/** @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();
}
/**
* Checks conditional independence of variable in a continuous data set using Fisher's Z test. See
* Spirtes, Glymour, and Scheines, "Causation, Prediction and Search," 2nd edition, page 94.
*
* @author Joseph Ramsey
* @author Frank Wimberly adapted IndTestCramerT for Fisher's Z
*/
public final class IndTestFisherZShortTriangular implements IndependenceTest {
/** The covariance matrix. */
private final ShortTriangularMatrix covMatrix;
/** The variables of the covariance matrix, in order. (Unmodifiable list.) */
private List<Node> variables;
/** The significance level of the independence tests. */
private double alpha;
/**
* The value of the Fisher's Z statistic associated with the las calculated partial correlation.
*/
private double fisherZ;
/**
* The FisherZD independence test, used when Fisher Z throws an exception (i.e., when there's a
* collinearity).
*/
private IndTestFisherZGeneralizedInverse deterministicTest;
/** Formats as 0.0000. */
private static NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
/** Stores a reference to the dataset being analyzed. */
private DataSet dataSet;
/** A stored p value, if the deterministic test was used. */
private double pValue = Double.NaN;
// ==========================CONSTRUCTORS=============================//
/**
* Constructs a new Independence test which checks independence facts based on the correlation
* matrix implied by the given data set (must be continuous). The given significance level is
* used.
*
* @param dataSet A data set containing only continuous columns.
* @param alpha The alpha level of the test.
*/
public IndTestFisherZShortTriangular(DataSet dataSet, double alpha) {
if (!(dataSet.isContinuous())) {
throw new IllegalArgumentException("Data set must be continuous.");
}
this.covMatrix = new ShortTriangularMatrix(dataSet.getNumColumns());
this.covMatrix.becomeCorrelationMatrix(dataSet);
this.variables = dataSet.getVariables();
setAlpha(alpha);
this.deterministicTest = new IndTestFisherZGeneralizedInverse(dataSet, alpha);
this.dataSet = dataSet;
}
/**
* Constructs a new Fisher Z independence test with the listed arguments.
*
* @param data A 2D continuous data set with no missing values.
* @param variables A list of variables, a subset of the variables of <code>data</code>.
* @param alpha The significance cutoff level. p values less than alpha will be reported as
* dependent.
*/
public IndTestFisherZShortTriangular(TetradMatrix data, List<Node> variables, double alpha) {
DataSet dataSet = ColtDataSet.makeContinuousData(variables, data);
this.covMatrix = new ShortTriangularMatrix(dataSet.getNumColumns());
this.covMatrix.becomeCorrelationMatrix(dataSet);
this.variables = dataSet.getVariables();
setAlpha(alpha);
this.deterministicTest = new IndTestFisherZGeneralizedInverse(dataSet, alpha);
}
// /**
// * Constructs a new independence test that will determine conditional
// * independence facts using the given correlation matrix and the given
// * significance level.
// */
// public IndTestFisherZShortTriangular(CovarianceMatrix corrMatrix, double alpha) {
// this.covMatrix = corrMatrix;
// this.variables = Collections.unmodifiableList(corrMatrix.getVariables());
// setAlpha(alpha);
// }
// ==========================PUBLIC METHODS=============================//
/** Creates a new IndTestCramerT instance for a subset of the variables. */
public IndependenceTest indTestSubset(List<Node> vars) {
// if (vars.isEmpty()) {
// throw new IllegalArgumentException("Subset may not be empty.");
// }
//
// for (Node ar : vars) {
// if (!variables.contains(ar)) {
// throw new IllegalArgumentException(
// "All vars must be original vars");
// }
// }
//
// int[] indices = new int[vars.size()];
//
// for (int i = 0; i < indices.length; i++) {
// indices[i] = variables.indexOf(vars.get(i));
// }
//
// CovarianceMatrix newCovMatrix = getSubmatrix(indices);
//
// double alphaNew = getAlpha();
// return new IndTestFisherZShortTriangular(newCovMatrix, alphaNew);
throw new UnsupportedOperationException();
}
/**
* 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;
}
private TetradMatrix subMatrix(Node x, Node y, List<Node> z) {
int dim = z.size() + 2;
int[] indices = new int[dim];
indices[0] = variables.indexOf(x);
indices[1] = variables.indexOf(y);
for (int k = 0; k < z.size(); k++) {
indices[k + 2] = variables.indexOf(z.get(k));
}
TetradMatrix submatrix = new TetradMatrix(dim, dim);
for (int i = 0; i < dim; i++) {
for (int j = 0; j < dim; j++) {
int i1 = indices[i];
int i2 = indices[j];
submatrix.set(i, j, covMatrix.getDouble(i1, i2));
}
}
return submatrix;
}
public boolean isIndependent(Node x, Node y, Node... z) {
return isIndependent(x, y, Arrays.asList(z));
}
public boolean isDependent(Node x, Node y, List<Node> z) {
return !isIndependent(x, y, z);
}
public boolean isDependent(Node x, Node y, Node... z) {
List<Node> zList = Arrays.asList(z);
return isDependent(x, y, zList);
}
/** @return the probability associated with the most recently computed independence test. */
public double getPValue() {
if (!Double.isNaN(this.pValue)) {
return Double.NaN;
} else {
return 2.0 * (1.0 - RandomUtil.getInstance().normalCdf(0, 1, Math.abs(fisherZ)));
}
}
/**
* Sets the significance level at which independence judgments should be made. Affects the cutoff
* for partial correlations to be considered statistically equal to zero.
