home | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Java example source code file (GLSMultipleLinearRegressionTest.java)

This example Java source code file (GLSMultipleLinearRegressionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

before, correlatedrandomvectorgenerator, descriptivestatistics, gaussianrandomgenerator, glsmultiplelinearregression, glsmultiplelinearregressiontest, jdkrandomgenerator, multiplelinearregressionabstracttest, olsmultiplelinearregression, override, realmatrix, realvector, seed, test

The GLSMultipleLinearRegressionTest.java Java example source code

/*
 * 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.math3.stat.regression;

import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.RealVector;
import org.apache.commons.math3.random.CorrelatedRandomVectorGenerator;
import org.apache.commons.math3.random.JDKRandomGenerator;
import org.apache.commons.math3.random.GaussianRandomGenerator;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.stat.correlation.Covariance;
import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics;

public class GLSMultipleLinearRegressionTest extends MultipleLinearRegressionAbstractTest {

    private double[] y;
    private double[][] x;
    private double[][] omega;
    private double[] longley = new double[] {
            60323,83.0,234289,2356,1590,107608,1947,
            61122,88.5,259426,2325,1456,108632,1948,
            60171,88.2,258054,3682,1616,109773,1949,
            61187,89.5,284599,3351,1650,110929,1950,
            63221,96.2,328975,2099,3099,112075,1951,
            63639,98.1,346999,1932,3594,113270,1952,
            64989,99.0,365385,1870,3547,115094,1953,
            63761,100.0,363112,3578,3350,116219,1954,
            66019,101.2,397469,2904,3048,117388,1955,
            67857,104.6,419180,2822,2857,118734,1956,
            68169,108.4,442769,2936,2798,120445,1957,
            66513,110.8,444546,4681,2637,121950,1958,
            68655,112.6,482704,3813,2552,123366,1959,
            69564,114.2,502601,3931,2514,125368,1960,
            69331,115.7,518173,4806,2572,127852,1961,
            70551,116.9,554894,4007,2827,130081,1962
        };

    @Before
    @Override
    public void setUp(){
        y = new double[]{11.0, 12.0, 13.0, 14.0, 15.0, 16.0};
        x = new double[6][];
        x[0] = new double[]{0, 0, 0, 0, 0};
        x[1] = new double[]{2.0, 0, 0, 0, 0};
        x[2] = new double[]{0, 3.0, 0, 0, 0};
        x[3] = new double[]{0, 0, 4.0, 0, 0};
        x[4] = new double[]{0, 0, 0, 5.0, 0};
        x[5] = new double[]{0, 0, 0, 0, 6.0};
        omega = new double[6][];
        omega[0] = new double[]{1.0, 0, 0, 0, 0, 0};
        omega[1] = new double[]{0, 2.0, 0, 0, 0, 0};
        omega[2] = new double[]{0, 0, 3.0, 0, 0, 0};
        omega[3] = new double[]{0, 0, 0, 4.0, 0, 0};
        omega[4] = new double[]{0, 0, 0, 0, 5.0, 0};
        omega[5] = new double[]{0, 0, 0, 0, 0, 6.0};
        super.setUp();
    }

    @Test(expected=IllegalArgumentException.class)
    public void cannotAddXSampleData() {
        createRegression().newSampleData(new double[]{}, null, null);
    }

    @Test(expected=IllegalArgumentException.class)
    public void cannotAddNullYSampleData() {
        createRegression().newSampleData(null, new double[][]{}, null);
    }

    @Test(expected=IllegalArgumentException.class)
    public void cannotAddSampleDataWithSizeMismatch() {
        double[] y = new double[]{1.0, 2.0};
        double[][] x = new double[1][];
        x[0] = new double[]{1.0, 0};
        createRegression().newSampleData(y, x, null);
    }

    @Test(expected=IllegalArgumentException.class)
    public void cannotAddNullCovarianceData() {
        createRegression().newSampleData(new double[]{}, new double[][]{}, null);
    }

    @Test(expected=IllegalArgumentException.class)
    public void notEnoughData() {
        double[]   reducedY = new double[y.length - 1];
        double[][] reducedX = new double[x.length - 1][];
        double[][] reducedO = new double[omega.length - 1][];
        System.arraycopy(y,     0, reducedY, 0, reducedY.length);
        System.arraycopy(x,     0, reducedX, 0, reducedX.length);
        System.arraycopy(omega, 0, reducedO, 0, reducedO.length);
        createRegression().newSampleData(reducedY, reducedX, reducedO);
    }

    @Test(expected=IllegalArgumentException.class)
    public void cannotAddCovarianceDataWithSampleSizeMismatch() {
        double[] y = new double[]{1.0, 2.0};
        double[][] x = new double[2][];
        x[0] = new double[]{1.0, 0};
        x[1] = new double[]{0, 1.0};
        double[][] omega = new double[1][];
        omega[0] = new double[]{1.0, 0};
        createRegression().newSampleData(y, x, omega);
    }

    @Test(expected=IllegalArgumentException.class)
    public void cannotAddCovarianceDataThatIsNotSquare() {
        double[] y = new double[]{1.0, 2.0};
        double[][] x = new double[2][];
        x[0] = new double[]{1.0, 0};
        x[1] = new double[]{0, 1.0};
        double[][] omega = new double[3][];
        omega[0] = new double[]{1.0, 0};
        omega[1] = new double[]{0, 1.0};
        omega[2] = new double[]{0, 2.0};
        createRegression().newSampleData(y, x, omega);
    }

    @Override
    protected GLSMultipleLinearRegression createRegression() {
        GLSMultipleLinearRegression regression = new GLSMultipleLinearRegression();
        regression.newSampleData(y, x, omega);
        return regression;
    }

