| /* |
| * 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.MathRuntimeException; |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| import org.apache.commons.math.linear.RealMatrix; |
| import org.apache.commons.math.linear.Array2DRowRealMatrix; |
| import org.apache.commons.math.linear.RealVector; |
| import org.apache.commons.math.linear.ArrayRealVector; |
| import org.apache.commons.math.stat.descriptive.moment.Variance; |
| import org.apache.commons.math.util.FastMath; |
| |
| /** |
| * Abstract base class for implementations of MultipleLinearRegression. |
| * @version $Revision: 1073459 $ $Date: 2011-02-22 20:18:12 +0100 (mar. 22 févr. 2011) $ |
| * @since 2.0 |
| */ |
| public abstract class AbstractMultipleLinearRegression implements |
| MultipleLinearRegression { |
| |
| /** X sample data. */ |
| protected RealMatrix X; |
| |
| /** Y sample data. */ |
| protected RealVector Y; |
| |
| /** Whether or not the regression model includes an intercept. True means no intercept. */ |
| private boolean noIntercept = false; |
| |
| /** |
| * @return true if the model has no intercept term; false otherwise |
| * @since 2.2 |
| */ |
| public boolean isNoIntercept() { |
| return noIntercept; |
| } |
| |
| /** |
| * @param noIntercept true means the model is to be estimated without an intercept term |
| * @since 2.2 |
| */ |
| public void setNoIntercept(boolean noIntercept) { |
| this.noIntercept = noIntercept; |
| } |
| |
| /** |
| * <p>Loads model x and y sample data from a flat input array, overriding any previous sample. |
| * </p> |
| * <p>Assumes that rows are concatenated with y values first in each row. For example, an input |
| * <code>data</code> array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with |
| * <code>nobs = 3</code> and <code>nvars = 2</code> creates a regression dataset with two |
| * independent variables, as below: |
| * <pre> |
| * y x[0] x[1] |
| * -------------- |
| * 1 2 3 |
| * 4 5 6 |
| * 7 8 9 |
| * </pre> |
| * </p> |
| * <p>Note that there is no need to add an initial unitary column (column of 1's) when |
| * specifying a model including an intercept term. If {@link #isNoIntercept()} is <code>true</code>, |
| * the X matrix will be created without an initial column of "1"s; otherwise this column will |
| * be added. |
| * </p> |
| * <p>Throws IllegalArgumentException if any of the following preconditions fail: |
| * <ul><li><code>data</code> cannot be null</li> |
| * <li><code>data.length = nobs * (nvars + 1)</li> |
| * <li><code>nobs > nvars</code></li></ul> |
| * </p> |
| * |
| * @param data input data array |
| * @param nobs number of observations (rows) |
| * @param nvars number of independent variables (columns, not counting y) |
| * @throws IllegalArgumentException if the preconditions are not met |
| */ |
| public void newSampleData(double[] data, int nobs, int nvars) { |
| if (data == null) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NULL_NOT_ALLOWED); |
| } |
| if (data.length != nobs * (nvars + 1)) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.INVALID_REGRESSION_ARRAY, data.length, nobs, nvars); |
| } |
| if (nobs <= nvars) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NOT_ENOUGH_DATA_FOR_NUMBER_OF_PREDICTORS); |
| } |
| double[] y = new double[nobs]; |
| final int cols = noIntercept ? nvars: nvars + 1; |
| double[][] x = new double[nobs][cols]; |
| int pointer = 0; |
| for (int i = 0; i < nobs; i++) { |
| y[i] = data[pointer++]; |
| if (!noIntercept) { |
| x[i][0] = 1.0d; |
| } |
| for (int j = noIntercept ? 0 : 1; j < cols; j++) { |
| x[i][j] = data[pointer++]; |
| } |
| } |
| this.X = new Array2DRowRealMatrix(x); |
| this.Y = new ArrayRealVector(y); |
| } |
| |
| /** |
| * Loads new y sample data, overriding any previous data. |
| * |
| * @param y the array representing the y sample |
| * @throws IllegalArgumentException if y is null or empty |
| */ |
| protected void newYSampleData(double[] y) { |
| if (y == null) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NULL_NOT_ALLOWED); |
| } |
| if (y.length == 0) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NO_DATA); |
| } |
| this.Y = new ArrayRealVector(y); |
| } |
| |
| /** |
| * <p>Loads new x sample data, overriding any previous data. |
| * </p> |
| * The input <code>x</code> array should have one row for each sample |
| * observation, with columns corresponding to independent variables. |
| * For example, if <pre> |
| * <code> x = new double[][] {{1, 2}, {3, 4}, {5, 6}} </code></pre> |
| * then <code>setXSampleData(x) </code> results in a model with two independent |
| * variables and 3 observations: |
| * <pre> |
| * x[0] x[1] |
| * ---------- |
| * 1 2 |
| * 3 4 |
| * 5 6 |
| * </pre> |
| * </p> |
| * <p>Note that there is no need to add an initial unitary column (column of 1's) when |
| * specifying a model including an intercept term. |
| * </p> |
| * @param x the rectangular array representing the x sample |
| * @throws IllegalArgumentException if x is null, empty or not rectangular |
| */ |
| protected void newXSampleData(double[][] x) { |
| if (x == null) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NULL_NOT_ALLOWED); |
| } |
| if (x.length == 0) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NO_DATA); |
| } |
| if (noIntercept) { |
| this.X = new Array2DRowRealMatrix(x, true); |
