/**
* Determines whether variable x is independent of variable y given a list of conditioning
* variables z.
*
* @param x the one variable being compared.
* @param y the second variable being compared.
* @param z the list of conditioning variables.
* @return true iff x _||_ y | z.
* @throws RuntimeException if a matrix singularity is encountered.
*/
public boolean isIndependent(Node x, Node y, List<Node> z) {
TetradMatrix submatrix = subMatrix(x, y, z);
double r = 0;
try {
r = StatUtils.partialCorrelation(submatrix);
if (Double.isNaN((r)) || r < -1. || r > 1.) throw new RuntimeException();
} catch (Exception e) {
DepthChoiceGenerator gen = new DepthChoiceGenerator(z.size(), z.size());
int[] choice;
while ((choice = gen.next()) != null) {
try {
List<Node> z2 = new ArrayList<Node>(z);
z2.removeAll(GraphUtils.asList(choice, z));
submatrix = subMatrix(x, y, z2);
r = StatUtils.partialCorrelation(submatrix);
} catch (Exception e2) {
continue;
}
// if (Double.isNaN(r)) continue;
//
// if (r > 1.) r = 1.;
// if (r < -1.) r = -1.;
if (Double.isNaN(r) || r < -1. || r > 1.) continue;
break;
}
}
// Either dividing by a zero standard deviation (in which case it's dependent) or doing a
// regression
// (effectively) with a multicolliarity
if (Double.isNaN(r)) {
int[] _z = new int[z.size()];
// for (int i = 0; i < _z.length; i++) _z[i] = i + 2;
//
//// double varx = StatUtils.partialVariance(submatrix, 0, _z); // submatrix.get(0,
// 0);
//// double vary = StatUtils.partialVariance(submatrix, 1, _z); //submatrix.get(1,
// 1);
//
// double varx = submatrix.get(0, 0);
// double vary = submatrix.get(1, 1);
//
// if (varx * vary == 0) {
return true;
// }
}
if (r > 1.) r = 1.;
if (r < -1.) r = -1.;
this.fisherZ =
Math.sqrt(sampleSize() - z.size() - 3.0) * 0.5 * (Math.log(1.0 + r) - Math.log(1.0 - r));
if (Double.isNaN(this.fisherZ)) {
throw new IllegalArgumentException(
"The Fisher's Z "
+ "score for independence fact "
+ x
+ " _||_ "
+ y
+ " | "
+ z
+ " is undefined. r = "
+ r);
}
boolean independent = getPValue() > alpha;
if (independent) {
TetradLogger.getInstance()
.log("independencies", SearchLogUtils.independenceFactMsg(x, y, z, getPValue()));
} else {
TetradLogger.getInstance()
.log("dependencies", SearchLogUtils.dependenceFactMsg(x, y, z, getPValue()));
}
return independent;
}
