Added G-test statistics. JIRA: MATH-878. Thanks to Radoslav Tsvetkov and Ted Dunning.
git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1405620 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz
parent
1cfa9491a2
commit
0987ae5a20
3
pom.xml
3
pom.xml
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@ -264,6 +264,9 @@
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<contributor>
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<name>Mauro Talevi</name>
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</contributor>
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<contributor>
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<name>Radoslav Tsvetkov</name>
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</contributor>
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<contributor>
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<name>Kim van der Linde</name>
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</contributor>
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@ -52,6 +52,9 @@ If the output is not quite correct, check for invisible trailing spaces!
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<body>
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<release version="3.1" date="TBD" description="
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">
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<action dev="psteitz" type="add" issue="MATH-878" due-to="Radoslav Tsvetkov">
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Added G-test statistics.
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</action>
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<action dev="erans" type="add" issue="MATH-883">
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New "getSquareRoot" method in class "EigenDecomposition" (package
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"o.a.c.m.linear").
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@ -0,0 +1,537 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math3.stat.inference;
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import org.apache.commons.math3.distribution.ChiSquaredDistribution;
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import org.apache.commons.math3.exception.DimensionMismatchException;
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import org.apache.commons.math3.exception.MaxCountExceededException;
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import org.apache.commons.math3.exception.NotPositiveException;
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import org.apache.commons.math3.exception.NotStrictlyPositiveException;
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import org.apache.commons.math3.exception.OutOfRangeException;
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import org.apache.commons.math3.exception.ZeroException;
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import org.apache.commons.math3.exception.util.LocalizedFormats;
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import org.apache.commons.math3.util.FastMath;
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import org.apache.commons.math3.util.MathArrays;
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/**
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* Implements <a href="http://en.wikipedia.org/wiki/G-test">G Test</a>
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* statistics.
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*
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* <p>This is known in statistical genetics as the McDonald-Kreitman test.
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* The implementation handles both known and unknown distributions.</p>
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*
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* <p>Two samples tests can be used when the distribution is unknown <i>a priori</i>
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* but provided by one sample, or when the hypothesis under test is that the two
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* samples come from the same underlying distribution.</p>
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*
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* @version $Id$
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* @since 3.1
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*/
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public class GTest {
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/**
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* Computes the <a href="http://en.wikipedia.org/wiki/G-test">G statistic
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* for Goodness of Fit</a> comparing {@code observed} and {@code expected}
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* frequency counts.
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*
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* <p>This statistic can be used to perform a G test (Log-Likelihood Ratio
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* Test) evaluating the null hypothesis that the observed counts follow the
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* expected distribution.</p>
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*
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* <p><strong>Preconditions</strong>: <ul>
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* <li>Expected counts must all be positive. </li>
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* <li>Observed counts must all be ≥ 0. </li>
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* <li>The observed and expected arrays must have the same length and their
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* common length must be at least 2. </li></ul></p>
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*
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* <p>If any of the preconditions are not met, a
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* {@code MathIllegalArgumentException} is thrown.</p>
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*
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* <p><strong>Note:</strong>This implementation rescales the
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* {@code expected} array if necessary to ensure that the sum of the
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* expected and observed counts are equal.</p>
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*
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* @param observed array of observed frequency counts
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* @param expected array of expected frequency counts
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* @return G-Test statistic
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* @throws NotPositiveException if {@code observed} has negative entries
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* @throws NotStrictlyPositiveException if {@code expected} has entries that
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* are not strictly positive
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* @throws DimensionMismatchException if the array lengths do not match or
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* are less than 2.
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*/
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public double gValueGoodnessOfFit(final double[] expected, final long[] observed)
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throws NotPositiveException, NotStrictlyPositiveException,
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DimensionMismatchException {
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if (expected.length < 2) {
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throw new DimensionMismatchException(expected.length, 2);
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}
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if (expected.length != observed.length) {
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throw new DimensionMismatchException(expected.length, observed.length);
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}
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MathArrays.checkPositive(expected);
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MathArrays.checkNonNegative(observed);
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double sumExpected = 0d;
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double sumObserved = 0d;
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for (int i = 0; i < observed.length; i++) {
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sumExpected += expected[i];
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sumObserved += observed[i];
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}
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double ratio = 1d;
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boolean rescale = false;
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if (Math.abs(sumExpected - sumObserved) > 10E-6) {
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ratio = sumObserved / sumExpected;
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rescale = true;
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}
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double sum = 0d;
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for (int i = 0; i < observed.length; i++) {
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final double dev = rescale ?
