AbstractMultipleLinearRegression.java

  1. /*
  2.  * Licensed to the Apache Software Foundation (ASF) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * The ASF licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *      http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.apache.commons.math4.legacy.stat.regression;

  19. import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
  20. import org.apache.commons.math4.legacy.exception.InsufficientDataException;
  21. import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  22. import org.apache.commons.math4.legacy.exception.NoDataException;
  23. import org.apache.commons.math4.legacy.exception.NullArgumentException;
  24. import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
  25. import org.apache.commons.math4.legacy.linear.Array2DRowRealMatrix;
  26. import org.apache.commons.math4.legacy.linear.ArrayRealVector;
  27. import org.apache.commons.math4.legacy.linear.NonSquareMatrixException;
  28. import org.apache.commons.math4.legacy.linear.RealMatrix;
  29. import org.apache.commons.math4.legacy.linear.RealVector;
  30. import org.apache.commons.math4.legacy.stat.descriptive.moment.Variance;
  31. import org.apache.commons.math4.core.jdkmath.JdkMath;

  33. /**
  34.  * Abstract base class for implementations of MultipleLinearRegression.
  35.  * @since 2.0
  36.  */
  37. public abstract class AbstractMultipleLinearRegression implements
  38.         MultipleLinearRegression {

  40.     /** X sample data. */
  41.     private RealMatrix xMatrix;

  43.     /** Y sample data. */
  44.     private RealVector yVector;

  46.     /** Whether or not the regression model includes an intercept.  True means no intercept. */
  47.     private boolean noIntercept;

  49.     /**
  50.      * @return the X sample data.
  51.      */
  52.     protected RealMatrix getX() {
  53.         return xMatrix;
  54.     }

  56.     /**
  57.      * @return the Y sample data.
  58.      */
  59.     protected RealVector getY() {
  60.         return yVector;
  61.     }

  63.     /**
  64.      * @return true if the model has no intercept term; false otherwise
  65.      * @since 2.2
  66.      */
  67.     public boolean isNoIntercept() {
  68.         return noIntercept;
  69.     }

  71.     /**
  72.      * @param noIntercept true means the model is to be estimated without an intercept term
  73.      * @since 2.2
  74.      */
  75.     public void setNoIntercept(boolean noIntercept) {
  76.         this.noIntercept = noIntercept;
  77.     }

  79.     /**
  80.      * <p>Loads model x and y sample data from a flat input array, overriding any previous sample.
  81.      * </p>
  82.      * <p>Assumes that rows are concatenated with y values first in each row.  For example, an input
  83.      * <code>data</code> array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with
  84.      * <code>nobs = 3</code> and <code>nvars = 2</code> creates a regression dataset with two
  85.      * independent variables, as below:
  86.      * <pre>
  87.      *   y   x[0]  x[1]
  88.      *   --------------
  89.      *   1     2     3
  90.      *   4     5     6
  91.      *   7     8     9
  92.      * </pre>
  93.      *
  94.      * <p>Note that there is no need to add an initial unitary column (column of 1's) when
  95.      * specifying a model including an intercept term.  If {@link #isNoIntercept()} is <code>true</code>,
  96.      * the X matrix will be created without an initial column of "1"s; otherwise this column will
  97.      * be added.
  98.      * </p>
  99.      * <p>Throws IllegalArgumentException if any of the following preconditions fail:
  100.      * <ul><li><code>data</code> cannot be null</li>
  101.      * <li><code>data.length = nobs * (nvars + 1)</code></li>
  102.      * <li>{@code nobs > nvars}</li></ul>
  103.      *
  104.      * @param data input data array
  105.      * @param nobs number of observations (rows)
  106.      * @param nvars number of independent variables (columns, not counting y)
  107.      * @throws NullArgumentException if the data array is null
  108.      * @throws DimensionMismatchException if the length of the data array is not equal
  109.      * to <code>nobs * (nvars + 1)</code>
  110.      * @throws InsufficientDataException if <code>nobs</code> is less than
  111.      * <code>nvars + 1</code>
  112.      */
  113.     public void newSampleData(double[] data, int nobs, int nvars) {
  114.         if (data == null) {
  115.             throw new NullArgumentException();
  116.         }
  117.         if (data.length != nobs * (nvars + 1)) {
  118.             throw new DimensionMismatchException(data.length, nobs * (nvars + 1));
  119.         }
  120.         if (nobs <= nvars) {
  121.             throw new InsufficientDataException(LocalizedFormats.INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE, nobs, nvars + 1);
  122.         }
  123.         double[] y = new double[nobs];
  124.         final int cols = noIntercept ? nvars: nvars + 1;
  125.         double[][] x = new double[nobs][cols];
  126.         int pointer = 0;
  127.         for (int i = 0; i < nobs; i++) {
  128.             y[i] = data[pointer++];
  129.             if (!noIntercept) {
  130.                 x[i][0] = 1.0d;
  131.             }
  132.             for (int j = noIntercept ? 0 : 1; j < cols; j++) {
  133.                 x[i][j] = data[pointer++];
  134.             }
  135.         }
  136.         this.xMatrix = new Array2DRowRealMatrix(x);
  137.         this.yVector = new ArrayRealVector(y);
  138.     }