*/
public void setAlpha(double alpha) {
if (alpha < 0.0 || alpha > 1.0) {
throw new IllegalArgumentException("Significance out of range.");
}
this.alpha = alpha;
// this.thresh = Double.NaN;
}
/** Gets the getModel significance level. */
public double getAlpha() {
return this.alpha;
}
/**
* @return the list of variables over which this independence checker is capable of determinine
* independence relations-- that is, all the variables in the given graph or the given data
* set.
*/
public List<Node> getVariables() {
return this.variables;
}
/** @return the variable with the given name. */
public Node getVariable(String name) {
for (int i = 0; i < getVariables().size(); i++) {
Node variable = getVariables().get(i);
if (variable.getName().equals(name)) {
return variable;
}
}
return null;
}
/** @return the list of variable varNames. */
public List<String> getVariableNames() {
List<Node> variables = getVariables();
List<String> variableNames = new ArrayList<String>();
for (Node variable1 : variables) {
variableNames.add(variable1.getName());
}
return variableNames;
}
/**
* If <code>isDeterminismAllowed()</code>, deters to IndTestFisherZD; otherwise throws
* UnsupportedOperationException.
*/
public boolean determines(List<Node> z, Node x) throws UnsupportedOperationException {
throw new UnsupportedOperationException();
// int[] parents = new int[z.size()];
//
// for (int j = 0; j < parents.length; j++) {
// parents[j] = covMatrix.getVariables().indexOf(z.get(j));
// }
//
// int i = covMatrix.getVariables().indexOf(x);
//
// TetradMatrix matrix2D = covMatrix.getMatrix();
// double variance = matrix2D.get(i, i);
//
// if (parents.length > 0) {
//
// // Regress z onto i, yielding regression coefficients b.
// TetradMatrix Czz =
// matrix2D.viewSelection(parents, parents);
// TetradMatrix inverse;
// try {
// inverse = TetradAlgebra.inverse(Czz);
//// inverse = MatrixUtils.ginverse(Czz);
// }
// catch (Exception e) {
// return true;
// }
//
// TetradVector Cyz = matrix2D.viewColumn(i);
// Cyz = Cyz.viewSelection(parents);
// TetradVector b = TetradAlgebra.times(inverse, Cyz);
//
// variance -= TetradAlgebra.times(Cyz, b);
// }
//
// return variance < 0.01;
}
/** @return the data set being analyzed. */
public DataSet getData() {
return dataSet;
}
@Override
public ICovarianceMatrix getCov() {
return null;
}
@Override
public List<DataSet> getDataSets() {
return null;
}
@Override
public int getSampleSize() {
return 0;
}
@Override
public List<TetradMatrix> getCovMatrices() {
return null;
}
public void shuffleVariables() {
List<Node> nodes = new ArrayList(this.variables);
Collections.shuffle(nodes);
this.variables = Collections.unmodifiableList(nodes);
}
/** @return a string representation of this test. */
public String toString() {
return "Fisher's Z, alpha = " + nf.format(getAlpha());
}
// ==========================PRIVATE METHODS============================//
/**
* Computes that value x such that P(abs(N(0,1) > x) < alpha. Note that this is a two sided test
* of the null hypothesis that the Fisher's Z value, which is distributed as N(0,1) is not equal
* to 0.0.
*/
private double cutoffGaussian(double alpha) {
double upperTail = 1.0 - alpha / 2.0;
double epsilon = 1e-14;
// Find an upper bound.
double lowerBound = -1.0;
double upperBound = 0.0;
while (ProbUtils.normalCdf(upperBound) < upperTail) {
lowerBound += 1.0;
upperBound += 1.0;
}
while (upperBound >= lowerBound + epsilon) {
double midPoint = lowerBound + (upperBound - lowerBound) / 2.0;
if (ProbUtils.normalCdf(midPoint) <= upperTail) {
lowerBound = midPoint;
} else {
upperBound = midPoint;
}
}
return lowerBound;
}
private int sampleSize() {
return dataSet.getNumRows();
}
// private CovarianceMatrix covMatrix() {
// return covMatrix;
// }
}
