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// For information as to what this class does, see the Javadoc, below. //
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, //
// 2007, 2008, 2009, 2010, 2014, 2015, 2022 by Peter Spirtes, Richard //
// Scheines, Joseph Ramsey, and Clark Glymour. //
// //
// This program is free software; you can redistribute it and/or modify //
// it under the terms of the GNU General Public License as published by //
// the Free Software Foundation; either version 2 of the License, or //
// (at your option) any later version. //
// //
// This program is distributed in the hope that it will be useful, //
// but WITHOUT ANY WARRANTY; without even the implied warranty of //
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
// GNU General Public License for more details. //
// //
// You should have received a copy of the GNU General Public License //
// along with this program; if not, write to the Free Software //
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA //
///////////////////////////////////////////////////////////////////////////////
package edu.cmu.tetrad.search.work_in_progress;
import edu.cmu.tetrad.data.CorrelationMatrix;
import edu.cmu.tetrad.data.DataSet;
import edu.cmu.tetrad.data.DataUtils;
import edu.cmu.tetrad.data.ICovarianceMatrix;
import edu.cmu.tetrad.graph.IndependenceFact;
import edu.cmu.tetrad.graph.Node;
import edu.cmu.tetrad.search.IndependenceTest;
import edu.cmu.tetrad.search.test.IndependenceResult;
import edu.cmu.tetrad.search.utils.LogUtilsSearch;
import edu.cmu.tetrad.util.*;
import org.apache.commons.math3.linear.SingularMatrixException;
import org.apache.commons.math3.util.FastMath;
import java.text.NumberFormat;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Set;
/**
* Checks conditional independence for continuous variables using Cramer's T-test formula (Cramer, Mathematical Methods
* of Statistics (1951), page 413).
*
* @author josephramsey
*/
public final class IndTestCramerT implements IndependenceTest {
/**
* Formats as 0.0000.
*/
private static final NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
/**
* The correlation matrix.
*/
private final ICovarianceMatrix covMatrix;
/**
* The variables of the correlation matrix, in order. (Unmodifiable list.)
*/
private final List variables;
/**
* The data set over which conditional independence judgements are being formed.
*/
private DataSet dataSet;
/**
* The significance level of the independence tests.
*/
private double alpha;
/**
* The last used partial correlation distribution function.
*/
private PartialCorrelationPdf pdf;
/**
* The cutoff value for 'alpha' area in the two tails of the partial correlation distribution function.
*/
private double cutoff;
/**
* The last calculated partial correlation, needed to calculate relative strength.
*/
private double storedR;
private boolean verbose;
//==========================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 with all continuous columns.
* @param alpha the alpha level of the test.
*/
public IndTestCramerT(DataSet dataSet, double alpha) {
if (!(dataSet.isContinuous())) {
throw new IllegalArgumentException("Data set must be continuous.");
}
this.dataSet = dataSet;
this.covMatrix = new CorrelationMatrix(dataSet);
this.variables =
Collections.unmodifiableList(this.covMatrix.getVariables());
setAlpha(alpha);
}
/**
* Constructs a new independence test that will determine conditional independence facts using the given correlation
* matrix and the given significance level.
*/
public IndTestCramerT(CorrelationMatrix covMatrix, double alpha) {
this.covMatrix = covMatrix;
this.variables =
Collections.unmodifiableList(covMatrix.getVariables());
setAlpha(alpha);
}
/**
* Constructs a new independence test that will determine conditional independence facts using the given correlation
* matrix and the given significance level.
*/
public IndTestCramerT(ICovarianceMatrix covMatrix, double alpha) {
CorrelationMatrix corrMatrix = new CorrelationMatrix(covMatrix);
this.variables =
Collections.unmodifiableList(corrMatrix.getVariables());
this.covMatrix = corrMatrix;
setAlpha(alpha);
}
//==========================PUBLIC METHODS=============================//
/**
* Creates a new IndTestCramerT instance for a subset of the variables.
*/
public IndependenceTest indTestSubset(List vars) {
if (vars.isEmpty()) {
throw new IllegalArgumentException("Subset may not be empty.");
}
for (Node var : vars) {
if (!this.variables.contains(var)) {
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] = this.variables.indexOf(vars.get(i));
}
ICovarianceMatrix newCorrMatrix = this.covMatrix.getSubmatrix(indices);
double alphaNew = getAlpha();
return new IndTestCramerT(newCorrMatrix, alphaNew);
}
/**
* 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 IndependenceResult checkIndependence(Node x, Node y, Set _z) {
if (_z == null) {
throw new NullPointerException();
}
for (Node node : _z) {
if (node == null) {
throw new NullPointerException();
}
}
List z = new ArrayList<>();
Collections.sort(z);
// Precondition: this.variables, this.corrMatrix properly set up.
//
// Postcondition: this.storedR and this.func should be the
// most recently calculated partial correlation and
// partial correlation distribution function, respectively.
//
// PROCEDURE:
// calculate the partial correlation of x and y given z
// by finding the submatrix of variables x, y, z1...zn,
// inverting it, and examining the value at position (0, 1)
// in the inverted matrix. the partial correlation is
// -1 * this value / the square root of the outerProduct of the
// diagonal elements on the same row and column as this
// value.
