/**
* Sets the covariance for the a<->b edge to the given covariance, if within range. Otherwise does
* nothing.
*
* @param a a <-> b
* @param b a <-> b
* @param covar The covariance of a <-> b.
* @return true if the coefficent was set (i.e. was within range), false if not.
*/
public boolean setErrorCovariance(Node a, Node b, final double covar) {
Edge edge = Edges.bidirectedEdge(semGraph.getExogenous(a), semGraph.getExogenous(b));
if (edgeParameters.get(edge) == null) {
throw new IllegalArgumentException("Not a covariance parameter in this model: " + edge);
}
if (editingEdge == null || !edge.equals(editingEdge)) {
range = getParameterRange(edge);
editingEdge = edge;
}
if (covar > range.getLow() && covar < range.getHigh()) {
edgeParameters.put(edge, covar);
return true;
} else {
return false;
}
// if (!paramInBounds(edge, coef)) {
// edgeParameters.put(edge, d);
// return false;
// }
//
// edgeParameters.put(edge, coef);
// return true;
// if (!paramInBounds(edge, covar)) {
// edgeParameters.put(edge, d);
// return false;
// }
//
// edgeParameters.put(edge, covar);
// return true;
}
private GeneralizedSemPm makeTypicalPm() {
List<Node> variableNodes = new ArrayList<>();
ContinuousVariable x1 = new ContinuousVariable("X1");
ContinuousVariable x2 = new ContinuousVariable("X2");
ContinuousVariable x3 = new ContinuousVariable("X3");
ContinuousVariable x4 = new ContinuousVariable("X4");
ContinuousVariable x5 = new ContinuousVariable("X5");
variableNodes.add(x1);
variableNodes.add(x2);
variableNodes.add(x3);
variableNodes.add(x4);
variableNodes.add(x5);
Graph _graph = new EdgeListGraph(variableNodes);
SemGraph graph = new SemGraph(_graph);
graph.addDirectedEdge(x1, x3);
graph.addDirectedEdge(x2, x3);
graph.addDirectedEdge(x3, x4);
graph.addDirectedEdge(x2, x4);
graph.addDirectedEdge(x4, x5);
graph.addDirectedEdge(x2, x5);
return new GeneralizedSemPm(graph);
}
/**
* @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);
}
@Test
public void test2() {
RandomUtil.getInstance().setSeed(2999983L);
int sampleSize = 1000;
List<Node> variableNodes = new ArrayList<>();
ContinuousVariable x1 = new ContinuousVariable("X1");
ContinuousVariable x2 = new ContinuousVariable("X2");
ContinuousVariable x3 = new ContinuousVariable("X3");
ContinuousVariable x4 = new ContinuousVariable("X4");
ContinuousVariable x5 = new ContinuousVariable("X5");
variableNodes.add(x1);
variableNodes.add(x2);
variableNodes.add(x3);
variableNodes.add(x4);
variableNodes.add(x5);
Graph _graph = new EdgeListGraph(variableNodes);
SemGraph graph = new SemGraph(_graph);
graph.addDirectedEdge(x1, x3);
graph.addDirectedEdge(x2, x3);
graph.addDirectedEdge(x3, x4);
graph.addDirectedEdge(x2, x4);
graph.addDirectedEdge(x4, x5);
graph.addDirectedEdge(x2, x5);
SemPm semPm = new SemPm(graph);
SemIm semIm = new SemIm(semPm);
DataSet dataSet = semIm.simulateData(sampleSize, false);
print(semPm);
GeneralizedSemPm _semPm = new GeneralizedSemPm(semPm);
GeneralizedSemIm _semIm = new GeneralizedSemIm(_semPm, semIm);
DataSet _dataSet = _semIm.simulateDataMinimizeSurface(sampleSize, false);
print(_semPm);
// System.out.println(_dataSet);
for (int j = 0; j < dataSet.getNumColumns(); j++) {
double[] col = dataSet.getDoubleData().getColumn(j).toArray();
double[] _col = _dataSet.getDoubleData().getColumn(j).toArray();
double mean = StatUtils.mean(col);
double _mean = StatUtils.mean(_col);
double variance = StatUtils.variance(col);
double _variance = StatUtils.variance(_col);
assertEquals(mean, _mean, 0.3);
assertEquals(1.0, variance / _variance, .2);
}
}
/**
* @param a a->b
* @param b a->b
* @return The coefficient for a->b.
