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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/stat/regression/GLSMultipleLinearRegression.html @ 13:cbf34dd4d7e6

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commons-math-2.1 added
author dwinter
date Tue, 04 Jan 2011 10:02:07 +0100
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12:970d26a94fb7 13:cbf34dd4d7e6
1 <HTML>
2 <BODY BGCOLOR="white">
3 <PRE>
4 <FONT color="green">001</FONT> /*<a name="line.1"></a>
5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
8 <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a>
11 <FONT color="green">008</FONT> *<a name="line.8"></a>
12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
13 <FONT color="green">010</FONT> *<a name="line.10"></a>
14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a>
18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a>
19 <FONT color="green">016</FONT> */<a name="line.16"></a>
20 <FONT color="green">017</FONT> package org.apache.commons.math.stat.regression;<a name="line.17"></a>
21 <FONT color="green">018</FONT> <a name="line.18"></a>
22 <FONT color="green">019</FONT> import org.apache.commons.math.linear.LUDecompositionImpl;<a name="line.19"></a>
23 <FONT color="green">020</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.20"></a>
24 <FONT color="green">021</FONT> import org.apache.commons.math.linear.Array2DRowRealMatrix;<a name="line.21"></a>
25 <FONT color="green">022</FONT> import org.apache.commons.math.linear.RealVector;<a name="line.22"></a>
26 <FONT color="green">023</FONT> <a name="line.23"></a>
27 <FONT color="green">024</FONT> <a name="line.24"></a>
28 <FONT color="green">025</FONT> /**<a name="line.25"></a>
29 <FONT color="green">026</FONT> * The GLS implementation of the multiple linear regression.<a name="line.26"></a>
30 <FONT color="green">027</FONT> *<a name="line.27"></a>
31 <FONT color="green">028</FONT> * GLS assumes a general covariance matrix Omega of the error<a name="line.28"></a>
32 <FONT color="green">029</FONT> * &lt;pre&gt;<a name="line.29"></a>
33 <FONT color="green">030</FONT> * u ~ N(0, Omega)<a name="line.30"></a>
34 <FONT color="green">031</FONT> * &lt;/pre&gt;<a name="line.31"></a>
35 <FONT color="green">032</FONT> *<a name="line.32"></a>
36 <FONT color="green">033</FONT> * Estimated by GLS,<a name="line.33"></a>
37 <FONT color="green">034</FONT> * &lt;pre&gt;<a name="line.34"></a>
38 <FONT color="green">035</FONT> * b=(X' Omega^-1 X)^-1X'Omega^-1 y<a name="line.35"></a>
39 <FONT color="green">036</FONT> * &lt;/pre&gt;<a name="line.36"></a>
40 <FONT color="green">037</FONT> * whose variance is<a name="line.37"></a>
41 <FONT color="green">038</FONT> * &lt;pre&gt;<a name="line.38"></a>
42 <FONT color="green">039</FONT> * Var(b)=(X' Omega^-1 X)^-1<a name="line.39"></a>
43 <FONT color="green">040</FONT> * &lt;/pre&gt;<a name="line.40"></a>
44 <FONT color="green">041</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.41"></a>
45 <FONT color="green">042</FONT> * @since 2.0<a name="line.42"></a>
46 <FONT color="green">043</FONT> */<a name="line.43"></a>
47 <FONT color="green">044</FONT> public class GLSMultipleLinearRegression extends AbstractMultipleLinearRegression {<a name="line.44"></a>
48 <FONT color="green">045</FONT> <a name="line.45"></a>
49 <FONT color="green">046</FONT> /** Covariance matrix. */<a name="line.46"></a>
50 <FONT color="green">047</FONT> private RealMatrix Omega;<a name="line.47"></a>
51 <FONT color="green">048</FONT> <a name="line.48"></a>
