private double getDerivative(Sextad sextad, Sigma sigma) {
Node a = sigma.getA();
Node b = sigma.getB();
Node n1 = sextad.getI();
Node n2 = sextad.getJ();
Node n3 = sextad.getK();
Node n4 = sextad.getL();
Node n5 = sextad.getM();
Node n6 = sextad.getN();
if (a == n1) {
if (b == n4) {
return r(n2, n5) * r(n3, n6) - r(n2, n6) * r(n3, n5);
} else if (b == n5) {
return -r(n2, n4) * r(n3, n6) + r(n3, n4) * r(n2, n6);
} else if (b == n6) {
return r(n2, n4) * r(n3, n5) - r(n3, n4) * r(n2, n5);
}
} else if (a == n2) {
if (b == n4) {
return r(n3, n5) * r(n1, n6) - r(n1, n5) * r(n3, n6);
} else if (b == n5) {
return r(n1, n4) * r(n3, n6) - r(n3, n4) * r(n1, n6);
} else if (b == n6) {
return -r(n1, n4) * r(n3, n5) + r(n3, n4) * r(n1, n5);
}
} else if (a == n3) {
if (b == n4) {
return r(n1, n5) * r(n2, n6) - r(n2, n5) * r(n1, n6);
} else if (b == n5) {
return -r(n1, n4) * r(n2, n6) + r(n2, n4) * r(n1, n6);
} else if (b == n6) {
return r(n1, n4) * r(n2, n5) - r(n2, n4) * r(n1, n5);
}
}
// symmetry
n6 = sextad.getI();
n5 = sextad.getJ();
n4 = sextad.getK();
n3 = sextad.getL();
n2 = sextad.getM();
n1 = sextad.getN();
if (a == n1) {
if (b == n4) {
return r(n2, n5) * r(n3, n6) - r(n2, n6) * r(n3, n5);
} else if (b == n5) {
return -r(n2, n4) * r(n3, n6) + r(n3, n4) * r(n2, n6);
} else if (b == n6) {
return r(n2, n4) * r(n3, n5) - r(n3, n4) * r(n2, n5);
}
} else if (a == n2) {
if (b == n4) {
return r(n3, n5) * r(n1, n6) - r(n1, n5) * r(n3, n6);
} else if (b == n5) {
return r(n1, n4) * r(n3, n6) - r(n3, n4) * r(n1, n6);
} else if (b == n6) {
return -r(n1, n4) * r(n3, n5) + r(n3, n4) * r(n1, n5);
}
} else if (a == n3) {
if (b == n4) {
return r(n1, n5) * r(n2, n6) - r(n2, n5) * r(n1, n6);
} else if (b == n5) {
return -r(n1, n4) * r(n2, n6) + r(n2, n4) * r(n1, n6);
} else if (b == n6) {
return r(n1, n4) * r(n2, n5) - r(n2, n4) * r(n1, n5);
}
}
return 0.0;
}
/**
* Takes a list of tetrads for the given data set and returns the chi square value for the test.
* We assume that the tetrads are non-redundant; if not, a matrix exception will be thrown.
*
* <p>Calculates the T statistic (Bollen and Ting, p. 161). This is significant if tests as
* significant using the Chi Square distribution with degrees of freedom equal to the number of
* nonredundant tetrads tested.
*/
@Override
// public double calcChiSquare1(Sextad... sextads) {
// this.storedSextads = sextads;
//
// this.df = sextads.length;
//
// // Need a list of symbolic covariances--i.e. covariances that appear in tetrads.
// Set<Sigma> boldSigmaSet = new LinkedHashSet<Sigma>();
// List<Sigma> boldSigma = new ArrayList<Sigma>();
//
// for (Sextad sextad : sextads) {
// boldSigmaSet.add(new Sigma(sextad.getI(), sextad.getL()));
// boldSigmaSet.add(new Sigma(sextad.getI(), sextad.getM()));
// boldSigmaSet.add(new Sigma(sextad.getI(), sextad.getN()));
//
// boldSigmaSet.add(new Sigma(sextad.getJ(), sextad.getL()));
// boldSigmaSet.add(new Sigma(sextad.getJ(), sextad.getM()));
// boldSigmaSet.add(new Sigma(sextad.getJ(), sextad.getN()));
//
// boldSigmaSet.add(new Sigma(sextad.getK(), sextad.getL()));
// boldSigmaSet.add(new Sigma(sextad.getK(), sextad.getM()));
// boldSigmaSet.add(new Sigma(sextad.getK(), sextad.getN()));
// }
//
// for (Sigma sigma : boldSigmaSet) {
// boldSigma.add(sigma);
// }
//
// // Need a matrix of variances and covariances of sample covariances.
