_INFINITY) {
initial = Double.MIN_VALUE;
} else if (initial == Double.POSITIVE_INFINITY) {
initial = Double.MAX_VALUE;
}
double value = initial;
// look upward for a point that fails.
double high = value + 1;
while (paramInBounds(edge, high)) {
high = value + 2 * (high - value);
if (high == Double.POSITIVE_INFINITY) {
break;
}
}
// find the boundary using binary search.
double rangeHigh;
if (high == Double.POSITIVE_INFINITY) {
rangeHigh = high;
} else {
double low = value;
while (high - low > 1e-10) {
double midpoint = (high + low) / 2.0;
if (paramInBounds(edge, midpoint)) {
low = midpoint;
} else {
high = midpoint;
}
}
rangeHigh = (high + low) / 2.0;
}
// look downard for a point that fails.
double low = value - 1;
while (paramInBounds(edge, low)) {
low = value - 2 * (value - low);
if (low == Double.NEGATIVE_INFINITY) {
break;
}
}
double rangeLow;
if (low == Double.NEGATIVE_INFINITY) {
rangeLow = low;
} else {
// find the boundary using binary search.
high = value;
while (high - low > 1e-10) {
double midpoint = (high + low) / 2.0;
if (paramInBounds(edge, midpoint)) {
high = midpoint;
} else {
low = midpoint;
}
}
rangeLow = (high + low) / 2.0;
}
if (Edges.isDirectedEdge(edge)) {
edgeParameters.put(edge, initial);
} else if (Edges.isBidirectedEdge(edge)) {
edgeParameters.put(edge, initial);
}
return new ParameterRange(edge, value, rangeLow, rangeHigh);
}
