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The Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.

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/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math.stat.regression;

import org.apache.commons.math.linear.LUDecompositionImpl;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.Array2DRowRealMatrix;
import org.apache.commons.math.linear.RealVector;


/**
 * The GLS implementation of the multiple linear regression.
 * 
 * GLS assumes a general covariance matrix Omega of the error
 * 
 * u ~ N(0, Omega)
 * 
* * Estimated by GLS, *
 * b=(X' Omega^-1 X)^-1X'Omega^-1 y
 * 
* whose variance is *
 * Var(b)=(X' Omega^-1 X)^-1
 * 
* @version $Revision: 783702 $ $Date: 2009-06-11 04:54:02 -0400 (Thu, 11 Jun 2009) $ * @since 2.0 */ public class GLSMultipleLinearRegression extends AbstractMultipleLinearRegression { /** Covariance matrix. */ private RealMatrix Omega; /** Inverse of covariance matrix. */ private RealMatrix OmegaInverse; /** Replace sample data, overriding any previous sample. * @param y y values of the sample * @param x x values of the sample * @param covariance array representing the covariance matrix */ public void newSampleData(double[] y, double[][] x, double[][] covariance) { validateSampleData(x, y); newYSampleData(y); newXSampleData(x); validateCovarianceData(x, covariance); newCovarianceData(covariance); } /** * Add the covariance data. * * @param omega the [n,n] array representing the covariance */ protected void newCovarianceData(double[][] omega){ this.Omega = new Array2DRowRealMatrix(omega); this.OmegaInverse = null; } /** * Get the inverse of the covariance. *

The inverse of the covariance matrix is lazily evaluated and cached.

* @return inverse of the covariance */ protected RealMatrix getOmegaInverse() { if (OmegaInverse == null) { OmegaInverse = new LUDecompositionImpl(Omega).getSolver().getInverse(); } return OmegaInverse; } /** * Calculates beta by GLS. *
     *  b=(X' Omega^-1 X)^-1X'Omega^-1 y
     * 
* @return beta */ @Override protected RealVector calculateBeta() { RealMatrix OI = getOmegaInverse(); RealMatrix XT = X.transpose(); RealMatrix XTOIX = XT.multiply(OI).multiply(X); RealMatrix inverse = new LUDecompositionImpl(XTOIX).getSolver().getInverse(); return inverse.multiply(XT).multiply(OI).operate(Y); } /** * Calculates the variance on the beta by GLS. *
     *  Var(b)=(X' Omega^-1 X)^-1
     * 
* @return The beta variance matrix */ @Override protected RealMatrix calculateBetaVariance() { RealMatrix OI = getOmegaInverse(); RealMatrix XTOIX = X.transpose().multiply(OI).multiply(X); return new LUDecompositionImpl(XTOIX).getSolver().getInverse(); } /** * Calculates the variance on the y by GLS. *
     *  Var(y)=Tr(u' Omega^-1 u)/(n-k)
     * 
* @return The Y variance */ @Override protected double calculateYVariance() { RealVector residuals = calculateResiduals(); double t = residuals.dotProduct(getOmegaInverse().operate(residuals)); return t / (X.getRowDimension() - X.getColumnDimension()); } }




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