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* 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,
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* See the License for the specific language governing permissions and
* limitations under the License.
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package org.apache.commons.math4.stat.correlation;
import org.apache.commons.math4.TestUtils;
import org.apache.commons.math4.distribution.TDistribution;
import org.apache.commons.math4.exception.MathIllegalArgumentException;
import org.apache.commons.math4.linear.BlockRealMatrix;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.stat.correlation.Covariance;
import org.apache.commons.math4.stat.correlation.PearsonsCorrelation;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class PearsonsCorrelationTest {
protected final double[] longleyData = new double[] {
60323,83.0,234289,2356,1590,107608,1947,
61122,88.5,259426,2325,1456,108632,1948,
60171,88.2,258054,3682,1616,109773,1949,
61187,89.5,284599,3351,1650,110929,1950,
63221,96.2,328975,2099,3099,112075,1951,
63639,98.1,346999,1932,3594,113270,1952,
64989,99.0,365385,1870,3547,115094,1953,
63761,100.0,363112,3578,3350,116219,1954,
66019,101.2,397469,2904,3048,117388,1955,
67857,104.6,419180,2822,2857,118734,1956,
68169,108.4,442769,2936,2798,120445,1957,
66513,110.8,444546,4681,2637,121950,1958,
68655,112.6,482704,3813,2552,123366,1959,
69564,114.2,502601,3931,2514,125368,1960,
69331,115.7,518173,4806,2572,127852,1961,
70551,116.9,554894,4007,2827,130081,1962
};
protected final double[] swissData = new double[] {
80.2,17.0,15,12,9.96,
83.1,45.1,6,9,84.84,
92.5,39.7,5,5,93.40,
85.8,36.5,12,7,33.77,
76.9,43.5,17,15,5.16,
76.1,35.3,9,7,90.57,
83.8,70.2,16,7,92.85,
92.4,67.8,14,8,97.16,
82.4,53.3,12,7,97.67,
82.9,45.2,16,13,91.38,
87.1,64.5,14,6,98.61,
64.1,62.0,21,12,8.52,
66.9,67.5,14,7,2.27,
68.9,60.7,19,12,4.43,
61.7,69.3,22,5,2.82,
68.3,72.6,18,2,24.20,
71.7,34.0,17,8,3.30,
55.7,19.4,26,28,12.11,
54.3,15.2,31,20,2.15,
65.1,73.0,19,9,2.84,
65.5,59.8,22,10,5.23,
65.0,55.1,14,3,4.52,
56.6,50.9,22,12,15.14,
57.4,54.1,20,6,4.20,
72.5,71.2,12,1,2.40,
74.2,58.1,14,8,5.23,
72.0,63.5,6,3,2.56,
60.5,60.8,16,10,7.72,
58.3,26.8,25,19,18.46,
65.4,49.5,15,8,6.10,
75.5,85.9,3,2,99.71,
69.3,84.9,7,6,99.68,
77.3,89.7,5,2,100.00,
70.5,78.2,12,6,98.96,
79.4,64.9,7,3,98.22,
65.0,75.9,9,9,99.06,
92.2,84.6,3,3,99.46,
79.3,63.1,13,13,96.83,
70.4,38.4,26,12,5.62,
65.7,7.7,29,11,13.79,
72.7,16.7,22,13,11.22,
64.4,17.6,35,32,16.92,
77.6,37.6,15,7,4.97,
67.6,18.7,25,7,8.65,
35.0,1.2,37,53,42.34,
44.7,46.6,16,29,50.43,
42.8,27.7,22,29,58.33
};
/**
* Test Longley dataset against R.
