Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.plugin
view libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| author | dwinter |
|---|---|
| date | Tue, 04 Jan 2011 10:02:07 +0100 |
| parents | |
| children |
line wrap: on
line source
<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.stat.regression;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import org.apache.commons.math.linear.Array2DRowRealMatrix;<a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.linear.LUDecompositionImpl;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.linear.QRDecomposition;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.linear.QRDecompositionImpl;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.linear.RealVector;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /**<a name="line.26"></a> <FONT color="green">027</FONT> * <p>Implements ordinary least squares (OLS) to estimate the parameters of a<a name="line.27"></a> <FONT color="green">028</FONT> * multiple linear regression model.</p><a name="line.28"></a> <FONT color="green">029</FONT> *<a name="line.29"></a> <FONT color="green">030</FONT> * <p>OLS assumes the covariance matrix of the error to be diagonal and with<a name="line.30"></a> <FONT color="green">031</FONT> * equal variance.</p><a name="line.31"></a> <FONT color="green">032</FONT> * <p><a name="line.32"></a> <FONT color="green">033</FONT> * u ~ N(0, &sigma;<sup>2</sup>I)<a name="line.33"></a> <FONT color="green">034</FONT> * </p><a name="line.34"></a> <FONT color="green">035</FONT> *<a name="line.35"></a> <FONT color="green">036</FONT> * <p>The regression coefficients, b, satisfy the normal equations:<a name="line.36"></a> <FONT color="green">037</FONT> * <p><a name="line.37"></a> <FONT color="green">038</FONT> * X<sup>T</sup> X b = X<sup>T</sup> y<a name="line.38"></a> <FONT color="green">039</FONT> * </p><a name="line.39"></a> <FONT color="green">040</FONT> *<a name="line.40"></a> <FONT color="green">041</FONT> * <p>To solve the normal equations, this implementation uses QR decomposition<a name="line.41"></a> <FONT color="green">042</FONT> * of the X matrix. (See {@link QRDecompositionImpl} for details on the<a name="line.42"></a> <FONT color="green">043</FONT> * decomposition algorithm.)<a name="line.43"></a> <FONT color="green">044</FONT> * </p><a name="line.44"></a> <FONT color="green">045</FONT> * <p>X<sup>T</sup>X b = X<sup>T</sup> y <br/><a name="line.45"></a> <FONT color="green">046</FONT> * (QR)<sup>T</sup> (QR) b = (QR)<sup>T</sup>y <br/><a name="line.46"></a> <FONT color="green">047</FONT> * R<sup>T</sup> (Q<sup>T</sup>Q) R b = R<sup>T</sup> Q<sup>T</sup> y <br/><a name="line.47"></a> <FONT color="green">048</FONT> * R<sup>T</sup> R b = R<sup>T</sup> Q<sup>T</sup> y <br/><a name="line.48"></a> <FONT color="green">049</FONT> * (R<sup>T</sup>)<sup>-1</sup> R<sup>T</sup> R b = (R<sup>T</sup>)<sup>-1</sup> R<sup>T</sup> Q<sup>T</sup> y <br/><a name="line.49"></a> <FONT color="green">050</FONT> * R b = Q<sup>T</sup> y<a name="line.50"></a> <FONT color="green">051</FONT> * </p><a name="line.51"></a> <FONT color="green">052</FONT> * Given Q and R, the last equation is solved by back-subsitution.</p><a name="line.52"></a> <FONT color="green">053</FONT> *<a name="line.53"></a> <FONT color="green">054</FONT> * @version $Revision: 825925 $ $Date: 2009-10-16 11:11:47 -0400 (Fri, 16 Oct 2009) $<a name="line.54"></a> <FONT color="green">055</FONT> * @since 2.0<a name="line.55"></a> <FONT color="green">056</FONT> */<a name="line.56"></a> <FONT color="green">057</FONT> public class OLSMultipleLinearRegression extends AbstractMultipleLinearRegression {<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /** Cached QR decomposition of X matrix */<a name="line.59"></a> <FONT color="green">060</FONT> private QRDecomposition qr = null;<a name="line.60"></a> <FONT color="green">061</FONT> <a name="line.61"></a> <FONT color="green">062</FONT> /**<a name="line.62"></a> <FONT color="green">063</FONT> * Loads model x and y sample data, overriding any previous sample.<a name="line.63"></a> <FONT color="green">064</FONT> *<a name="line.64"></a> <FONT color="green">065</FONT> * Computes and caches QR decomposition of the X matrix.