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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.test;
import cern.colt.matrix.DoubleMatrix1D;
import cern.colt.matrix.DoubleMatrix2D;
import cern.colt.matrix.impl.DenseDoubleMatrix2D;
import cern.colt.matrix.linalg.Algebra;
import cern.jet.math.Functions;
import edu.cmu.tetrad.data.DataSet;
import edu.cmu.tetrad.graph.IndependenceFact;
import edu.cmu.tetrad.graph.Node;
import edu.cmu.tetrad.regression.Regression;
import edu.cmu.tetrad.regression.RegressionDataset;
import edu.cmu.tetrad.regression.RegressionResult;
import edu.cmu.tetrad.search.IndependenceTest;
import edu.cmu.tetrad.search.utils.LogUtilsSearch;
import edu.cmu.tetrad.util.Matrix;
import edu.cmu.tetrad.util.NumberFormatUtil;
import edu.cmu.tetrad.util.TetradLogger;
import java.text.NumberFormat;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Set;
/**
* Checks independence of X _||_ Y | Z for variables X and Y and list Z of variables by regressing X on {Y} U Z and
* testing whether the coefficient for Y is zero.
*
* @author josephramsey
* @author Frank Wimberly
*/
public final class IndTestRegression implements IndependenceTest {
/**
* The standard number formatter for Tetrad.
*/
private static final NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
/**
* The correlation matrix.
*/
private final DoubleMatrix2D data;
/**
* The variables of the correlation matrix, in order. (Unmodifiable list.)
*/
private final List variables;
private final DataSet dataSet;
/**
* 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 fishersZ;
private boolean verbose;
/**
* 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 IndTestRegression(DataSet dataSet, double alpha) {
if (!(alpha >= 0 && alpha <= 1)) {
throw new IllegalArgumentException("Alpha mut be in [0, 1]");
}
this.dataSet = dataSet;
this.data = new DenseDoubleMatrix2D(dataSet.getDoubleData().toArray());
this.variables = Collections.unmodifiableList(dataSet.getVariables());
setAlpha(alpha);
}
/**
* Creates a new IndTestCramerT instance for a subset of the variables.
*/
public IndependenceTest indTestSubset(List vars) {
return null;
}
/**
* Determines whether variable x is independent of variable y given a list of conditioning variables z.
*
* @param xVar the one variable being compared.
* @param yVar the second variable being compared.
* @param zList the list of conditioning variables.
* @return true iff x _||_ y | z.
* @throws RuntimeException if a matrix singularity is encountered.
*/
public IndependenceResult checkIndependence(Node xVar, Node yVar, Set zList) {
if (zList == null) {
throw new NullPointerException();
}
for (Node node : zList) {
if (node == null) {
throw new NullPointerException();
}
}
List regressors = new ArrayList<>();
regressors.add(this.dataSet.getVariable(yVar.getName()));
for (Node zVar : zList) {
regressors.add(this.dataSet.getVariable(zVar.getName()));
}
Regression regression = new RegressionDataset(this.dataSet);
RegressionResult result;
try {
result = regression.regress(xVar, regressors);
} catch (Exception e) {
return new IndependenceResult(new IndependenceFact(xVar, yVar, zList),
false, Double.NaN, Double.NaN);
}
double p = result.getP()[1];
if (Double.isNaN(p)) {
throw new RuntimeException("Undefined p-value encountered when testing " +
LogUtilsSearch.independenceFact(xVar, yVar, zList));
}
boolean independent = p > this.alpha;
if (this.verbose) {
if (independent) {
TetradLogger.getInstance().log("independencies", LogUtilsSearch.independenceFactMsg(xVar, yVar, zList, p));
} else {
TetradLogger.getInstance().log("dependencies", LogUtilsSearch.dependenceFactMsg(xVar, yVar, zList, p));
}
}
if (this.verbose) {
if (independent) {
TetradLogger.getInstance().forceLogMessage(
LogUtilsSearch.independenceFactMsg(xVar, yVar, zList, p));
}
}
return new IndependenceResult(new IndependenceFact(xVar, yVar, zList),
independent, p, getAlpha() - p);
}
/**
* Gets the getModel significance level.
*/
public double getAlpha() {
return this.alpha;
}
/**
* 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;
}
/**
* @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;
}
public String toString() {
return "Linear Regression Test, alpha = " + IndTestRegression.nf.format(getAlpha());
}
public boolean determines(List zList, Node xVar) {
if (zList == null) {
throw new NullPointerException();
}
for (Node node : zList) {
if (node == null) {
throw new NullPointerException();
}
}
int size = zList.size();
int[] zCols = new int[size];
int xIndex = getVariables().indexOf(xVar);
for (int i = 0; i < zList.size(); i++) {
zCols[i] = getVariables().indexOf(zList.get(i));
}
int[] zRows = new int[this.data.rows()];
for (int i = 0; i < this.data.rows(); i++) {
zRows[i] = i;
}
DoubleMatrix2D Z = this.data.viewSelection(zRows, zCols);
DoubleMatrix1D x = this.data.viewColumn(xIndex);
DoubleMatrix2D Zt = new Algebra().transpose(Z);
DoubleMatrix2D ZtZ = new Algebra().mult(Zt, Z);
DoubleMatrix2D G = new DenseDoubleMatrix2D(new Matrix(ZtZ.toArray()).inverse().toArray());
// Bug in Colt? Need to make a copy before multiplying to avoid
// a ClassCastException.
DoubleMatrix2D Zt2 = Zt.like();
Zt2.assign(Zt);
DoubleMatrix2D GZt = new Algebra().mult(G, Zt2);
DoubleMatrix1D b_x = new Algebra().mult(GZt, x);
DoubleMatrix1D xPred = new Algebra().mult(Z, b_x);
DoubleMatrix1D xRes = xPred.copy().assign(x, Functions.minus);
double SSE = xRes.aggregate(Functions.plus, Functions.square);
boolean determined = SSE < 0.0001;
if (determined) {
StringBuilder sb = new StringBuilder();
sb.append("Determination found: ").append(xVar).append(
" is determined by {");
for (int i = 0; i < zList.size(); i++) {
sb.append(zList.get(i));
if (i < zList.size() - 1) {
sb.append(", ");
}
}
sb.append("}");
TetradLogger.getInstance().log("independencies", sb.toString());
}
return determined;
}
public DataSet getData() {
return this.dataSet;
}
public boolean isVerbose() {
return this.verbose;
}
public void setVerbose(boolean verbose) {
this.verbose = verbose;
}
}