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FastMath.log((double) observed[i] / (ratio * expected[i])) :
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FastMath.log((double) observed[i] / expected[i]);
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sum += ((double) observed[i]) * dev;
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}
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return 2d * sum;
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}
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/**
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* Returns the <i>observed significance level</i>, or <a href=
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* "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"> p-value</a>,
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* associated with a G-Test for goodness of fit</a> comparing the
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* {@code observed} frequency counts to those in the {@code expected} array.
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*
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* <p>The number returned is the smallest significance level at which one
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* can reject the null hypothesis that the observed counts conform to the
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* frequency distribution described by the expected counts.</p>
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*
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* <p>The probability returned is the tail probability beyond
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* {@link #gValueGoodnessOfFit(double[], long[]) gValueGoodnessOfFit(expected, observed)}
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* in the ChiSquare distribution with degrees of freedom one less than the
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* common length of {@code expected} and {@code observed}.</p>
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*
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* <p> <strong>Preconditions</strong>: <ul>
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* <li>Expected counts must all be positive. </li>
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* <li>Observed counts must all be ≥ 0. </li>
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* <li>The observed and expected arrays must have the
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* same length and their common length must be at least 2.</li>
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* </ul></p>
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*
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* <p>If any of the preconditions are not met, a
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* {@code MathIllegalArgumentException} is thrown.</p>
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*
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* <p><strong>Note:</strong>This implementation rescales the
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* {@code expected} array if necessary to ensure that the sum of the
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* expected and observed counts are equal.</p>
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*
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* @param observed array of observed frequency counts
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* @param expected array of expected frequency counts
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* @return p-value
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* @throws NotPositiveException if {@code observed} has negative entries
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* @throws NotStrictlyPositiveException if {@code expected} has entries that
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* are not strictly positive
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* @throws DimensionMismatchException if the array lengths do not match or
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* are less than 2.
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* @throws MaxCountExceededException if an error occurs computing the
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* p-value.
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*/
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public double gTestGoodnessOfFitPValue(final double[] expected, final long[] observed)
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throws NotPositiveException, NotStrictlyPositiveException,
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DimensionMismatchException, MaxCountExceededException {
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final ChiSquaredDistribution distribution =
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new ChiSquaredDistribution(expected.length - 1.0);
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return 1.0 - distribution.cumulativeProbability(
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gValueGoodnessOfFit(expected, observed));
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}
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/**
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* Returns the intrinsic (Hardy-Weinberg proportions) p-Value, as described
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* in p64-69 of McDonald, J.H. 2009. Handbook of Biological Statistics
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* (2nd ed.). Sparky House Publishing, Baltimore, Maryland.
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*
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* <p> The probability returned is the tail probability beyond
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* {@link #gValueGoodnessOfFit(double[], long[]) gValueGoodnessOfFit(expected, observed)}
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* in the ChiSquare distribution with degrees of freedom two less than the
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* common length of {@code expected} and {@code observed}.</p>
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*
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* @param observed array of observed frequency counts
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* @param expected array of expected frequency counts
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* @return p-value
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* @throws NotPositiveException if {@code observed} has negative entries
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* @throws NotStrictlyPositiveException {@code expected} has entries that are
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* not strictly positive
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* @throws DimensionMismatchException if the array lengths do not match or
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* are less than 2.
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* @throws MaxCountExceededException if an error occurs computing the
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* p-value.
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*/
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public double gTestGoodnessOfFitIntrinsicPValue(final double[] expected, final long[] observed)
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throws NotPositiveException, NotStrictlyPositiveException,
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DimensionMismatchException, MaxCountExceededException {
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final ChiSquaredDistribution distribution =
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new ChiSquaredDistribution(expected.length - 2.0);
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return 1.0 - distribution.cumulativeProbability(
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gValueGoodnessOfFit(expected, observed));
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}
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/**
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* Performs a G-Test (Log-Likelihood Ratio Test) for goodness of fit
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* evaluating the null hypothesis that the observed counts conform to the
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* frequency distribution described by the expected counts, with
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* significance level {@code alpha}. Returns true iff the null
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* hypothesis can be rejected with {@code 100 * (1 - alpha)} percent confidence.
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*
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* <p><strong>Example:</strong><br> To test the hypothesis that
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* {@code observed} follows {@code expected} at the 99% level,
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* use </p><p>
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* {@code gTest(expected, observed, 0.01)}</p>
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*
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* <p>Returns true iff {@link #gTestGoodnessOfFitPValue(double[], long[])
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* gTestGoodnessOfFitPValue(expected, observed)} < alpha</p>
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*
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* <p><strong>Preconditions</strong>: <ul>
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* <li>Expected counts must all be positive. </li>
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* <li>Observed counts must all be ≥ 0. </li>
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* <li>The observed and expected arrays must have the same length and their
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* common length must be at least 2.
