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.math3.stat.regression;

  19. import org.apache.commons.math3.exception.DimensionMismatchException;
  20. import org.apache.commons.math3.exception.InsufficientDataException;
  21. import org.apache.commons.math3.exception.MathIllegalArgumentException;
  22. import org.apache.commons.math3.exception.NoDataException;
  23. import org.apache.commons.math3.exception.NullArgumentException;
  24. import org.apache.commons.math3.exception.util.LocalizedFormats;
  25. import org.apache.commons.math3.linear.NonSquareMatrixException;
  26. import org.apache.commons.math3.linear.RealMatrix;
  27. import org.apache.commons.math3.linear.Array2DRowRealMatrix;
  28. import org.apache.commons.math3.linear.RealVector;
  29. import org.apache.commons.math3.linear.ArrayRealVector;
  30. import org.apache.commons.math3.stat.descriptive.moment.Variance;
  31. import org.apache.commons.math3.util.FastMath;

  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 = false;

  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.      * </p>
  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)</li>
  102.      * <li><code>nobs > nvars</code></li></ul>
  103.      * </p>
  104.      *
  105.      * @param data input data array
  106.      * @param nobs number of observations (rows)
  107.      * @param nvars number of independent variables (columns, not counting y)
  108.      * @throws NullArgumentException if the data array is null
  109.      * @throws DimensionMismatchException if the length of the data array is not equal
  110.      * to <code>nobs * (nvars + 1)</code>
  111.      * @throws InsufficientDataException if <code>nobs</code> is less than
  112.      * <code>nvars + 1</code>
  113.      */
  114.     public void newSampleData(double[] data, int nobs, int nvars) {
  115.         if (data == null) {
  116.             throw new NullArgumentException();
  117.         }
  118.         if (data.length != nobs * (nvars + 1)) {
  119.             throw new DimensionMismatchException(data.length, nobs * (nvars + 1));
  120.         }
  121.         if (nobs <= nvars) {
  122.             throw new InsufficientDataException(LocalizedFormats.INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE, nobs, nvars + 1);
  123.         }
  124.         double[] y = new double[nobs];
  125.         final int cols = noIntercept ? nvars: nvars + 1;
  126.         double[][] x = new double[nobs][cols];
  127.         int pointer = 0;
  128.         for (int i = 0; i < nobs; i++) {
  129.             y[i] = data[pointer++];
  130.             if (!noIntercept) {
  131.                 x[i][0] = 1.0d;
  132.             }
  133.             for (int j = noIntercept ? 0 : 1; j < cols; j++) {
  134.                 x[i][j] = data[pointer++];
  135.             }
  136.         }
  137.         this.xMatrix = new Array2DRowRealMatrix(x);
  138.         this.yVector = new ArrayRealVector(y);
  139.     }

  141.     /**
  142.      * Loads new y sample data, overriding any previous data.
  143.      *
  144.      * @param y the array representing the y sample
  145.      * @throws NullArgumentException if y is null
  146.      * @throws NoDataException if y is empty
  147.      */
  148.     protected void newYSampleData(double[] y) {
  149.         if (y == null) {
  150.             throw new NullArgumentException();
  151.         }
  152.         if (y.length == 0) {
  153.             throw new NoDataException();
  154.         }
  155.         this.yVector = new ArrayRealVector(y);
  156.     }

  158.     /**
  159.      * <p>Loads new x sample data, overriding any previous data.
  160.      * </p>
  161.      * The input <code>x</code> array should have one row for each sample
  162.      * observation, with columns corresponding to independent variables.
  163.      * For example, if <pre>
  164.      * <code> x = new double[][] {{1, 2}, {3, 4}, {5, 6}} </code></pre>
  165.      * then <code>setXSampleData(x) </code> results in a model with two independent
  166.      * variables and 3 observations:
  167.      * <pre>
  168.      *   x[0]  x[1]
  169.      *   ----------
  170.      *     1    2
  171.      *     3    4
  172.      *     5    6
  173.      * </pre>
  174.      * </p>
  175.      * <p>Note that there is no need to add an initial unitary column (column of 1's) when
  176.      * specifying a model including an intercept term.
  177.      * </p>
  178.      * @param x the rectangular array representing the x sample
  179.      * @throws NullArgumentException if x is null
  180.      * @throws NoDataException if x is empty
  181.      * @throws DimensionMismatchException if x is not rectangular
  182.      */
  183.     protected void newXSampleData(double[][] x) {
  184.         if (x == null) {
  185.             throw new NullArgumentException();
  186.         }
  187.         if (x.length == 0) {
  188.             throw new NoDataException();
  189.         }
  190.         if (noIntercept) {
  191.             this.xMatrix = new Array2DRowRealMatrix(x, true);
  192.         } else { // Augment design matrix with initial unitary column
  193.             final int nVars = x[0].length;
  194.             final double[][] xAug = new double[x.length][nVars + 1];
  195.             for (int i = 0; i < x.length; i++) {
  196.                 if (x[i].length != nVars) {
  197.                     throw new DimensionMismatchException(x[i].length, nVars);
  198.                 }
  199.                 xAug[i][0] = 1.0d;
  200.                 System.arraycopy(x[i], 0, xAug[i], 1, nVars);
  201.             }
  202.             this.xMatrix = new Array2DRowRealMatrix(xAug, false);
  203.         }
  204.     }

