Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 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.math.stat.regression; |
| 18 | |
| 19 | import org.apache.commons.math.linear.LUDecompositionImpl; |
| 20 | import org.apache.commons.math.linear.RealMatrix; |
| 21 | import org.apache.commons.math.linear.Array2DRowRealMatrix; |
| 22 | import org.apache.commons.math.linear.RealVector; |
| 23 | |
| 24 | /** |
| 25 | * The GLS implementation of the multiple linear regression. |
| 26 | * |
| 27 | * GLS assumes a general covariance matrix Omega of the error |
| 28 | * <pre> |
| 29 | * u ~ N(0, Omega) |
| 30 | * </pre> |
| 31 | * |
| 32 | * Estimated by GLS, |
| 33 | * <pre> |
| 34 | * b=(X' Omega^-1 X)^-1X'Omega^-1 y |
| 35 | * </pre> |
| 36 | * whose variance is |
| 37 | * <pre> |
| 38 | * Var(b)=(X' Omega^-1 X)^-1 |
| 39 | * </pre> |
| 40 | * @version $Revision: 1073460 $ $Date: 2011-02-22 20:22:39 +0100 (mar. 22 févr. 2011) $ |
| 41 | * @since 2.0 |
| 42 | */ |
| 43 | public class GLSMultipleLinearRegression extends AbstractMultipleLinearRegression { |
| 44 | |
| 45 | /** Covariance matrix. */ |
| 46 | private RealMatrix Omega; |
| 47 | |
| 48 | /** Inverse of covariance matrix. */ |
| 49 | private RealMatrix OmegaInverse; |
| 50 | |
| 51 | /** Replace sample data, overriding any previous sample. |
| 52 | * @param y y values of the sample |
| 53 | * @param x x values of the sample |
| 54 | * @param covariance array representing the covariance matrix |
| 55 | */ |
| 56 | public void newSampleData(double[] y, double[][] x, double[][] covariance) { |
| 57 | validateSampleData(x, y); |
| 58 | newYSampleData(y); |
| 59 | newXSampleData(x); |
| 60 | validateCovarianceData(x, covariance); |
| 61 | newCovarianceData(covariance); |
| 62 | } |
| 63 | |
| 64 | /** |
| 65 | * Add the covariance data. |
| 66 | * |
| 67 | * @param omega the [n,n] array representing the covariance |
| 68 | */ |
| 69 | protected void newCovarianceData(double[][] omega){ |
| 70 | this.Omega = new Array2DRowRealMatrix(omega); |
| 71 | this.OmegaInverse = null; |
| 72 | } |
| 73 | |
| 74 | /** |
| 75 | * Get the inverse of the covariance. |
| 76 | * <p>The inverse of the covariance matrix is lazily evaluated and cached.</p> |
| 77 | * @return inverse of the covariance |
| 78 | */ |
| 79 | protected RealMatrix getOmegaInverse() { |
| 80 | if (OmegaInverse == null) { |
| 81 | OmegaInverse = new LUDecompositionImpl(Omega).getSolver().getInverse(); |
| 82 | } |
| 83 | return OmegaInverse; |
| 84 | } |
| 85 | |
| 86 | /** |
| 87 | * Calculates beta by GLS. |
| 88 | * <pre> |
| 89 | * b=(X' Omega^-1 X)^-1X'Omega^-1 y |
| 90 | * </pre> |
| 91 | * @return beta |
| 92 | */ |
| 93 | @Override |
| 94 | protected RealVector calculateBeta() { |
| 95 | RealMatrix OI = getOmegaInverse(); |
| 96 | RealMatrix XT = X.transpose(); |
| 97 | RealMatrix XTOIX = XT.multiply(OI).multiply(X); |
| 98 | RealMatrix inverse = new LUDecompositionImpl(XTOIX).getSolver().getInverse(); |
| 99 | return inverse.multiply(XT).multiply(OI).operate(Y); |
| 100 | } |
| 101 | |
| 102 | /** |
| 103 | * Calculates the variance on the beta. |
| 104 | * <pre> |
| 105 | * Var(b)=(X' Omega^-1 X)^-1 |
| 106 | * </pre> |
| 107 | * @return The beta variance matrix |
| 108 | */ |
| 109 | @Override |
| 110 | protected RealMatrix calculateBetaVariance() { |
| 111 | RealMatrix OI = getOmegaInverse(); |
| 112 | RealMatrix XTOIX = X.transpose().multiply(OI).multiply(X); |
| 113 | return new LUDecompositionImpl(XTOIX).getSolver().getInverse(); |
| 114 | } |
| 115 | |
| 116 | |
| 117 | /** |
| 118 | * Calculates the estimated variance of the error term using the formula |
| 119 | * <pre> |
| 120 | * Var(u) = Tr(u' Omega^-1 u)/(n-k) |
| 121 | * </pre> |
| 122 | * where n and k are the row and column dimensions of the design |
| 123 | * matrix X. |
| 124 | * |
| 125 | * @return error variance |
| 126 | * @since 2.2 |
| 127 | */ |
| 128 | @Override |
| 129 | protected double calculateErrorVariance() { |
| 130 | RealVector residuals = calculateResiduals(); |
| 131 | double t = residuals.dotProduct(getOmegaInverse().operate(residuals)); |
| 132 | return t / (X.getRowDimension() - X.getColumnDimension()); |
| 133 | |
| 134 | } |
| 135 | |
| 136 | } |