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* <li> {@code 0 < alpha < 0.5} </li></ul></p>
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*
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* <p>If any of the preconditions are not met, a
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* {@code MathIllegalArgumentException} is thrown.</p>
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*
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* <p><strong>Note:</strong>This implementation rescales the
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* {@code expected} array if necessary to ensure that the sum of the
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* expected and observed counts are equal.</p>
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*
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* @param observed array of observed frequency counts
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* @param expected array of expected frequency counts
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* @param alpha significance level of the test
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* @return true iff null hypothesis can be rejected with confidence 1 -
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* alpha
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* @throws NotPositiveException if {@code observed} has negative entries
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* @throws NotStrictlyPositiveException if {@code expected} has entries that
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* are not strictly positive
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* @throws DimensionMismatchException if the array lengths do not match or
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* are less than 2.
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* @throws MaxCountExceededException if an error occurs computing the
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* p-value.
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* @throws OutOfRangeException if alpha is not strictly greater than zero
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* and less than or equal to 0.5
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*/
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public boolean gTestGoodnessOfFit(final double[] expected, final long[] observed,
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final double alpha)
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throws NotPositiveException, NotStrictlyPositiveException,
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DimensionMismatchException, OutOfRangeException, MaxCountExceededException {
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if ((alpha <= 0) || (alpha > 0.5)) {
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throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL,
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alpha, 0, 0.5);
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}
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return gTestGoodnessOfFitPValue(expected, observed) < alpha;
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}
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/**
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* Calculates the <a href=
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* "http://en.wikipedia.org/wiki/Entropy_%28information_theory%29">Shannon
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* entropy</a> for 2 Dimensional Matrix. The value returned is the entropy
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* of the vector formed by concatenating the rows (or columns) of {@code k}
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* to form a vector. See {@link #entropy(long[])}.
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*
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* @param k 2 Dimensional Matrix of long values (for ex. the counts of a
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* trials)
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* @return Shannon Entropy of the given Matrix
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*
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*/
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private double entropy(final long[][] k) {
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double h = 0d;
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double sum_k = 0d;
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for (int i = 0; i < k.length; i++) {
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for (int j = 0; j < k[i].length; j++) {
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sum_k += (double) k[i][j];
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}
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}
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for (int i = 0; i < k.length; i++) {
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for (int j = 0; j < k[i].length; j++) {
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if (k[i][j] != 0) {
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final double p_ij = (double) k[i][j] / sum_k;
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h += p_ij * Math.log(p_ij);
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}
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}
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}
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return -h;
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}
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/**
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* Calculates the <a href="http://en.wikipedia.org/wiki/Entropy_%28information_theory%29">
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* Shannon entropy</a> for a vector. The values of {@code k} are taken to be
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* incidence counts of the values of a random variable. What is returned is <br/>
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* ∑p<sub>i</sub>log(p<sub>i</sub><br/>
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* where p<sub>i</sub> = k[i] / (sum of elements in k)
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*
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* @param k Vector (for ex. Row Sums of a trials)
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* @return Shannon Entropy of the given Vector
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*
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*/
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private double entropy(final long[] k) {
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double h = 0d;
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double sum_k = 0d;
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for (int i = 0; i < k.length; i++) {
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sum_k += (double) k[i];
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}
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for (int i = 0; i < k.length; i++) {
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if (k[i] != 0) {
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final double p_i = (double) k[i] / sum_k;
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h += p_i * Math.log(p_i);
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}
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}
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return -h;
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}
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/**
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* <p>Computes a G (Log-Likelihood Ratio) two sample test statistic for
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* independence comparing frequency counts in
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* {@code observed1} and {@codeobserved2}. The sums of frequency
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* counts in the two samples are not required to be the same. The formula
|
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* used to compute the test statistic is </p>
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*
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* <p>{@code 2 * totalSum * [H(rowSums) + H(colSums) - H(k)]}</p>
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*
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* <p> where {@code H} is the
|
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* <a href="http://en.wikipedia.org/wiki/Entropy_%28information_theory%29">
|
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* Shannon Entropy</a> of the random variable formed by viewing the elements
|
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* of the argument array as incidence counts; <br/>
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* {@code k} is a matrix with rows {@code [observed1, observed2]}; <br/>
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* {@code rowSums, colSums} are the row/col sums of {@code k}; <br>
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* and {@code totalSum} is the overall sum of all entries in {@code k}.</p>
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*
|
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* <p>This statistic can be used to perform a G test evaluating the null
|
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* hypothesis that both observed counts are independent </p>
|
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*
|
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* <p> <strong>Preconditions</strong>: <ul>
|
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* <li>Observed counts must be non-negative. </li>
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* <li>Observed counts for a specific bin must not both be zero. </li>
|
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* <li>Observed counts for a specific sample must not all be 0. </li>
|
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* <li>The arrays {@code observed1} and {@code observed2} must have
|
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* the same length and their common length must be at least 2. </li></ul></p>
|
||||
*
|
||||
* <p>If any of the preconditions are not met, a
|
||||
* {@code MathIllegalArgumentException} is thrown.</p>
|
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*
|
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* @param observed1 array of observed frequency counts of the first data set
|
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* @param observed2 array of observed frequency counts of the second data
|
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* set
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* @return G-Test statistic
|
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* @throws DimensionMismatchException the the lengths of the arrays do not
|
||||
* match or their common length is less than 2
|
||||
* @throws NotPositiveException if any entry in {@code observed1} or
|
||||
* {@code observed2} is negative
|
||||
* @throws ZeroException if either all counts of
|
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* {@code observed1} or {@code observed2} are zero, or if the count
|
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* at the same index is zero for both arrays.