*/
@Test
public void testLongly() {
RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
double[] rData = new double[] {
1.000000000000000, 0.9708985250610560, 0.9835516111796693, 0.5024980838759942,
0.4573073999764817, 0.960390571594376, 0.9713294591921188,
0.970898525061056, 1.0000000000000000, 0.9915891780247822, 0.6206333925590966,
0.4647441876006747, 0.979163432977498, 0.9911491900672053,
0.983551611179669, 0.9915891780247822, 1.0000000000000000, 0.6042609398895580,
0.4464367918926265, 0.991090069458478, 0.9952734837647849,
0.502498083875994, 0.6206333925590966, 0.6042609398895580, 1.0000000000000000,
-0.1774206295018783, 0.686551516365312, 0.6682566045621746,
0.457307399976482, 0.4647441876006747, 0.4464367918926265, -0.1774206295018783,
1.0000000000000000, 0.364416267189032, 0.4172451498349454,
0.960390571594376, 0.9791634329774981, 0.9910900694584777, 0.6865515163653120,
0.3644162671890320, 1.000000000000000, 0.9939528462329257,
0.971329459192119, 0.9911491900672053, 0.9952734837647849, 0.6682566045621746,
0.4172451498349454, 0.993952846232926, 1.0000000000000000
};
TestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 7, 7), correlationMatrix, 10E-15);
double[] rPvalues = new double[] {
4.38904690369668e-10,
8.36353208910623e-12, 7.8159700933611e-14,
0.0472894097790304, 0.01030636128354301, 0.01316878049026582,
0.0749178049642416, 0.06971758330341182, 0.0830166169296545, 0.510948586323452,
3.693245043123738e-09, 4.327782576751815e-11, 1.167954621905665e-13, 0.00331028281967516, 0.1652293725106684,
3.95834476307755e-10, 1.114663916723657e-13, 1.332267629550188e-15, 0.00466039138541463, 0.1078477071581498, 7.771561172376096e-15
};
RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 7);
fillUpper(rPMatrix, 0d);
TestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
}
/**
* Test R Swiss fertility dataset against R.
*/
@Test
public void testSwissFertility() {
RealMatrix matrix = createRealMatrix(swissData, 47, 5);
PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
double[] rData = new double[] {
1.0000000000000000, 0.3530791836199747, -0.6458827064572875, -0.6637888570350691, 0.4636847006517939,
0.3530791836199747, 1.0000000000000000,-0.6865422086171366, -0.6395225189483201, 0.4010950530487398,
-0.6458827064572875, -0.6865422086171366, 1.0000000000000000, 0.6984152962884830, -0.5727418060641666,
-0.6637888570350691, -0.6395225189483201, 0.6984152962884830, 1.0000000000000000, -0.1538589170909148,
0.4636847006517939, 0.4010950530487398, -0.5727418060641666, -0.1538589170909148, 1.0000000000000000
};
TestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 5, 5), correlationMatrix, 10E-15);
double[] rPvalues = new double[] {
0.01491720061472623,
9.45043734069043e-07, 9.95151527133974e-08,
3.658616965962355e-07, 1.304590105694471e-06, 4.811397236181847e-08,
0.001028523190118147, 0.005204433539191644, 2.588307925380906e-05, 0.301807756132683
};
RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 5);
fillUpper(rPMatrix, 0d);
TestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
}
/**
* Test p-value near 0. JIRA: MATH-371
*/
@Test
public void testPValueNearZero() {
/*
* Create a dataset that has r -> 1, p -> 0 as dimension increases.
* Prior to the fix for MATH-371, p vanished for dimension >= 14.
* Post fix, p-values diminish smoothly, vanishing at dimension = 127.
* Tested value is ~1E-303.