//
// Design consideration:
// Minimize object creation by reusing submatrix and condition
// arrays and inverting submatrix in place.
// Create index array for the given variables.
int size = z.size() + 2;
int[] indices = new int[size];
indices[0] = getVariables().indexOf(x);
indices[1] = getVariables().indexOf(y);
for (int i = 0; i < z.size(); i++) {
indices[i + 2] = getVariables().indexOf(z.get(i));
}
// Extract submatrix of correlation matrix using this index array.
Matrix submatrix =
covMatrix().getMatrix().getSelection(indices, indices);
// Check for missing values.
if (DataUtils.containsMissingValue(submatrix)) {
throw new IllegalArgumentException(
"Please remove or impute missing values first.");
}
try {
submatrix = submatrix.inverse();
} catch (SingularMatrixException e) {
throw new RuntimeException("Singularity encountered when testing " +
LogUtilsSearch.independenceFact(x, y, _z));
}
double a = -1.0 * submatrix.get(0, 1);
double b = FastMath.sqrt(submatrix.get(0, 0) * submatrix.get(1, 1));
this.storedR = a / b; // Store R so P value can be calculated.
if (FastMath.abs(this.storedR) > 1) {
this.storedR = FastMath.signum(this.storedR);
}
if (Double.isNaN(this.storedR)) {
throw new IllegalArgumentException("Conditional correlation cannot be computed: " + LogUtilsSearch.independenceFact(x, y, _z));
}
// Determine whether this partial correlation is statistically
// nondifferent from zero.
boolean independent = isZero(this.storedR, size, getAlpha());
double pValue = getPValue();
if (Double.isNaN(pValue)) {
throw new RuntimeException("Undefined p-value encountered for test: " + LogUtilsSearch.independenceFact(x, y, _z));
}
if (this.verbose) {
if (independent) {
TetradLogger.getInstance().forceLogMessage(
LogUtilsSearch.independenceFactMsg(x, y, _z, pValue));
}
}
return new IndependenceResult(new IndependenceFact(x, y, _z), independent, pValue, alpha - pValue);
}
/**
* @return the probability associated with the most recently computed independence test.
*/
public double getPValue() {
return 2.0 * Integrator.getArea(pdf(), FastMath.abs(this.storedR), 1.0, 100);
}
/**
* @return the getModel significance level.
*/
public double getAlpha() {
return this.alpha;
}
/**
* Sets the significance level for future tests.
*/
public void setAlpha(double alpha) {
if (alpha < 0.0 || alpha > 1.0) {
throw new IllegalArgumentException("Significance out of range.");
}
this.alpha = alpha;
}
private ICovarianceMatrix covMatrix() {
return this.covMatrix;
}
/**
* @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 getVariables() {
return this.variables;
}
/**
* @return the variable with the given name, or null if there is no such variable.
*/
public boolean determines(List z, Node x) throws UnsupportedOperationException {
int[] parents = new int[z.size()];
for (int j = 0; j < parents.length; j++) {
parents[j] = this.covMatrix.getVariables().indexOf(z.get(j));
}
int i = this.covMatrix.getVariables().indexOf(x);
Matrix matrix2D = this.covMatrix.getMatrix();
double variance = matrix2D.get(i, i);
if (parents.length > 0) {
// Regress z onto i, yielding regression coefficients b.
Matrix Czz =
matrix2D.getSelection(parents, parents);
Matrix inverse;
try {
inverse = Czz.inverse();
// inverse = MatrixUtils.ginverse(Czz);
} catch (Exception e) {
return true;
}
Vector Cyz = matrix2D.getColumn(i);
Cyz = Cyz.viewSelection(parents);
Vector b = inverse.times(Cyz);
variance -= Cyz.dotProduct(b);
}
return variance < 0.01;
}
public DataSet getData() {
return this.dataSet;
}
/**
* @return a string representation of this test.
*/
public String toString() {
return "Partial Correlation T Test, alpha = " + IndTestCramerT.nf.format(getAlpha());
}
//==========================PRIVATE METHODS============================//
/**
* Tests whether the given correlation is statistically non-different from zero by determining whether |storedR| <=
* the cutoff calculated by placing an area equal to the significance level in the two tails of the relevant partial
* correlation distribution function.
*
* @param r the sample correlation.
* @param k the number of compared variables.
* @param alpha the alpha level.
* @return true if the sample correlation is statically non-different from zero, false if not.
*/
private boolean isZero(double r, int k, double alpha) {
if (pdf() == null || pdf().getK() != k) {
this.cutoff = cutoff(k, alpha);
}
return FastMath.abs(r) <= this.cutoff;
}
private double cutoff(int k, double alpha) {
this.pdf = new PartialCorrelationPdf(sampleSize() - 1, k);
final double upperBound = 1.0;
final double delta = 0.00001;
return CutoffFinder.getCutoff(pdf(), upperBound, alpha, delta);
}
private int sampleSize() {
return covMatrix().getSampleSize();
}
private PartialCorrelationPdf pdf() {
return this.pdf;
}
public boolean isVerbose() {
return this.verbose;
}
public void setVerbose(boolean verbose) {
this.verbose = verbose;
}
}