*/
public double getErrorCovariance(Node a, Node b) {
Edge edge = Edges.bidirectedEdge(semGraph.getExogenous(a), semGraph.getExogenous(b));
Double d = edgeParameters.get(edge);
if (d == null) {
throw new IllegalArgumentException("Not a covariance parameter in this model: " + edge);
}
return d;
}
public List<Node> getErrorNodes() {
List<Node> errorNodes = new ArrayList<Node>();
for (Node node : getVariableNodes()) {
errorNodes.add(semGraph.getExogenous(node));
}
return errorNodes;
}
private boolean paramInBounds(Edge edge, double newValue) {
edgeParameters.put(edge, newValue);
Map<Node, Double> errorVariances = new HashMap<Node, Double>();
for (Node node : semPm.getVariableNodes()) {
Node error = semGraph.getExogenous(node);
double d2 = calculateErrorVarianceFromParams(error);
if (Double.isNaN(d2)) {
return false;
}
errorVariances.put(error, d2);
}
if (!MatrixUtils.isPositiveDefinite(errCovar(errorVariances))) {
return false;
}
return true;
}
@Test
public void test1() {
GeneralizedSemPm pm = makeTypicalPm();
print(pm);
Node x1 = pm.getNode("X1");
Node x2 = pm.getNode("X2");
Node x3 = pm.getNode("X3");
Node x4 = pm.getNode("X4");
Node x5 = pm.getNode("X5");
SemGraph graph = pm.getGraph();
List<Node> variablesNodes = pm.getVariableNodes();
print(variablesNodes);
List<Node> errorNodes = pm.getErrorNodes();
print(errorNodes);
try {
pm.setNodeExpression(x1, "cos(B1) + E_X1");
print(pm);
String b1 = "B1";
String b2 = "B2";
String b3 = "B3";
Set<Node> nodes = pm.getReferencingNodes(b1);
assertTrue(nodes.contains(x1));
assertTrue(!nodes.contains(x2) && !nodes.contains(x2));
Set<String> referencedParameters = pm.getReferencedParameters(x3);
print("Parameters referenced by X3 are: " + referencedParameters);
assertTrue(referencedParameters.contains(b1) && referencedParameters.contains(b2));
assertTrue(!(referencedParameters.contains(b1) && referencedParameters.contains(b3)));
Node e_x3 = pm.getNode("E_X3");
//
for (Node node : pm.getNodes()) {
Set<Node> referencingNodes = pm.getReferencingNodes(node);
print("Nodes referencing " + node + " are: " + referencingNodes);
}
for (Node node : pm.getVariableNodes()) {
Set<Node> referencingNodes = pm.getReferencedNodes(node);
print("Nodes referenced by " + node + " are: " + referencingNodes);
}
Set<Node> referencingX3 = pm.getReferencingNodes(x3);
assertTrue(referencingX3.contains(x4));
assertTrue(!referencingX3.contains(x5));
Set<Node> referencedByX3 = pm.getReferencedNodes(x3);
assertTrue(
referencedByX3.contains(x1)
&& referencedByX3.contains(x2)
&& referencedByX3.contains(e_x3)
&& !referencedByX3.contains(x4));
pm.setNodeExpression(x5, "a * E^X2 + X4 + E_X5");
Node e_x5 = pm.getErrorNode(x5);
graph.setShowErrorTerms(true);
assertTrue(e_x5.equals(graph.getExogenous(x5)));
pm.setNodeExpression(e_x5, "Beta(3, 5)");
print(pm);
assertEquals("Split(-1.5,-.5,.5,1.5)", pm.getParameterExpressionString(b1));
pm.setParameterExpression(b1, "N(0, 2)");
assertEquals("N(0, 2)", pm.getParameterExpressionString(b1));
GeneralizedSemIm im = new GeneralizedSemIm(pm);
print(im);
DataSet dataSet = im.simulateDataAvoidInfinity(10, false);
print(dataSet);
} catch (ParseException e) {
e.printStackTrace();
}
}
@Test
public void test3() {
RandomUtil.getInstance().setSeed(49293843L);
List<Node> variableNodes = new ArrayList<>();
ContinuousVariable x1 = new ContinuousVariable("X1");
ContinuousVariable x2 = new ContinuousVariable("X2");
ContinuousVariable x3 = new ContinuousVariable("X3");
ContinuousVariable x4 = new ContinuousVariable("X4");
ContinuousVariable x5 = new ContinuousVariable("X5");
variableNodes.add(x1);
variableNodes.add(x2);
variableNodes.add(x3);
variableNodes.add(x4);
variableNodes.add(x5);
Graph _graph = new EdgeListGraph(variableNodes);
SemGraph graph = new SemGraph(_graph);
graph.setShowErrorTerms(true);
Node e1 = graph.getExogenous(x1);
Node e2 = graph.getExogenous(x2);
Node e3 = graph.getExogenous(x3);
Node e4 = graph.getExogenous(x4);
Node e5 = graph.getExogenous(x5);
graph.addDirectedEdge(x1, x3);
graph.addDirectedEdge(x1, x2);
graph.addDirectedEdge(x2, x3);
graph.addDirectedEdge(x3, x4);
graph.addDirectedEdge(x2, x4);
graph.addDirectedEdge(x4, x5);
graph.addDirectedEdge(x2, x5);
graph.addDirectedEdge(x5, x1);