52 <FONT color="green">049</FONT> /** Inverse of covariance matrix. */<a name="line.49"></a>
53 <FONT color="green">050</FONT> private RealMatrix OmegaInverse;<a name="line.50"></a>
54 <FONT color="green">051</FONT> <a name="line.51"></a>
55 <FONT color="green">052</FONT> /** Replace sample data, overriding any previous sample.<a name="line.52"></a>
56 <FONT color="green">053</FONT> * @param y y values of the sample<a name="line.53"></a>
57 <FONT color="green">054</FONT> * @param x x values of the sample<a name="line.54"></a>
58 <FONT color="green">055</FONT> * @param covariance array representing the covariance matrix<a name="line.55"></a>
59 <FONT color="green">056</FONT> */<a name="line.56"></a>
60 <FONT color="green">057</FONT> public void newSampleData(double[] y, double[][] x, double[][] covariance) {<a name="line.57"></a>
61 <FONT color="green">058</FONT> validateSampleData(x, y);<a name="line.58"></a>
62 <FONT color="green">059</FONT> newYSampleData(y);<a name="line.59"></a>
63 <FONT color="green">060</FONT> newXSampleData(x);<a name="line.60"></a>
64 <FONT color="green">061</FONT> validateCovarianceData(x, covariance);<a name="line.61"></a>
65 <FONT color="green">062</FONT> newCovarianceData(covariance);<a name="line.62"></a>
66 <FONT color="green">063</FONT> }<a name="line.63"></a>
67 <FONT color="green">064</FONT> <a name="line.64"></a>
68 <FONT color="green">065</FONT> /**<a name="line.65"></a>
69 <FONT color="green">066</FONT> * Add the covariance data.<a name="line.66"></a>
70 <FONT color="green">067</FONT> *<a name="line.67"></a>
71 <FONT color="green">068</FONT> * @param omega the [n,n] array representing the covariance<a name="line.68"></a>
72 <FONT color="green">069</FONT> */<a name="line.69"></a>
73 <FONT color="green">070</FONT> protected void newCovarianceData(double[][] omega){<a name="line.70"></a>
74 <FONT color="green">071</FONT> this.Omega = new Array2DRowRealMatrix(omega);<a name="line.71"></a>
75 <FONT color="green">072</FONT> this.OmegaInverse = null;<a name="line.72"></a>
76 <FONT color="green">073</FONT> }<a name="line.73"></a>
77 <FONT color="green">074</FONT> <a name="line.74"></a>
78 <FONT color="green">075</FONT> /**<a name="line.75"></a>
79 <FONT color="green">076</FONT> * Get the inverse of the covariance.<a name="line.76"></a>
80 <FONT color="green">077</FONT> * &lt;p&gt;The inverse of the covariance matrix is lazily evaluated and cached.&lt;/p&gt;<a name="line.77"></a>
81 <FONT color="green">078</FONT> * @return inverse of the covariance<a name="line.78"></a>
82 <FONT color="green">079</FONT> */<a name="line.79"></a>
83 <FONT color="green">080</FONT> protected RealMatrix getOmegaInverse() {<a name="line.80"></a>
84 <FONT color="green">081</FONT> if (OmegaInverse == null) {<a name="line.81"></a>
85 <FONT color="green">082</FONT> OmegaInverse = new LUDecompositionImpl(Omega).getSolver().getInverse();<a name="line.82"></a>
86 <FONT color="green">083</FONT> }<a name="line.83"></a>
87 <FONT color="green">084</FONT> return OmegaInverse;<a name="line.84"></a>
88 <FONT color="green">085</FONT> }<a name="line.85"></a>
89 <FONT color="green">086</FONT> <a name="line.86"></a>
90 <FONT color="green">087</FONT> /**<a name="line.87"></a>
91 <FONT color="green">088</FONT> * Calculates beta by GLS.<a name="line.88"></a>
92 <FONT color="green">089</FONT> * &lt;pre&gt;<a name="line.89"></a>
93 <FONT color="green">090</FONT> * b=(X' Omega^-1 X)^-1X'Omega^-1 y<a name="line.90"></a>