| } else { // Augment design matrix with initial unitary column |
| final int nVars = x[0].length; |
| final double[][] xAug = new double[x.length][nVars + 1]; |
| for (int i = 0; i < x.length; i++) { |
| if (x[i].length != nVars) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.DIFFERENT_ROWS_LENGTHS, |
| x[i].length, nVars); |
| } |
| xAug[i][0] = 1.0d; |
| System.arraycopy(x[i], 0, xAug[i], 1, nVars); |
| } |
| this.X = new Array2DRowRealMatrix(xAug, false); |
| } |
| } |
| |
| /** |
| * Validates sample data. Checks that |
| * <ul><li>Neither x nor y is null or empty;</li> |
| * <li>The length (i.e. number of rows) of x equals the length of y</li> |
| * <li>x has at least one more row than it has columns (i.e. there is |
| * sufficient data to estimate regression coefficients for each of the |
| * columns in x plus an intercept.</li> |
| * </ul> |
| * |
| * @param x the [n,k] array representing the x data |
| * @param y the [n,1] array representing the y data |
| * @throws IllegalArgumentException if any of the checks fail |
| * |
| */ |
| protected void validateSampleData(double[][] x, double[] y) { |
| if ((x == null) || (y == null) || (x.length != y.length)) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, |
| (x == null) ? 0 : x.length, |
| (y == null) ? 0 : y.length); |
| } |
| if (x.length == 0) { // Must be no y data either |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NO_DATA); |
| } |
| if (x[0].length + 1 > x.length) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NOT_ENOUGH_DATA_FOR_NUMBER_OF_PREDICTORS, |
| x.length, x[0].length); |
| } |
| } |
| |
| /** |
| * Validates that the x data and covariance matrix have the same |
| * number of rows and that the covariance matrix is square. |
| * |
| * @param x the [n,k] array representing the x sample |
| * @param covariance the [n,n] array representing the covariance matrix |
| * @throws IllegalArgumentException if the number of rows in x is not equal |
| * to the number of rows in covariance or covariance is not square. |
| */ |
| protected void validateCovarianceData(double[][] x, double[][] covariance) { |
| if (x.length != covariance.length) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, x.length, covariance.length); |
| } |
| if (covariance.length > 0 && covariance.length != covariance[0].length) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.NON_SQUARE_MATRIX, |
| covariance.length, covariance[0].length); |
| } |
| } |
| |
| /** |
| * {@inheritDoc} |
| */ |
| public double[] estimateRegressionParameters() { |
| RealVector b = calculateBeta(); |
| return b.getData(); |
| } |
| |
| /** |
| * {@inheritDoc} |
| */ |
| public double[] estimateResiduals() { |
| RealVector b = calculateBeta(); |
| RealVector e = Y.subtract(X.operate(b)); |
| return e.getData(); |
| } |
| |
| /** |
| * {@inheritDoc} |
| */ |
| public double[][] estimateRegressionParametersVariance() { |
| return calculateBetaVariance().getData(); |
| } |
| |
| /** |
| * {@inheritDoc} |
| */ |
| public double[] estimateRegressionParametersStandardErrors() { |
| double[][] betaVariance = estimateRegressionParametersVariance(); |
| double sigma = calculateErrorVariance(); |
| int length = betaVariance[0].length; |
| double[] result = new double[length]; |
| for (int i = 0; i < length; i++) { |
| result[i] = FastMath.sqrt(sigma * betaVariance[i][i]); |
| } |
| return result; |
| } |
| |
| /** |
| * {@inheritDoc} |
| */ |
| public double estimateRegressandVariance() { |
| return calculateYVariance(); |
| } |
| |
| /** |
| * Estimates the variance of the error. |
| * |
| * @return estimate of the error variance |
| * @since 2.2 |
| */ |
| public double estimateErrorVariance() { |
| return calculateErrorVariance(); |
| |
| } |
| |
| /** |
| * Estimates the standard error of the regression. |
| * |
| * @return regression standard error |
| * @since 2.2 |
| */ |
| public double estimateRegressionStandardError() { |
| return Math.sqrt(estimateErrorVariance()); |
| } |
| |
| /** |
| * Calculates the beta of multiple linear regression in matrix notation. |
| * |
| * @return beta |
| */ |
| protected abstract RealVector calculateBeta(); |
| |
| /** |
| * Calculates the beta variance of multiple linear regression in matrix |
| * notation. |
| * |
| * @return beta variance |
| */ |
| protected abstract RealMatrix calculateBetaVariance(); |
| |
| |
| /** |
| * Calculates the variance of the y values. |
| * |
| * @return Y variance |
| */ |
| protected double calculateYVariance() { |
| return new Variance().evaluate(Y.getData()); |
| } |
| |
| /** |
| * <p>Calculates the variance of the error term.</p> |
| * Uses the formula <pre> |
| * var(u) = u · u / (n - k) |
| * </pre> |
| * where n and k are the row and column dimensions of the design |
| * matrix X. |
| * |
| * @return error variance estimate |
| * @since 2.2 |
| */ |
| protected double calculateErrorVariance() { |
| RealVector residuals = calculateResiduals(); |
| return residuals.dotProduct(residuals) / |
| (X.getRowDimension() - X.getColumnDimension()); |
| } |
| |
| /** |
| * Calculates the residuals of multiple linear regression in matrix |
| * notation. |
| * |
| * <pre> |
| * u = y - X * b |
| * </pre> |
| * |
| * @return The residuals [n,1] matrix |
| */ |
| protected RealVector calculateResiduals() { |
| RealVector b = calculateBeta(); |
| return Y.subtract(X.operate(b)); |
| } |
| |
| } |