// TetradMatrix sigma_ss = TetradMatrix.instance(boldSigma.size(), boldSigma.size());
//
// for (int i = 0; i < boldSigma.size(); i++) {
// for (int j = 0; j < boldSigma.size(); j++) {
// Sigma sigmaef = boldSigma.get(i);
// Sigma sigmagh = boldSigma.get(j);
//
// Node e = sigmaef.getA();
// Node f = sigmaef.getB();
// Node g = sigmagh.getA();
// Node h = sigmagh.getB();
//
// if (cov != null && cov instanceof CorrelationMatrix) {
//
//// Assumes multinormality. Using formula 23. (Not implementing formula 22 because
// that case
//// does not come up.)
// double rr = 0.5 * (r(e, f) * r(g, h))
// * (r(e, g) * r(e, g) + r(e, h) * r(e, h) + r(f, g) * r(f, g) + r(f,
// h) * r(f, h))
// + r(e, g) * r(f, h) + r(e, h) * r(f, g)
// - r(e, f) * (r(f, g) * r(f, h) + r(e, g) * r(e, h))
// - r(g, h) * (r(f, g) * r(e, g) + r(f, h) * r(e, h));
//
// sigma_ss.set(i, j, rr);
// } else if (cov != null && dataSet == null) {
//
// // Assumes multinormality--see p. 160.
// double _ss = r(e, g) * r(f, h) + r(e, h) * r(f, g); // + or -? Different
// advise. + in the code.
// sigma_ss.set(i, j, _ss);
// } else {
// double _ss = sxyzw(e, f, g, h) - r(e, f) * r(g, h);
// sigma_ss.set(i, j, _ss);
// }
// }
// }
//
// // Need a matrix of of population estimates of partial derivatives of tetrads
// // with respect to covariances in boldSigma.
// TetradMatrix del = TetradMatrix.instance(boldSigma.size(), sextads.length);
//
// for (int i = 0; i < boldSigma.size(); i++) {
// for (int j = 0; j < sextads.length; j++) {
// Sigma sigma = boldSigma.get(i);
// Sextad sextad = sextads[j];
//
// Node m1 = sextad.getI();
// Node m2 = sextad.getJ();
// Node m3 = sextad.getK();
// Node m4 = sextad.getL();
// Node m5 = sextad.getM();
// Node m6 = sextad.getN();
//
// double derivative = getDerivative(m1, m2, m3, m4, m5, m6, sigma.getA(),
// sigma.getB());
// del.set(i, j, derivative);
// }
// }
//
// // Need a vector of population estimates of the sextads.
// TetradMatrix t = TetradMatrix.instance(sextads.length, 1);
//
// for (int i = 0; i < sextads.length; i++) {
// Sextad sextad = sextads[i];
//
// List<Node> nodes = new ArrayList<Node>();
//
// nodes.add(sextad.getI());
// nodes.add(sextad.getJ());
// nodes.add(sextad.getK());
// nodes.add(sextad.getL());
// nodes.add(sextad.getM());
// nodes.add(sextad.getN());
//
// TetradMatrix m = TetradMatrix.instance(3, 3);
//
// for (int k1 = 0; k1 < 3; k1++) {
// for (int k2 = 0; k2 < 3; k2++) {
// m.set(k1, k2, r(nodes.get(k1), nodes.get(3+k2)));
// }
// }
//
// double value = TetradAlgebra.det(m);
// t.set(i, 0, value);
// this.storedValue = value;
// }
//
// // Now multiply to get Sigma_tt
// TetradMatrix w1 = TetradAlgebra.times(del.transpose(), sigma_ss);
// TetradMatrix sigma_tt = TetradAlgebra.times(w1, del);
//
// // And now invert and multiply to get T.
// TetradMatrix v0 = TetradAlgebra.inverse(sigma_tt);
// TetradMatrix v1 = TetradAlgebra.times(t.transpose(), v0);
// TetradMatrix v2 = TetradAlgebra.times(v1, t);
// double chisq = N * v2.get(0, 0);
//
// this.chisq = chisq;
// return chisq;
// }
public double calcChiSquare(Sextad... sextads) {
this.storedSextads = sextads;
this.df = 4; // sextads.length;
List<Sigma> boldSigma = new ArrayList<Sigma>();
List<Node> _nodes = new ArrayList<Node>(sextads[0].getNodes());
for (int i = 0; i < _nodes.size(); i++) {
for (int j = i + 1; j < _nodes.size(); j++) {
boldSigma.add(new Sigma(_nodes.get(i), _nodes.get(j)));
}
}
// Need a matrix of variances and covariances of sample covariances.