94 <FONT color="green">091</FONT> * &lt;/pre&gt;<a name="line.91"></a>
95 <FONT color="green">092</FONT> * @return beta<a name="line.92"></a>
96 <FONT color="green">093</FONT> */<a name="line.93"></a>
97 <FONT color="green">094</FONT> @Override<a name="line.94"></a>
98 <FONT color="green">095</FONT> protected RealVector calculateBeta() {<a name="line.95"></a>
99 <FONT color="green">096</FONT> RealMatrix OI = getOmegaInverse();<a name="line.96"></a>
100 <FONT color="green">097</FONT> RealMatrix XT = X.transpose();<a name="line.97"></a>
101 <FONT color="green">098</FONT> RealMatrix XTOIX = XT.multiply(OI).multiply(X);<a name="line.98"></a>
102 <FONT color="green">099</FONT> RealMatrix inverse = new LUDecompositionImpl(XTOIX).getSolver().getInverse();<a name="line.99"></a>
103 <FONT color="green">100</FONT> return inverse.multiply(XT).multiply(OI).operate(Y);<a name="line.100"></a>
104 <FONT color="green">101</FONT> }<a name="line.101"></a>
105 <FONT color="green">102</FONT> <a name="line.102"></a>
106 <FONT color="green">103</FONT> /**<a name="line.103"></a>
107 <FONT color="green">104</FONT> * Calculates the variance on the beta by GLS.<a name="line.104"></a>
108 <FONT color="green">105</FONT> * &lt;pre&gt;<a name="line.105"></a>
109 <FONT color="green">106</FONT> * Var(b)=(X' Omega^-1 X)^-1<a name="line.106"></a>
110 <FONT color="green">107</FONT> * &lt;/pre&gt;<a name="line.107"></a>
111 <FONT color="green">108</FONT> * @return The beta variance matrix<a name="line.108"></a>
112 <FONT color="green">109</FONT> */<a name="line.109"></a>
113 <FONT color="green">110</FONT> @Override<a name="line.110"></a>
114 <FONT color="green">111</FONT> protected RealMatrix calculateBetaVariance() {<a name="line.111"></a>
115 <FONT color="green">112</FONT> RealMatrix OI = getOmegaInverse();<a name="line.112"></a>
116 <FONT color="green">113</FONT> RealMatrix XTOIX = X.transpose().multiply(OI).multiply(X);<a name="line.113"></a>
117 <FONT color="green">114</FONT> return new LUDecompositionImpl(XTOIX).getSolver().getInverse();<a name="line.114"></a>
118 <FONT color="green">115</FONT> }<a name="line.115"></a>
119 <FONT color="green">116</FONT> <a name="line.116"></a>
120 <FONT color="green">117</FONT> /**<a name="line.117"></a>
121 <FONT color="green">118</FONT> * Calculates the variance on the y by GLS.<a name="line.118"></a>
122 <FONT color="green">119</FONT> * &lt;pre&gt;<a name="line.119"></a>
123 <FONT color="green">120</FONT> * Var(y)=Tr(u' Omega^-1 u)/(n-k)<a name="line.120"></a>
124 <FONT color="green">121</FONT> * &lt;/pre&gt;<a name="line.121"></a>
125 <FONT color="green">122</FONT> * @return The Y variance<a name="line.122"></a>
126 <FONT color="green">123</FONT> */<a name="line.123"></a>
127 <FONT color="green">124</FONT> @Override<a name="line.124"></a>
128 <FONT color="green">125</FONT> protected double calculateYVariance() {<a name="line.125"></a>
129 <FONT color="green">126</FONT> RealVector residuals = calculateResiduals();<a name="line.126"></a>
130 <FONT color="green">127</FONT> double t = residuals.dotProduct(getOmegaInverse().operate(residuals));<a name="line.127"></a>
131 <FONT color="green">128</FONT> return t / (X.getRowDimension() - X.getColumnDimension());<a name="line.128"></a>
132 <FONT color="green">129</FONT> }<a name="line.129"></a>
133 <FONT color="green">130</FONT> <a name="line.130"></a>
134 <FONT color="green">131</FONT> }<a name="line.131"></a>
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195 </PRE>
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