<a name="line.65"></a> <FONT color="green">066</FONT> * @param y the [n,1] array representing the y sample<a name="line.66"></a> <FONT color="green">067</FONT> * @param x the [n,k] array representing the x sample<a name="line.67"></a> <FONT color="green">068</FONT> * @throws IllegalArgumentException if the x and y array data are not<a name="line.68"></a> <FONT color="green">069</FONT> * compatible for the regression<a name="line.69"></a> <FONT color="green">070</FONT> */<a name="line.70"></a> <FONT color="green">071</FONT> public void newSampleData(double[] y, double[][] x) {<a name="line.71"></a> <FONT color="green">072</FONT> validateSampleData(x, y);<a name="line.72"></a> <FONT color="green">073</FONT> newYSampleData(y);<a name="line.73"></a> <FONT color="green">074</FONT> newXSampleData(x);<a name="line.74"></a> <FONT color="green">075</FONT> }<a name="line.75"></a> <FONT color="green">076</FONT> <a name="line.76"></a> <FONT color="green">077</FONT> /**<a name="line.77"></a> <FONT color="green">078</FONT> * {@inheritDoc}<a name="line.78"></a> <FONT color="green">079</FONT> *<a name="line.79"></a> <FONT color="green">080</FONT> * Computes and caches QR decomposition of the X matrix<a name="line.80"></a> <FONT color="green">081</FONT> */<a name="line.81"></a> <FONT color="green">082</FONT> @Override<a name="line.82"></a> <FONT color="green">083</FONT> public void newSampleData(double[] data, int nobs, int nvars) {<a name="line.83"></a> <FONT color="green">084</FONT> super.newSampleData(data, nobs, nvars);<a name="line.84"></a> <FONT color="green">085</FONT> qr = new QRDecompositionImpl(X);<a name="line.85"></a> <FONT color="green">086</FONT> }<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> /**<a name="line.88"></a> <FONT color="green">089</FONT> * <p>Compute the "hat" matrix.<a name="line.89"></a> <FONT color="green">090</FONT> * </p><a name="line.90"></a> <FONT color="green">091</FONT> * <p>The hat matrix is defined in terms of the design matrix X<a name="line.91"></a> <FONT color="green">092</FONT> * by X(X<sup>T</sup>X)<sup>-1</sup>X<sup>T</sup><a name="line.92"></a> <FONT color="green">093</FONT> * </p><a name="line.93"></a> <FONT color="green">094</FONT> * <p>The implementation here uses the QR decomposition to compute the<a name="line.94"></a> <FONT color="green">095</FONT> * hat matrix as Q I<sub>p</sub>Q<sup>T</sup> where I<sub>p</sub> is the<a name="line.95"></a> <FONT color="green">096</FONT> * p-dimensional identity matrix augmented by 0's. This computational<a name="line.96"></a> <FONT color="green">097</FONT> * formula is from "The Hat Matrix in Regression and ANOVA",<a name="line.97"></a> <FONT color="green">098</FONT> * David C. Hoaglin and Roy E. Welsch,<a name="line.98"></a> <FONT color="green">099</FONT> * <i>The American Statistician</i>, Vol. 32, No. 1 (Feb., 1978), pp. 17-22.<a name="line.99"></a> <FONT color="green">100</FONT> *<a name="line.100"></a> <FONT color="green">101</FONT> * @return the hat matrix<a name="line.101"></a> <FONT color="green">102</FONT> */<a name="line.102"></a> <FONT color="green">103</FONT> public RealMatrix calculateHat() {<a name="line.103"></a> <FONT color="green">104</FONT> // Create augmented identity matrix<a name="line.104"></a> <FONT color="green">105</FONT> RealMatrix Q = qr.getQ();<a name="line.105"></a> <FONT color="green">106</FONT> final int p = qr.getR().getColumnDimension();<a name="line.106"></a> <FONT color="green">107</FONT> final int n = Q.getColumnDimension();<a name="line.107"></a> <FONT color="green">108</FONT> Array2DRowRealMatrix augI = new Array2DRowRealMatrix(n, n);<a name="line.108"></a> <FONT color="green">109</FONT> double[][] augIData = augI.getDataRef();<a name="line.109"></a> <FONT color="green">110</FONT> for (int i = 0; i < n; i++) {<a name="line.110"></a> <FONT color="green">111</FONT> for (int j =0; j < n; j++) {<a name="line.111"></a> <FONT color="green">112</FONT> if (i == j && i < p) {<a name="line.112"></a> <FONT color="green">113</FONT> augIData[i][j] = 1d;<a name="line.113"></a> <FONT color="green">114</FONT> } else {<a name="line.114"></a> <FONT color="green">115</FONT> augIData[i][j] = 0d;<a name="line.115"></a> <FONT color="green">116</FONT> }<a name="line.116"></a> <FONT color="green">117</FONT> }<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> <a name="line.119"></a> <FONT color="green">120</FONT> // Compute and return Hat matrix<a name="line.120"></a> <FONT color="green">121</FONT> return Q.multiply(augI).multiply(Q.transpose());<a name="line.121"></a> <FONT