TetradMatrix sigma_ss = new TetradMatrix(boldSigma.size(), boldSigma.size());
for (int i = 0; i < boldSigma.size(); i++) {
for (int j = i; j < boldSigma.size(); j++) {
Sigma sigmaef = boldSigma.get(i);
Sigma sigmagh = boldSigma.get(j);
Node e = sigmaef.getA();
Node f = sigmaef.getB();
Node g = sigmagh.getA();
Node h = sigmagh.getB();
if (cov != null && cov instanceof CorrelationMatrix) {
// Assumes multinormality. Using formula 23. (Not implementing formula 22
// because that case
// does not come up.)
double rr =
0.5
* (r(e, f) * r(g, h))
* (r(e, g) * r(e, g)
+ r(e, h) * r(e, h)
+ r(f, g) * r(f, g)
+ r(f, h) * r(f, h))
+ r(e, g) * r(f, h)
+ r(e, h) * r(f, g)
- r(e, f) * (r(f, g) * r(f, h) + r(e, g) * r(e, h))
- r(g, h) * (r(f, g) * r(e, g) + r(f, h) * r(e, h));
sigma_ss.set(i, j, rr);
sigma_ss.set(j, i, rr);
} else if (cov != null && dataSet == null) {
// Assumes multinormality--see p. 160.
double _ss =
r(e, g) * r(f, h) + r(e, h) * r(f, g); // + or -? Different advise. + in the code.
// double _ss = r(e, g) * r(f, h) - r(e, h) * r(g, f); // shouldn't
// this be a tetrad?
sigma_ss.set(i, j, _ss);
sigma_ss.set(j, i, _ss);
} else {
double _ss = sxyzw(e, f, g, h) - r(e, f) * r(g, h);
sigma_ss.set(i, j, _ss);
sigma_ss.set(j, i, _ss);
}
}
}
// Need a matrix of of population estimates of partial derivatives of tetrads
// with respect to covariances in boldSigma.
TetradMatrix del = new TetradMatrix(boldSigma.size(), sextads.length);
for (int j = 0; j < sextads.length; j++) {
Sextad sextad = sextads[j];
for (int i = 0; i < boldSigma.size(); i++) {
Sigma sigma = boldSigma.get(i);
double derivative = getDerivative(sextad, sigma);
del.set(i, j, derivative);
}
}
// Need a vector of population estimates of the sextads.
TetradMatrix t = new TetradMatrix(sextads.length, 1);
for (int i = 0; i < sextads.length; i++) {
Sextad sextad = sextads[i];
List<Node> nodes = sextad.getNodes();
TetradMatrix m = new TetradMatrix(3, 3);
for (int k1 = 0; k1 < 3; k1++) {
for (int k2 = 0; k2 < 3; k2++) {
m.set(k1, k2, r(nodes.get(k1), nodes.get(3 + k2)));
}
}
double det = m.det();
t.set(i, 0, det);
this.storedValue = det; // ?
}
// for (int i = 0; i < sextads.length; i++) {
// Sextad sextad = sextads[i];
//
// List<Node> nodes = new ArrayList<Node>();
//
// nodes.add(sextad.getI());
// nodes.add(sextad.getJ());
// nodes.add(sextad.getK());
// nodes.add(sextad.getL());
// nodes.add(sextad.getM());
// nodes.add(sextad.getN());
//
// TetradMatrix m = TetradMatrix.instance(3, 3);
//
// for (int k1 = 0; k1 < 3; k1++) {
// for (int k2 = 0; k2 < 3; k2++) {
// m.set(k1, k2, r(nodes.get(k1), nodes.get(3+k2)));
// }
// }
//
// double value = TetradAlgebra.det(m);
// t.set(i, 0, value);
// this.storedValue = value;
// }
TetradMatrix sigma_tt = del.transpose().times(sigma_ss).times(del);
try {
this.chisq = N * t.transpose().times(sigma_tt.inverse()).times(t).get(0, 0);
return chisq;
} catch (Exception e) {
return Double.NaN;
}
}