  206.     /**
  207.      * Validates sample data.  Checks that
  208.      * <ul><li>Neither x nor y is null or empty;</li>
  209.      * <li>The length (i.e. number of rows) of x equals the length of y</li>
  210.      * <li>x has at least one more row than it has columns (i.e. there is
  211.      * sufficient data to estimate regression coefficients for each of the
  212.      * columns in x plus an intercept.</li>
  213.      * </ul>
  214.      *
  215.      * @param x the [n,k] array representing the x data
  216.      * @param y the [n,1] array representing the y data
  217.      * @throws NullArgumentException if {@code x} or {@code y} is null
  218.      * @throws DimensionMismatchException if {@code x} and {@code y} do not
  219.      * have the same length
  220.      * @throws NoDataException if {@code x} or {@code y} are zero-length
  221.      * @throws MathIllegalArgumentException if the number of rows of {@code x}
  222.      * is not larger than the number of columns + 1
  223.      */
  224.     protected void validateSampleData(double[][] x, double[] y) throws MathIllegalArgumentException {
  225.         if ((x == null) || (y == null)) {
  226.             throw new NullArgumentException();
  227.         }
  228.         if (x.length != y.length) {
  229.             throw new DimensionMismatchException(y.length, x.length);
  230.         }
  231.         if (x.length == 0) {  // Must be no y data either
  232.             throw new NoDataException();
  233.         }
  234.         if (x[0].length + 1 > x.length) {
  235.             throw new MathIllegalArgumentException(
  236.                     LocalizedFormats.NOT_ENOUGH_DATA_FOR_NUMBER_OF_PREDICTORS,
  237.                     x.length, x[0].length);
  238.         }
  239.     }

  241.     /**
  242.      * Validates that the x data and covariance matrix have the same
  243.      * number of rows and that the covariance matrix is square.
  244.      *
  245.      * @param x the [n,k] array representing the x sample
  246.      * @param covariance the [n,n] array representing the covariance matrix
  247.      * @throws DimensionMismatchException if the number of rows in x is not equal
  248.      * to the number of rows in covariance
  249.      * @throws NonSquareMatrixException if the covariance matrix is not square
  250.      */
  251.     protected void validateCovarianceData(double[][] x, double[][] covariance) {
  252.         if (x.length != covariance.length) {
  253.             throw new DimensionMismatchException(x.length, covariance.length);
  254.         }
  255.         if (covariance.length > 0 && covariance.length != covariance[0].length) {
  256.             throw new NonSquareMatrixException(covariance.length, covariance[0].length);
  257.         }
  258.     }

  260.     /**
  261.      * {@inheritDoc}
  262.      */
  263.     public double[] estimateRegressionParameters() {
  264.         RealVector b = calculateBeta();
  265.         return b.toArray();
  266.     }

  268.     /**
  269.      * {@inheritDoc}
  270.      */
  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.     public double[][] estimateRegressionParametersVariance() {
  281.         return calculateBetaVariance().getData();
  282.     }

  284.     /**
  285.      * {@inheritDoc}
  286.      */
  287.     public double[] estimateRegressionParametersStandardErrors() {
  288.         double[][] betaVariance = estimateRegressionParametersVariance();
  289.         double sigma = calculateErrorVariance();
  290.         int length = betaVariance[0].length;
  291.         double[] result = new double[length];
  292.         for (int i = 0; i < length; i++) {
  293.             result[i] = FastMath.sqrt(sigma * betaVariance[i][i]);
  294.         }
  295.         return result;
  296.     }

  298.     /**
  299.      * {@inheritDoc}
  300.      */
  301.     public double estimateRegressandVariance() {
  302.         return calculateYVariance();
  303.     }

  305.     /**
  306.      * Estimates the variance of the error.
  307.      *
  308.      * @return estimate of the error variance
  309.      * @since 2.2
  310.      */
  311.     public double estimateErrorVariance() {
  312.         return calculateErrorVariance();

  314.     }

  316.     /**
  317.      * Estimates the standard error of the regression.
  318.      *
  319.      * @return regression standard error
  320.      * @since 2.2
  321.      */
  322.     public double estimateRegressionStandardError() {
  323.         return FastMath.sqrt(estimateErrorVariance());
  324.     }

  326.     /**
  327.      * Calculates the beta of multiple linear regression in matrix notation.
  328.      *
  329.      * @return beta
  330.      */
  331.     protected abstract RealVector calculateBeta();

  333.     /**
  334.      * Calculates the beta variance of multiple linear regression in matrix
  335.      * notation.
  336.      *
  337.      * @return beta variance
  338.      */
  339.     protected abstract RealMatrix calculateBetaVariance();


  342.     /**
  343.      * Calculates the variance of the y values.
  344.      *
  345.      * @return Y variance
  346.      */
  347.     protected double calculateYVariance() {
  348.         return new Variance().evaluate(yVector.toArray());
  349.     }

  351.     /**
  352.      * <p>Calculates the variance of the error term.</p>
  353.      * Uses the formula <pre>
  354.      * var(u) = u &middot; u / (n - k)
  355.      * </pre>
  356.      * where n and k are the row and column dimensions of the design
  357.      * matrix X.
  358.      *
  359.      * @return error variance estimate
  360.      * @since 2.2
  361.      */
  362.     protected double calculateErrorVariance() {
  363.         RealVector residuals = calculateResiduals();
  364.         return residuals.dotProduct(residuals) /
  365.                (xMatrix.getRowDimension() - xMatrix.getColumnDimension());
  366.     }

  368.     /**
  369.      * Calculates the residuals of multiple linear regression in matrix
  370.      * notation.
  371.      *
  372.      * <pre>
  373.      * u = y - X * b
  374.      * </pre>
  375.      *
  376.      * @return The residuals [n,1] matrix
  377.      */
  378.     protected RealVector calculateResiduals() {
  379.         RealVector b = calculateBeta();
  380.         return yVector.subtract(xMatrix.operate(b));
  381.     }

  383. }
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