color="green">122</FONT> }<a name="line.122"></a> <FONT color="green">123</FONT> <a name="line.123"></a> <FONT color="green">124</FONT> /**<a name="line.124"></a> <FONT color="green">125</FONT> * Loads new x sample data, overriding any previous sample<a name="line.125"></a> <FONT color="green">126</FONT> *<a name="line.126"></a> <FONT color="green">127</FONT> * @param x the [n,k] array representing the x sample<a name="line.127"></a> <FONT color="green">128</FONT> */<a name="line.128"></a> <FONT color="green">129</FONT> @Override<a name="line.129"></a> <FONT color="green">130</FONT> protected void newXSampleData(double[][] x) {<a name="line.130"></a> <FONT color="green">131</FONT> this.X = new Array2DRowRealMatrix(x);<a name="line.131"></a> <FONT color="green">132</FONT> qr = new QRDecompositionImpl(X);<a name="line.132"></a> <FONT color="green">133</FONT> }<a name="line.133"></a> <FONT color="green">134</FONT> <a name="line.134"></a> <FONT color="green">135</FONT> /**<a name="line.135"></a> <FONT color="green">136</FONT> * Calculates regression coefficients using OLS.<a name="line.136"></a> <FONT color="green">137</FONT> *<a name="line.137"></a> <FONT color="green">138</FONT> * @return beta<a name="line.138"></a> <FONT color="green">139</FONT> */<a name="line.139"></a> <FONT color="green">140</FONT> @Override<a name="line.140"></a> <FONT color="green">141</FONT> protected RealVector calculateBeta() {<a name="line.141"></a> <FONT color="green">142</FONT> return qr.getSolver().solve(Y);<a name="line.142"></a> <FONT color="green">143</FONT> }<a name="line.143"></a> <FONT color="green">144</FONT> <a name="line.144"></a> <FONT color="green">145</FONT> /**<a name="line.145"></a> <FONT color="green">146</FONT> * <p>Calculates the variance on the beta by OLS.<a name="line.146"></a> <FONT color="green">147</FONT> * </p><a name="line.147"></a> <FONT color="green">148</FONT> * <p>Var(b) = (X<sup>T</sup>X)<sup>-1</sup><a name="line.148"></a> <FONT color="green">149</FONT> * </p><a name="line.149"></a> <FONT color="green">150</FONT> * <p>Uses QR decomposition to reduce (X<sup>T</sup>X)<sup>-1</sup><a name="line.150"></a> <FONT color="green">151</FONT> * to (R<sup>T</sup>R)<sup>-1</sup>, with only the top p rows of<a name="line.151"></a> <FONT color="green">152</FONT> * R included, where p = the length of the beta vector.</p><a name="line.152"></a> <FONT color="green">153</FONT> *<a name="line.153"></a> <FONT color="green">154</FONT> * @return The beta variance<a name="line.154"></a> <FONT color="green">155</FONT> */<a name="line.155"></a> <FONT color="green">156</FONT> @Override<a name="line.156"></a> <FONT color="green">157</FONT> protected RealMatrix calculateBetaVariance() {<a name="line.157"></a> <FONT color="green">158</FONT> int p = X.getColumnDimension();<a name="line.158"></a> <FONT color="green">159</FONT> RealMatrix Raug = qr.getR().getSubMatrix(0, p - 1 , 0, p - 1);<a name="line.159"></a> <FONT color="green">160</FONT> RealMatrix Rinv = new LUDecompositionImpl(Raug).getSolver().getInverse();<a name="line.160"></a> <FONT color="green">161</FONT> return Rinv.multiply(Rinv.transpose());<a name="line.161"></a> <FONT color="green">162</FONT> }<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> <a name="line.164"></a> <FONT color="green">165</FONT> /**<a name="line.165"></a> <FONT color="green">166</FONT> * <p>Calculates the variance on the Y by OLS.<a name="line.166"></a> <FONT color="green">167</FONT> * </p><a name="line.167"></a> <FONT color="green">168</FONT> * <p> Var(y) = Tr(u<sup>T</sup>u)/(n - k)<a name="line.168"></a> <FONT color="green">169</FONT> * </p><a name="line.169"></a> <FONT color="green">170</FONT> * @return The Y variance<a name="line.170"></a> <FONT color="green">171</FONT> */<a name="line.171"></a> <FONT color="green">172</FONT> @Override<a name="line.172"></a> <FONT color="green">173</FONT> protected double calculateYVariance() {<a name="line.173"></a> <FONT color="green">174</FONT> RealVector residuals = calculateResiduals();<a name="line.174"></a> <FONT color="green">175</FONT> return residuals.dotProduct(residuals) /<a name="line.175"></a> <FONT color="green">176</FONT> (X.getRowDimension() - X.getColumnDimension());<a name="line.176"></a> <FONT color="green">177</FONT> }<a name="line.177"></a> <FONT color="green">178</FONT> <a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> </PRE> </BODY> </HTML>