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*/
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public double gValueDataSetsComparison(final long[] observed1, final long[] observed2)
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throws DimensionMismatchException, NotPositiveException, ZeroException {
|
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// Make sure lengths are same
|
||||
if (observed1.length < 2) {
|
||||
throw new DimensionMismatchException(observed1.length, 2);
|
||||
}
|
||||
if (observed1.length != observed2.length) {
|
||||
throw new DimensionMismatchException(observed1.length, observed2.length);
|
||||
}
|
||||
|
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// Ensure non-negative counts
|
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MathArrays.checkNonNegative(observed1);
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MathArrays.checkNonNegative(observed2);
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// Compute and compare count sums
|
||||
long countSum1 = 0;
|
||||
long countSum2 = 0;
|
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|
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// Compute and compare count sums
|
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final long[] collSums = new long[observed1.length];
|
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final long[][] k = new long[2][observed1.length];
|
||||
|
||||
for (int i = 0; i < observed1.length; i++) {
|
||||
if (observed1[i] == 0 && observed2[i] == 0) {
|
||||
throw new ZeroException(LocalizedFormats.OBSERVED_COUNTS_BOTTH_ZERO_FOR_ENTRY, i);
|
||||
} else {
|
||||
countSum1 += observed1[i];
|
||||
countSum2 += observed2[i];
|
||||
collSums[i] = observed1[i] + observed2[i];
|
||||
k[0][i] = observed1[i];
|
||||
k[1][i] = observed2[i];
|
||||
}
|
||||
}
|
||||
// Ensure neither sample is uniformly 0
|
||||
if (countSum1 == 0 || countSum2 == 0) {
|
||||
throw new ZeroException();
|
||||
}
|
||||
final long[] rowSums = {countSum1, countSum2};
|
||||
final double sum = (double) countSum1 + (double) countSum2;
|
||||
return 2 * sum * (entropy(rowSums) + entropy(collSums) - entropy(k));
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculates the root log-likelihood ratio for 2 state Datasets. See
|
||||
* {@link #gValueDataSetsComparison(long[], long[] )}.
|
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*
|
||||
* <p>Given two events A and B, let k11 be the number of times both events
|
||||
* occur, k12 the incidence of B without A, k21 the count of A without B,
|
||||
* and k22 the number of times neither A nor B occurs. What is returned
|
||||
* by this method is </p>
|
||||
*
|
||||
* <p>{@code (sgn) sqrt(gValueDataSetsComparison({k11, k12}, {k21, k22})}</p>
|
||||
*
|
||||
* <p>where {@code sgn} is -1 if {@code k11 / (k11 + k12) < k21 / (k21 + k22))};<br/>
|
||||
* 1 otherwise.</p>
|
||||
*
|
||||
* <p>Signed root LLR has two advantages over the basic LLR: a) it is positive
|
||||
* where k11 is bigger than expected, negative where it is lower b) if there is
|
||||
* no difference it is asymptotically normally distributed. This allows one
|
||||
* to talk about "number of standard deviations" which is a more common frame
|
||||
* of reference than the chi^2 distribution.</p>
|
||||
*
|
||||
* @param k11 number of times the two events occurred together (AB)
|
||||
* @param k12 number of times the second event occurred WITHOUT the
|
||||
* first event (notA,B)
|
||||
* @param k21 number of times the first event occurred WITHOUT the
|
||||
* second event (A, notB)
|
||||
* @param k22 number of times something else occurred (i.e. was neither
|
||||
* of these events (notA, notB)
|
||||
* @return root log-likelihood ratio
|
||||
*
|
||||
*/
|
||||
public double rootLogLikelihoodRatio(final long k11, long k12,
|
||||
final long k21, final long k22) {
|
||||
final double llr = gValueDataSetsComparison(
|
||||
new long[]{k11, k12}, new long[]{k21, k22});
|
||||