*/
int dimension = 120;
double[][] data = new double[dimension][2];
for (int i = 0; i < dimension; i++) {
data[i][0] = i;
data[i][1] = i + 1/((double)i + 1);
}
PearsonsCorrelation corrInstance = new PearsonsCorrelation(data);
Assert.assertTrue(corrInstance.getCorrelationPValues().getEntry(0, 1) > 0);
}
/**
* Constant column
*/
@Test
public void testConstant() {
double[] noVariance = new double[] {1, 1, 1, 1};
double[] values = new double[] {1, 2, 3, 4};
Assert.assertTrue(Double.isNaN(new PearsonsCorrelation().correlation(noVariance, values)));
Assert.assertTrue(Double.isNaN(new PearsonsCorrelation().correlation(values, noVariance)));
}
/**
* Insufficient data
*/
@Test
public void testInsufficientData() {
double[] one = new double[] {1};
double[] two = new double[] {2};
try {
new PearsonsCorrelation().correlation(one, two);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// Expected
}
RealMatrix matrix = new BlockRealMatrix(new double[][] {{0},{1}});
try {
new PearsonsCorrelation(matrix);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// Expected
}
}
/**
* Verify that direct t-tests using standard error estimates are consistent
* with reported p-values
*/
@Test
public void testStdErrorConsistency() {
TDistribution tDistribution = new TDistribution(45);
RealMatrix matrix = createRealMatrix(swissData, 47, 5);
PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
RealMatrix rValues = corrInstance.getCorrelationMatrix();
RealMatrix pValues = corrInstance.getCorrelationPValues();
RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
for (int i = 0; i < 5; i++) {
for (int j = 0; j < i; j++) {
double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
double p = 2 * (1 - tDistribution.cumulativeProbability(t));
Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
}
}
}
/**
* Verify that creating correlation from covariance gives same results as
* direct computation from the original matrix
*/
@Test
public void testCovarianceConsistency() {
RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
Covariance covInstance = new Covariance(matrix);
PearsonsCorrelation corrFromCovInstance = new PearsonsCorrelation(covInstance);
TestUtils.assertEquals("correlation values", corrInstance.getCorrelationMatrix(),
corrFromCovInstance.getCorrelationMatrix(), 10E-15);
TestUtils.assertEquals("p values", corrInstance.getCorrelationPValues(),
corrFromCovInstance.getCorrelationPValues(), 10E-15);
TestUtils.assertEquals("standard errors", corrInstance.getCorrelationStandardErrors(),
corrFromCovInstance.getCorrelationStandardErrors(), 10E-15);
PearsonsCorrelation corrFromCovInstance2 =
new PearsonsCorrelation(covInstance.getCovarianceMatrix(), 16);
TestUtils.assertEquals("correlation values", corrInstance.getCorrelationMatrix(),
corrFromCovInstance2.getCorrelationMatrix(), 10E-15);
TestUtils.assertEquals("p values", corrInstance.getCorrelationPValues(),
corrFromCovInstance2.getCorrelationPValues(), 10E-15);
TestUtils.assertEquals("standard errors", corrInstance.getCorrelationStandardErrors(),
corrFromCovInstance2.getCorrelationStandardErrors(), 10E-15);
}
@Test
public void testConsistency() {
RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
double[][] data = matrix.getData();
double[] x = matrix.getColumn(0);
double[] y = matrix.getColumn(1);
Assert.assertEquals(new PearsonsCorrelation().correlation(x, y),
corrInstance.getCorrelationMatrix().getEntry(0, 1), Double.MIN_VALUE);
TestUtils.assertEquals("Correlation matrix", corrInstance.getCorrelationMatrix(),
new PearsonsCorrelation().computeCorrelationMatrix(data), Double.MIN_VALUE);
}
protected RealMatrix createRealMatrix(double[] data, int nRows, int nCols) {
double[][] matrixData = new double[nRows][nCols];
int ptr = 0;
for (int i = 0; i < nRows; i++) {
System.arraycopy(data, ptr, matrixData[i], 0, nCols);
ptr += nCols;
}
return new BlockRealMatrix(matrixData);
}
protected RealMatrix createLowerTriangularRealMatrix(double[] data, int dimension) {
int ptr = 0;
RealMatrix result = new BlockRealMatrix(dimension, dimension);
for (int i = 1; i < dimension; i++) {
for (int j = 0; j < i; j++) {
result.setEntry(i, j, data[ptr]);
ptr++;
}
}
return result;
}
protected void fillUpper(RealMatrix matrix, double diagonalValue) {
int dimension = matrix.getColumnDimension();
for (int i = 0; i < dimension; i++) {
matrix.setEntry(i, i, diagonalValue);
for (int j = i+1; j < dimension; j++) {
matrix.setEntry(i, j, matrix.getEntry(j, i));
}
}
}
}