    @Override
    protected int getNumberOfRegressors() {
        return x[0].length + 1;
    }

    @Override
    protected int getSampleSize() {
        return y.length;
    }

    /**
     * test calculateYVariance
     */
    @Test
    public void testYVariance() {

        // assumes: y = new double[]{11.0, 12.0, 13.0, 14.0, 15.0, 16.0};

        GLSMultipleLinearRegression model = new GLSMultipleLinearRegression();
        model.newSampleData(y, x, omega);
        TestUtils.assertEquals(model.calculateYVariance(), 3.5, 0);
    }

    /**
     * Verifies that setting X, Y and covariance separately has the same effect as newSample(X,Y,cov).
     */
    @Test
    public void testNewSample2() {
        double[] y = new double[] {1, 2, 3, 4};
        double[][] x = new double[][] {
          {19, 22, 33},
          {20, 30, 40},
          {25, 35, 45},
          {27, 37, 47}
        };
        double[][] covariance = MatrixUtils.createRealIdentityMatrix(4).scalarMultiply(2).getData();
        GLSMultipleLinearRegression regression = new GLSMultipleLinearRegression();
        regression.newSampleData(y, x, covariance);
        RealMatrix combinedX = regression.getX().copy();
        RealVector combinedY = regression.getY().copy();
        RealMatrix combinedCovInv = regression.getOmegaInverse();
        regression.newXSampleData(x);
        regression.newYSampleData(y);
        Assert.assertEquals(combinedX, regression.getX());
        Assert.assertEquals(combinedY, regression.getY());
        Assert.assertEquals(combinedCovInv, regression.getOmegaInverse());
    }

    /**
     * Verifies that GLS with identity covariance matrix gives the same results
     * as OLS.
     */
    @Test
    public void testGLSOLSConsistency() {
        RealMatrix identityCov = MatrixUtils.createRealIdentityMatrix(16);
        GLSMultipleLinearRegression glsModel = new GLSMultipleLinearRegression();
        OLSMultipleLinearRegression olsModel = new OLSMultipleLinearRegression();
        glsModel.newSampleData(longley, 16, 6);
        olsModel.newSampleData(longley, 16, 6);
        glsModel.newCovarianceData(identityCov.getData());
        double[] olsBeta = olsModel.calculateBeta().toArray();
        double[] glsBeta = glsModel.calculateBeta().toArray();
        // TODO:  Should have assertRelativelyEquals(double[], double[], eps) in TestUtils
        //        Should also add RealVector and RealMatrix versions
        for (int i = 0; i < olsBeta.length; i++) {
            TestUtils.assertRelativelyEquals(olsBeta[i], glsBeta[i], 10E-7);
        }
    }

    /**
     * Generate an error covariance matrix and sample data representing models
     * with this error structure. Then verify that GLS estimated coefficients,
     * on average, perform better than OLS.
     */
    @Test
    public void testGLSEfficiency() {
        RandomGenerator rg = new JDKRandomGenerator();
        rg.setSeed(200);  // Seed has been selected to generate non-trivial covariance

        // Assume model has 16 observations (will use Longley data).  Start by generating
        // non-constant variances for the 16 error terms.
        final int nObs = 16;
        double[] sigma = new double[nObs];
        for (int i = 0; i < nObs; i++) {
            sigma[i] = 10 * rg.nextDouble();
        }

        // Now generate 1000 error vectors to use to estimate the covariance matrix
        // Columns are draws on N(0, sigma[col])
        final int numSeeds = 1000;
        RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
        for (int i = 0; i < numSeeds; i++) {
            for (int j = 0; j < nObs; j++) {
                errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
            }
        }

        // Get covariance matrix for columns
        RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();

        // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
        GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
        double[] errorMeans = new double[nObs];  // Counting on init to 0 here
        CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
         1.0e-12 * cov.getNorm(), rawGenerator);

        // Now start generating models.  Use Longley X matrix on LHS
        // and Longley OLS beta vector as "true" beta.  Generate
        // Y values by XB + u where u is a CorrelatedRandomVector generated
        // from cov.
        OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
        ols.newSampleData(longley, nObs, 6);
        final RealVector b = ols.calculateBeta().copy();
        final RealMatrix x = ols.getX().copy();

        // Create a GLS model to reuse
        GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
        gls.newSampleData(longley, nObs, 6);
        gls.newCovarianceData(cov.getData());

        // Create aggregators for stats measuring model performance
        DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
        DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();

        // Generate Y vectors for 10000 models, estimate GLS and OLS and
        // Verify that OLS estimates are better
        final int nModels = 10000;
        for (int i = 0; i < nModels; i++) {

            // Generate y = xb + u with u cov
            RealVector u = MatrixUtils.createRealVector(gen.nextVector());
            double[] y = u.add(x.operate(b)).toArray();

            // Estimate OLS parameters
            ols.newYSampleData(y);
            RealVector olsBeta = ols.calculateBeta();

            // Estimate GLS parameters
            gls.newYSampleData(y);
            RealVector glsBeta = gls.calculateBeta();

            // Record deviations from "true" beta
            double dist = olsBeta.getDistance(b);
            olsBetaStats.addValue(dist * dist);
            dist = glsBeta.getDistance(b);
            glsBetaStats.addValue(dist * dist);

        }

        // Verify that GLS is on average more efficient, lower variance
        assert(olsBetaStats.getMean() > 1.5 * glsBetaStats.getMean());
        assert(olsBetaStats.getStandardDeviation() > glsBetaStats.getStandardDeviation());
    }

}

Other Java examples (source code examples)

Here is a short list of links related to this Java GLSMultipleLinearRegressionTest.java source code file:



my book on functional programming

 

new blog posts

 

Copyright 1998-2021 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.