double sqrt = FastMath.sqrt(llr);
|
||||
if ((double) k11 / (k11 + k12) < (double) k21 / (k21 + k22)) {
|
||||
sqrt = -sqrt;
|
||||
}
|
||||
return sqrt;
|
||||
}
|
||||
|
||||
/**
|
||||
* <p>Returns the <i>observed significance level</i>, or <a href=
|
||||
* "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue">
|
||||
* p-value</a>, associated with a G-Value (Log-Likelihood Ratio) for two
|
||||
* sample test comparing bin frequency counts in {@code observed1} and
|
||||
* {@code observed2}.</p>
|
||||
*
|
||||
* <p>The number returned is the smallest significance level at which one
|
||||
* can reject the null hypothesis that the observed counts conform to the
|
||||
* same distribution. </p>
|
||||
*
|
||||
* <p>See {@link #gTestGoodnessOfFitPValue(double[], long[])} for details
|
||||
* on how the p-value is computed. The degrees of of freedom used to
|
||||
* perform the test is one less than the common length of the input observed
|
||||
* count arrays.</p>
|
||||
*
|
||||
* <p><strong>Preconditions</strong>:
|
||||
* <ul> <li>Observed counts must be non-negative. </li>
|
||||
* <li>Observed counts for a specific bin must not both be zero. </li>
|
||||
* <li>Observed counts for a specific sample must not all be 0. </li>
|
||||
* <li>The arrays {@code observed1} and {@ode observed2} must
|
||||
* have the same length and their common length must be at least 2. </li>
|
||||
* </ul><p>
|
||||
* <p> If any of the preconditions are not met, a
|
||||
* {@code MathIllegalArgumentException} is thrown.</p>
|
||||
*
|
||||
* @param observed1 array of observed frequency counts of the first data set
|
||||
* @param observed2 array of observed frequency counts of the second data
|
||||
* set
|
||||
* @return p-value
|
||||
* @throws DimensionMismatchException the the length of the arrays does not
|
||||
* match or their common length is less than 2
|
||||
* @throws NotPositiveException if any of the entries in {@code observed1} or
|
||||
* {@code observed2} are negative
|
||||
* @throws ZeroException if either all counts of {@code observed1} or
|
||||
* {@code observed2} are zero, or if the count at some index is
|
||||
* zero for both arrays
|
||||
* @throws MaxCountExceededException if an error occurs computing the
|
||||
* p-value.
|
||||
*/
|
||||
public double gTestDataSetsComparisonPValue(final long[] observed1,
|
||||
final long[] observed2)
|
||||
throws DimensionMismatchException, NotPositiveException, ZeroException,
|
||||
MaxCountExceededException {
|
||||
final ChiSquaredDistribution distribution = new ChiSquaredDistribution(
|
||||
(double) observed1.length - 1);
|
||||
return 1 - distribution.cumulativeProbability(
|
||||
gValueDataSetsComparison(observed1, observed2));
|
||||
}
|
||||
|
||||
/**
|
||||
* <p>Performs a G-Test (Log-Likelihood Ratio Test) comparing two binned
|
||||
* data sets. The test evaluates the null hypothesis that the two lists
|
||||
* of observed counts conform to the same frequency distribution, with
|
||||
* significance level {@code alpha}. Returns true iff the null
|
||||
* hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
|
||||
* </p>
|
||||
* <p>See {@link #gValueDataSetsComparison(long[], long[])} for details
|
||||
* on the formula used to compute the G (LLR) statistic used in the test and
|
||||
* {@link #gTestGoodnessOfFitPValue(double[], long[])} for information on how
|
||||
* the observed significance level is computed. The degrees of of freedom used
|
||||
* to perform the test is one less than the common length of the input observed
|
||||
* count arrays. </p>
|
||||
*
|
||||
* <strong>Preconditions</strong>: <ul>
|
||||
* <li>Observed counts must be non-negative. </li>
|
||||
* <li>Observed counts for a specific bin must not both be zero. </li>
|
||||
* <li>Observed counts for a specific sample must not all be 0. </li>
|
||||
* <li>The arrays {@code observed1} and {@code observed2} must
|
||||
* have the same length and their common length must be at least 2. </li>
|
||||