  140.     /**
  141.      * Loads new y sample data, overriding any previous data.
  142.      *
  143.      * @param y the array representing the y sample
  144.      * @throws NullArgumentException if y is null
  145.      * @throws NoDataException if y is empty
  146.      */
  147.     protected void newYSampleData(double[] y) {
  148.         if (y == null) {
  149.             throw new NullArgumentException();
  150.         }
  151.         if (y.length == 0) {
  152.             throw new NoDataException();
  153.         }
  154.         this.yVector = new ArrayRealVector(y);
  155.     }

  157.     /**
  158.      * <p>Loads new x sample data, overriding any previous data.
  159.      * </p>
  160.      * The input <code>x</code> array should have one row for each sample
  161.      * observation, with columns corresponding to independent variables.
  162.      * For example, if <pre>
  163.      * <code> x = new double[][] {{1, 2}, {3, 4}, {5, 6}} </code></pre>
  164.      * then <code>setXSampleData(x) </code> results in a model with two independent
  165.      * variables and 3 observations:
  166.      * <pre>
  167.      *   x[0]  x[1]
  168.      *   ----------
  169.      *     1    2
  170.      *     3    4
  171.      *     5    6
  172.      * </pre>
  173.      * <p>Note that there is no need to add an initial unitary column (column of 1's) when
  174.      * specifying a model including an intercept term.
  175.      * </p>
  176.      * @param x the rectangular array representing the x sample
  177.      * @throws NullArgumentException if x is null
  178.      * @throws NoDataException if x is empty
  179.      * @throws DimensionMismatchException if x is not rectangular
  180.      */
  181.     protected void newXSampleData(double[][] x) {
  182.         if (x == null) {
  183.             throw new NullArgumentException();
  184.         }
  185.         if (x.length == 0) {
  186.             throw new NoDataException();
  187.         }
  188.         if (noIntercept) {
  189.             this.xMatrix = new Array2DRowRealMatrix(x, true);
  190.         } else { // Augment design matrix with initial unitary column
  191.             final int nVars = x[0].length;
  192.             final double[][] xAug = new double[x.length][nVars + 1];
  193.             for (int i = 0; i < x.length; i++) {
  194.                 if (x[i].length != nVars) {
  195.                     throw new DimensionMismatchException(x[i].length, nVars);
  196.                 }
  197.                 xAug[i][0] = 1.0d;
  198.                 System.arraycopy(x[i], 0, xAug[i], 1, nVars);
  199.             }
  200.             this.xMatrix = new Array2DRowRealMatrix(xAug, false);
  201.         }
  202.     }

  204.     /**
  205.      * Validates sample data.  Checks that
  206.      * <ul><li>Neither x nor y is null or empty;</li>
  207.      * <li>The length (i.e. number of rows) of x equals the length of y</li>
  208.      * <li>x has at least one more row than it has columns (i.e. there is
  209.      * sufficient data to estimate regression coefficients for each of the
  210.      * columns in x plus an intercept.</li>
  211.      * </ul>
  212.      *
  213.      * @param x the [n,k] array representing the x data
  214.      * @param y the [n,1] array representing the y data
  215.      * @throws NullArgumentException if {@code x} or {@code y} is null
  216.      * @throws DimensionMismatchException if {@code x} and {@code y} do not
  217.      * have the same length
  218.      * @throws NoDataException if {@code x} or {@code y} are zero-length
  219.      * @throws MathIllegalArgumentException if the number of rows of {@code x}
  220.      * is not larger than the number of columns + 1
  221.      */
  222.     protected void validateSampleData(double[][] x, double[] y) throws MathIllegalArgumentException {
  223.         if (x == null || y == null) {
  224.             throw new NullArgumentException();
  225.         }
  226.         if (x.length != y.length) {
  227.             throw new DimensionMismatchException(y.length, x.length);
  228.         }
  229.         if (x.length == 0) {  // Must be no y data either
  230.             throw new NoDataException();
  231.         }
  232.         if (x[0].length + 1 > x.length) {
  233.             throw new MathIllegalArgumentException(
  234.                     LocalizedFormats.NOT_ENOUGH_DATA_FOR_NUMBER_OF_PREDICTORS,
  235.                     x.length, x[0].length);
  236.         }
  237.     }