GeneralizedSemPm pm = new GeneralizedSemPm(graph);
List<Node> variablesNodes = pm.getVariableNodes();
print(variablesNodes);
List<Node> errorNodes = pm.getErrorNodes();
print(errorNodes);
try {
pm.setNodeExpression(x1, "cos(b1) + a1 * X5 + E_X1");
pm.setNodeExpression(x2, "a2 * X1 + E_X2");
pm.setNodeExpression(x3, "tan(a3*X2 + a4*X1) + E_X3");
pm.setNodeExpression(x4, "0.1 * E^X2 + X3 + E_X4");
pm.setNodeExpression(x5, "0.1 * E^X4 + a6* X2 + E_X5");
pm.setNodeExpression(e1, "U(0, 1)");
pm.setNodeExpression(e2, "U(0, 1)");
pm.setNodeExpression(e3, "U(0, 1)");
pm.setNodeExpression(e4, "U(0, 1)");
pm.setNodeExpression(e5, "U(0, 1)");
GeneralizedSemIm im = new GeneralizedSemIm(pm);
print(im);
DataSet dataSet = im.simulateDataNSteps(1000, false);
// System.out.println(dataSet);
double[] d1 = dataSet.getDoubleData().getColumn(0).toArray();
double[] d2 = dataSet.getDoubleData().getColumn(1).toArray();
double cov = StatUtils.covariance(d1, d2);
assertEquals(-0.002, cov, 0.001);
} catch (ParseException e) {
e.printStackTrace();
}
}
/**
* 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);
}
public ParameterRange getCovarianceRange(Node a, Node b) {
return getParameterRange(
Edges.bidirectedEdge(semGraph.getExogenous(a), semGraph.getExogenous(b)));
}
/**
* Constructs a new standardized SEM IM from the freeParameters in the given SEM IM.
*
* @param im Stop asking me for these things! The given SEM IM!!!
* @param initialization CALCULATE_FROM_SEM if the initial values will be calculated from the
* given SEM IM; INITIALIZE_FROM_DATA if data will be simulated from the given SEM,
* standardized, and estimated.
*/
public StandardizedSemIm(SemIm im, Initialization initialization) {
this.semPm = new SemPm(im.getSemPm());
this.semGraph = new SemGraph(semPm.getGraph());
semGraph.setShowErrorTerms(true);
if (semGraph.existsDirectedCycle()) {
throw new IllegalArgumentException("The cyclic case is not handled.");
}
if (initialization == Initialization.CALCULATE_FROM_SEM) {
// This code calculates the new coefficients directly from the old ones.
edgeParameters = new HashMap<Edge, Double>();
List<Node> nodes = im.getVariableNodes();
TetradMatrix impliedCovar = im.getImplCovar(true);
for (Parameter parameter : im.getSemPm().getParameters()) {
if (parameter.getType() == ParamType.COEF) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
int aindex = nodes.indexOf(a);
int bindex = nodes.indexOf(b);
double vara = impliedCovar.get(aindex, aindex);
double stda = Math.sqrt(vara);
double varb = impliedCovar.get(bindex, bindex);
double stdb = Math.sqrt(varb);
double oldCoef = im.getEdgeCoef(a, b);
double newCoef = (stda / stdb) * oldCoef;
edgeParameters.put(Edges.directedEdge(a, b), newCoef);
} else if (parameter.getType() == ParamType.COVAR) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
Node exoa = semGraph.getExogenous(a);
Node exob = semGraph.getExogenous(b);
double covar = im.getErrCovar(a, b) / Math.sqrt(im.getErrVar(a) * im.getErrVar(b));
edgeParameters.put(Edges.bidirectedEdge(exoa, exob), covar);
}
}
} else {
// This code estimates the new coefficients from simulated data from the old model.
DataSet dataSet = im.simulateData(1000, false);
TetradMatrix _dataSet = dataSet.getDoubleData();
_dataSet = DataUtils.standardizeData(_dataSet);
DataSet dataSetStandardized = ColtDataSet.makeData(dataSet.getVariables(), _dataSet);
SemEstimator estimator = new SemEstimator(dataSetStandardized, im.getSemPm());
SemIm imStandardized = estimator.estimate();
edgeParameters = new HashMap<Edge, Double>();
for (Parameter parameter : imStandardized.getSemPm().getParameters()) {
if (parameter.getType() == ParamType.COEF) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
double coef = imStandardized.getEdgeCoef(a, b);
edgeParameters.put(Edges.directedEdge(a, b), coef);
} else if (parameter.getType() == ParamType.COVAR) {
Node a = parameter.getNodeA();
Node b = parameter.getNodeB();
Node exoa = semGraph.getExogenous(a);
Node exob = semGraph.getExogenous(b);
double covar = -im.getErrCovar(a, b) / Math.sqrt(im.getErrVar(a) * im.getErrVar(b));
edgeParameters.put(Edges.bidirectedEdge(exoa, exob), covar);
}
}
}
this.measuredNodes = Collections.unmodifiableList(semPm.getMeasuredNodes());
}