* <li>{@code 0 < alpha < 0.5} </li></ul></p>
|
||||
*
|
||||
* <p>If any of the preconditions are not met, a
|
||||
* {@code MathIllegalArgumentException} is thrown.</p>
|
||||
*
|
||||
* @param observed1 array of observed frequency counts of the first data set
|
||||
* @param observed2 array of observed frequency counts of the second data
|
||||
* set
|
||||
* @param alpha significance level of the test
|
||||
* @return true iff null hypothesis can be rejected with confidence 1 -
|
||||
* alpha
|
||||
* @throws DimensionMismatchException the the length of the arrays does not
|
||||
* match
|
||||
* @throws NotPositiveException if any of the entries in {@code observed1} or
|
||||
* {@code observed2} are negative
|
||||
* @throws ZeroException if either all counts of {@code observed1} or
|
||||
* {@code observed2} are zero, or if the count at some index is
|
||||
* zero for both arrays
|
||||
* @throws OutOfRangeException if {@code alpha} is not in the range
|
||||
* (0, 0.5]
|
||||
* @throws MaxCountExceededException if an error occurs performing the test
|
||||
*/
|
||||
public boolean gTestDataSetsComparison(
|
||||
final long[] observed1,
|
||||
final long[] observed2,
|
||||
final double alpha)
|
||||
throws DimensionMismatchException, NotPositiveException,
|
||||
ZeroException, OutOfRangeException, MaxCountExceededException {
|
||||
|
||||
if (alpha <= 0 || alpha > 0.5) {
|
||||
throw new OutOfRangeException(
|
||||
LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL, alpha, 0, 0.5);
|
||||
}
|
||||
return gTestDataSetsComparisonPValue(observed1, observed2) < alpha;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,290 @@
|
|||
/*
|
||||
* 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.math3.stat.inference;
|
||||
|
||||
import org.apache.commons.math3.exception.DimensionMismatchException;
|
||||
import org.apache.commons.math3.exception.NotPositiveException;
|
||||
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
|
||||
import org.apache.commons.math3.exception.OutOfRangeException;
|
||||
import org.apache.commons.math3.exception.ZeroException;
|
||||
import org.junit.Assert;
|
||||
import org.junit.Test;
|
||||
|
||||
/**
|
||||
* Test cases for the GTest class.
|
||||
*
|
||||
* Data for the tests are from p64-69 in: McDonald, J.H. 2009. Handbook of
|
||||
* Biological Statistics (2nd ed.). Sparky House Publishing, Baltimore,
|
||||
* Maryland.
|
||||
*
|
||||
*/
|
||||
public class GTestTest {
|
||||
|
||||
protected GTest testStatistic = new GTest();
|
||||
|
||||
@Test
|
||||
public void testGTestGoodnesOfFit1() throws Exception {
|
||||
final double[] exp = new double[]{
|
||||
3d, 1d
|
||||
};
|
||||
|
||||
final long[] obs = new long[]{
|
||||
423, 133
|
||||
};
|
||||
|
||||
Assert.assertEquals("G test statistic",
|
||||
0.348721, testStatistic.gValueGoodnessOfFit(exp, obs), 1E-6);
|
||||
final double p_gtgf = testStatistic.gTestGoodnessOfFitPValue(exp, obs);
|
||||
Assert.assertEquals("g-Test p-value", 0.55483, p_gtgf, 1E-5);
|
||||
|
||||
Assert.assertFalse(testStatistic.gTestGoodnessOfFit(exp, obs, 0.05));
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testGTestGoodnesOfFit2() throws Exception {
|
||||
final double[] exp = new double[]{
|
||||
0.54d, 0.40d, 0.05d, 0.01d
|
||||
};
|
||||
|
||||
final long[] obs = new long[]{
|
||||
70, 79, 3, 4
|
||||
};
|
||||
Assert.assertEquals("G test statistic",
|
||||
13.144799, testStatistic.gValueGoodnessOfFit(exp, obs), 1E-6);
|
||||
final double p_gtgf = testStatistic.gTestGoodnessOfFitPValue(exp, obs);
|
||||
Assert.assertEquals("g-Test p-value", 0.004333, p_gtgf, 1E-5);
|
||||
|
||||
Assert.assertTrue(testStatistic.gTestGoodnessOfFit(exp, obs, 0.05));
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testGTestGoodnesOfFit3() throws Exception {
|
||||
final double[] exp = new double[]{
|
||||
0.167d, 0.483d, 0.350d
|
||||
};
|
||||
|
||||
final long[] obs = new long[]{
|
||||
14, 21, 25
|
||||
};
|
||||
|
||||
Assert.assertEquals("G test statistic",
|