  239.     /**
  240.      * Validates that the x data and covariance matrix have the same
  241.      * number of rows and that the covariance matrix is square.
  242.      *
  243.      * @param x the [n,k] array representing the x sample
  244.      * @param covariance the [n,n] array representing the covariance matrix
  245.      * @throws DimensionMismatchException if the number of rows in x is not equal
  246.      * to the number of rows in covariance
  247.      * @throws NonSquareMatrixException if the covariance matrix is not square
  248.      */
  249.     protected void validateCovarianceData(double[][] x, double[][] covariance) {
  250.         if (x.length != covariance.length) {
  251.             throw new DimensionMismatchException(x.length, covariance.length);
  252.         }
  253.         if (covariance.length > 0 && covariance.length != covariance[0].length) {
  254.             throw new NonSquareMatrixException(covariance.length, covariance[0].length);
  255.         }
  256.     }

  258.     /**
  259.      * {@inheritDoc}
  260.      */
  261.     @Override
  262.     public double[] estimateRegressionParameters() {
  263.         RealVector b = calculateBeta();
  264.         return b.toArray();
  265.     }

  267.     /**
  268.      * {@inheritDoc}
  269.      */
  270.     @Override
  271.     public double[] estimateResiduals() {
  272.         RealVector b = calculateBeta();
  273.         RealVector e = yVector.subtract(xMatrix.operate(b));
  274.         return e.toArray();
  275.     }

  277.     /**
  278.      * {@inheritDoc}
  279.      */
  280.     @Override
  281.     public double[][] estimateRegressionParametersVariance() {
  282.         return calculateBetaVariance().getData();
  283.     }

  285.     /**
  286.      * {@inheritDoc}
  287.      */
  288.     @Override
  289.     public double[] estimateRegressionParametersStandardErrors() {
  290.         double[][] betaVariance = estimateRegressionParametersVariance();
  291.         double sigma = calculateErrorVariance();
  292.         int length = betaVariance[0].length;
  293.         double[] result = new double[length];
  294.         for (int i = 0; i < length; i++) {
  295.             result[i] = JdkMath.sqrt(sigma * betaVariance[i][i]);
  296.         }
  297.         return result;
  298.     }

  300.     /**
  301.      * {@inheritDoc}
  302.      */
  303.     @Override
  304.     public double estimateRegressandVariance() {
  305.         return calculateYVariance();
  306.     }

  308.     /**
  309.      * Estimates the variance of the error.
  310.      *
  311.      * @return estimate of the error variance
  312.      * @since 2.2
  313.      */
  314.     public double estimateErrorVariance() {
  315.         return calculateErrorVariance();
  316.     }

  318.     /**
  319.      * Estimates the standard error of the regression.
  320.      *
  321.      * @return regression standard error
  322.      * @since 2.2
  323.      */
  324.     public double estimateRegressionStandardError() {
  325.         return JdkMath.sqrt(estimateErrorVariance());
  326.     }

  328.     /**
  329.      * Calculates the beta of multiple linear regression in matrix notation.
  330.      *
  331.      * @return beta
  332.      */
  333.     protected abstract RealVector calculateBeta();

  335.     /**
  336.      * Calculates the beta variance of multiple linear regression in matrix
  337.      * notation.
  338.      *
  339.      * @return beta variance
  340.      */
  341.     protected abstract RealMatrix calculateBetaVariance();


  344.     /**
  345.      * Calculates the variance of the y values.
  346.      *
  347.      * @return Y variance
  348.      */
  349.     protected double calculateYVariance() {
  350.         return new Variance().evaluate(yVector.toArray());
  351.     }

  353.     /**
  354.      * <p>Calculates the variance of the error term.</p>
  355.      * Uses the formula <pre>
  356.      * var(u) = u &middot; u / (n - k)
  357.      * </pre>
  358.      * where n and k are the row and column dimensions of the design
  359.      * matrix X.
  360.      *
  361.      * @return error variance estimate
  362.      * @since 2.2
  363.      */
  364.     protected double calculateErrorVariance() {
  365.         RealVector residuals = calculateResiduals();
  366.         return residuals.dotProduct(residuals) /
  367.                (xMatrix.getRowDimension() - xMatrix.getColumnDimension());
  368.     }

  370.     /**
  371.      * Calculates the residuals of multiple linear regression in matrix
  372.      * notation.
  373.      *
  374.      * <pre>
  375.      * u = y - X * b
  376.      * </pre>
  377.      *
  378.      * @return The residuals [n,1] matrix
  379.      */
  380.     protected RealVector calculateResiduals() {
  381.         RealVector b = calculateBeta();
  382.         return yVector.subtract(xMatrix.operate(b));
  383.     }
  384. }
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