||||
4.5554, testStatistic.gValueGoodnessOfFit(exp, obs), 1E-4);
|
||||
// Intrinisic (Hardy-Weinberg proportions) P-Value should be 0.033
|
||||
final double p_gtgf = testStatistic.gTestGoodnessOfFitIntrinsicPValue(exp, obs);
|
||||
Assert.assertEquals("g-Test p-value", 0.0328, p_gtgf, 1E-4);
|
||||
|
||||
Assert.assertFalse(testStatistic.gTestGoodnessOfFit(exp, obs, 0.05));
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testGTestIndependance1() throws Exception {
|
||||
final long[] obs1 = new long[]{
|
||||
268, 199, 42
|
||||
};
|
||||
|
||||
final long[] obs2 = new long[]{
|
||||
807, 759, 184
|
||||
};
|
||||
|
||||
final double g = testStatistic.gValueDataSetsComparison(obs1, obs2);
|
||||
|
||||
Assert.assertEquals("G test statistic",
|
||||
7.3008170, g, 1E-6);
|
||||
final double p_gti = testStatistic.gTestDataSetsComparisonPValue(obs1, obs2);
|
||||
|
||||
Assert.assertEquals("g-Test p-value", 0.0259805, p_gti, 1E-6);
|
||||
Assert.assertTrue(testStatistic.gTestDataSetsComparison(obs1, obs2, 0.05));
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testGTestIndependance2() throws Exception {
|
||||
final long[] obs1 = new long[]{
|
||||
127, 99, 264
|
||||
};
|
||||
|
||||
final long[] obs2 = new long[]{
|
||||
116, 67, 161
|
||||
};
|
||||
|
||||
final double g = testStatistic.gValueDataSetsComparison(obs1, obs2);
|
||||
|
||||
Assert.assertEquals("G test statistic",
|
||||
6.227288, g, 1E-6);
|
||||
final double p_gti = testStatistic.gTestDataSetsComparisonPValue(obs1, obs2);
|
||||
|
||||
Assert.assertEquals("g-Test p-value", 0.04443, p_gti, 1E-5);
|
||||
Assert.assertTrue(testStatistic.gTestDataSetsComparison(obs1, obs2, 0.05));
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testGTestIndependance3() throws Exception {
|
||||
final long[] obs1 = new long[]{
|
||||
190, 149
|
||||
};
|
||||
|
||||
final long[] obs2 = new long[]{
|
||||
42, 49
|
||||
};
|
||||
|
||||
final double g = testStatistic.gValueDataSetsComparison(obs1, obs2);
|
||||
Assert.assertEquals("G test statistic",
|
||||
2.8187, g, 1E-4);
|
||||
final double p_gti = testStatistic.gTestDataSetsComparisonPValue(obs1, obs2);
|
||||
Assert.assertEquals("g-Test p-value", 0.09317325, p_gti, 1E-6);
|
||||
|
||||
Assert.assertFalse(testStatistic.gTestDataSetsComparison(obs1, obs2, 0.05));
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testGTestSetsComparisonBadCounts() {
|
||||
long[] observed1 = {10, -1, 12, 10, 15};
|
||||
long[] observed2 = {15, 10, 10, 15, 5};
|
||||
try {
|
||||
testStatistic.gTestDataSetsComparisonPValue(
|
||||
observed1, observed2);
|
||||
Assert.fail("Expecting NotPositiveException - negative count");
|
||||
} catch (NotPositiveException ex) {
|
||||
// expected
|
||||
}
|
||||
long[] observed3 = {10, 0, 12, 10, 15};
|
||||
long[] observed4 = {15, 0, 10, 15, 5};
|
||||
try {
|
||||
testStatistic.gTestDataSetsComparisonPValue(
|
||||
observed3, observed4);
|
||||
Assert.fail("Expecting ZeroException - double 0's");
|
||||
} catch (ZeroException ex) {
|
||||
// expected
|
||||
}
|
||||
long[] observed5 = {10, 10, 12, 10, 15};
|
||||
long[] observed6 = {0, 0, 0, 0, 0};
|
||||
try {
|
||||
testStatistic.gTestDataSetsComparisonPValue(
|
||||
observed5, observed6);
|
||||
Assert.fail("Expecting ZeroException - vanishing counts");
|
||||
} catch (ZeroException ex) {
|
||||
// expected
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testUnmatchedArrays() {
|
||||
final long[] observed = { 0, 1, 2, 3 };
|
||||
final double[] expected = { 1, 1, 2 };
|
||||
final long[] observed2 = {3, 4};
|
||||
try {
|
||||
testStatistic.gTestGoodnessOfFitPValue(expected, observed);
|
||||
Assert.fail("arrays have different lengths, DimensionMismatchException expected");
|
||||
} catch (DimensionMismatchException ex) {
|
||||
// expected
|
||||
}
|
||||
try {
|
||||
testStatistic.gTestDataSetsComparisonPValue(observed, observed2);
|
||||
Assert.fail("arrays have different lengths, DimensionMismatchException expected");
|
||||
} catch (DimensionMismatchException ex) {
|
||||
// expected
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testNegativeObservedCounts() {
|
||||
final long[] observed = { 0, 1, 2, -3 };
|
||||
final double[] expected = { 1, 1, 2, 3};
|
||||
final long[] observed2 = {3, 4, 5, 0};
|
||||
try {
|
||||
testStatistic.gTestGoodnessOfFitPValue(expected, observed);
|
||||
Assert.fail("negative observed count, NotPositiveException expected");
|
||||
} catch (NotPositiveException ex) {
|
||||
// expected
|
||||
}
|
||||
try {
|
||||
testStatistic.gTestDataSetsComparisonPValue(observed, observed2);
|
||||
Assert.fail("negative observed count, NotPositiveException expected");
|
||||
} catch (NotPositiveException ex) {
|
||||
// expected
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testZeroExpectedCounts() {
|
||||
final long[] observed = { 0, 1, 2, -3 };
|
||||
final double[] expected = { 1, 0, 2, 3};
|
||||
try {
|
||||
testStatistic.gTestGoodnessOfFitPValue(expected, observed);
|
||||
Assert.fail("zero expected count, NotStrictlyPositiveException expected");
|
||||
} catch (NotStrictlyPositiveException ex) {
|
||||
// expected
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testBadAlpha() {
|
||||
final long[] observed = { 0, 1, 2, 3 };
|
||||
final double[] expected = { 1, 2, 2, 3};
|
||||
final long[] observed2 = { 0, 2, 2, 3 };
|
||||
try {
|
||||
testStatistic.gTestGoodnessOfFit(expected, observed, 0.8);
|
||||
Assert.fail("zero expected count, NotStrictlyPositiveException expected");
|
||||
} catch (OutOfRangeException ex) {
|
||||
// expected
|
||||
}
|
||||
try {
|
||||
testStatistic.gTestDataSetsComparison(observed, observed2, -0.5);
|
||||
Assert.fail("zero expected count, NotStrictlyPositiveException expected");
|
||||
} catch (OutOfRangeException ex) {
|
||||
// expected
|
||||
}
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testScaling() {
|
||||
final long[] observed = {9, 11, 10, 8, 12};
|
||||
final double[] expected1 = {10, 10, 10, 10, 10};
|
||||
final double[] expected2 = {1000, 1000, 1000, 1000, 1000};
|
||||
final double[] expected3 = {1, 1, 1, 1, 1};
|
||||
final double tol = 1E-15;
|
||||
Assert.assertEquals(
|
||||
testStatistic.gTestGoodnessOfFitPValue(expected1, observed),
|
||||
testStatistic.gTestGoodnessOfFitPValue(expected2, observed),
|
||||
tol);
|
||||
Assert.assertEquals(
|
||||
testStatistic.gTestGoodnessOfFitPValue(expected1, observed),
|
||||
testStatistic.gTestGoodnessOfFitPValue(expected3, observed),
|
||||
tol);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testRootLogLikelihood() {
|
||||
// positive where k11 is bigger than expected.
|
||||
Assert.assertTrue(testStatistic.rootLogLikelihoodRatio(904, 21060, 1144, 283012) > 0.0);
|
||||
|
||||
// negative because k11 is lower than expected
|
||||
Assert.assertTrue(testStatistic.rootLogLikelihoodRatio(36, 21928, 60280, 623876) < 0.0);
|
||||
|
||||
Assert.assertEquals(Math.sqrt(2.772589), testStatistic.rootLogLikelihoodRatio(1, 0, 0, 1), 0.000001);
|
||||
Assert.assertEquals(-Math.sqrt(2.772589), testStatistic.rootLogLikelihoodRatio(0, 1, 1, 0), 0.000001);
|
||||
Assert.assertEquals(Math.sqrt(27.72589), testStatistic.rootLogLikelihoodRatio(10, 0, 0, 10), 0.00001);
|
||||
|
||||
Assert.assertEquals(Math.sqrt(39.33052), testStatistic.rootLogLikelihoodRatio(5, 1995, 0, 100000), 0.00001);
|
||||
Assert.assertEquals(-Math.sqrt(39.33052), testStatistic.rootLogLikelihoodRatio(0, 100000, 5, 1995), 0.00001);
|
||||
|
||||
Assert.assertEquals(Math.sqrt(4730.737), testStatistic.rootLogLikelihoodRatio(1000, 1995, 1000, 100000), 0.001);
|
||||
Assert.assertEquals(-Math.sqrt(4730.737), testStatistic.rootLogLikelihoodRatio(1000, 100000, 1000, 1995), 0.001);
|
||||
|
||||
Assert.assertEquals(Math.sqrt(5734.343), testStatistic.rootLogLikelihoodRatio(1000, 1000, 1000, 100000), 0.001);
|
||||
Assert.assertEquals(Math.sqrt(5714.932), testStatistic.rootLogLikelihoodRatio(1000, 1000, 1000, 99000), 0.001);
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue