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* 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.regression;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.InsufficientDataException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.linear.NonSquareMatrixException;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.RealVector;
import org.apache.commons.math3.linear.ArrayRealVector;
import org.apache.commons.math3.stat.descriptive.moment.Variance;
import org.apache.commons.math3.util.FastMath;
/**
* Abstract base class for implementations of MultipleLinearRegression.
* @since 2.0
*/
public abstract class AbstractMultipleLinearRegression implements
MultipleLinearRegression {
/** X sample data. */
private RealMatrix xMatrix;
/** Y sample data. */
private RealVector yVector;
/** Whether or not the regression model includes an intercept. True means no intercept. */
private boolean noIntercept = false;
/**
* @return the X sample data.
*/
protected RealMatrix getX() {
return xMatrix;
}
/**
* @return the Y sample data.
*/
protected RealVector getY() {
return yVector;
}
/**
* @return true if the model has no intercept term; false otherwise
* @since 2.2
*/
public boolean isNoIntercept() {
return noIntercept;
}
/**
* @param noIntercept true means the model is to be estimated without an intercept term
* @since 2.2
*/
public void setNoIntercept(boolean noIntercept) {
this.noIntercept = noIntercept;
}
/**
* <p>Loads model x and y sample data from a flat input array, overriding any previous sample.
* </p>
* <p>Assumes that rows are concatenated with y values first in each row. For example, an input
* <code>data</code> array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with
* <code>nobs = 3</code> and <code>nvars = 2</code> creates a regression dataset with two
* independent variables, as below:
* <pre>
* y x[0] x[1]
* --------------
* 1 2 3
* 4 5 6
* 7 8 9
* </pre>
* </p>
* <p>Note that there is no need to add an initial unitary column (column of 1's) when
* specifying a model including an intercept term. If {@link #isNoIntercept()} is <code>true</code>,
* the X matrix will be created without an initial column of "1"s; otherwise this column will
* be added.
* </p>
* <p>Throws IllegalArgumentException if any of the following preconditions fail:
* <ul><li><code>data</code> cannot be null</li>
* <li><code>data.length = nobs * (nvars + 1)</li>
* <li><code>nobs > nvars</code></li></ul>
* </p>
*
* @param data input data array
* @param nobs number of observations (rows)
* @param nvars number of independent variables (columns, not counting y)
* @throws NullArgumentException if the data array is null
* @throws DimensionMismatchException if the length of the data array is not equal
* to <code>nobs * (nvars + 1)</code>
* @throws InsufficientDataException if <code>nobs</code> is less than
* <code>nvars + 1</code>
*/
public void newSampleData(double[] data, int nobs, int nvars) {
if (data == null) {
throw new NullArgumentException();
}
if (data.length != nobs * (nvars + 1)) {
throw new DimensionMismatchException(data.length, nobs * (nvars + 1));
}
if (nobs <= nvars) {
throw new InsufficientDataException(LocalizedFormats.INSUFFICIENT_OBSERVED_POINTS_IN_SAMPLE, nobs, nvars + 1);
}
double[] y = new double[nobs];
final int cols = noIntercept ? nvars: nvars + 1;
double[][] x = new double[nobs][cols];
int pointer = 0;
for (int i = 0; i < nobs; i++) {
y[i] = data[pointer++];
if (!noIntercept) {
x[i][0] = 1.0d;
}
for (int j = noIntercept ? 0 : 1; j < cols; j++) {
x[i][j] = data[pointer++];
}
}
this.xMatrix = new Array2DRowRealMatrix(x);
this.yVector = new ArrayRealVector(y);
}
/**
* Loads new y sample data, overriding any previous data.
*
* @param y the array representing the y sample
* @throws NullArgumentException if y is null
* @throws NoDataException if y is empty
*/
protected void newYSampleData(double[] y) {
if (y == null) {
throw new NullArgumentException();
}
if (y.length == 0) {
throw new NoDataException();
}
this.yVector = new ArrayRealVector(y);
}
/**
* <p>Loads new x sample data, overriding any previous data.
* </p>
* The input <code>x</code> array should have one row for each sample
* observation, with columns corresponding to independent variables.
* For example, if <pre>
* <code> x = new double[][] {{1, 2}, {3, 4}, {5, 6}} </code></pre>
* then <code>setXSampleData(x) </code> results in a model with two independent
* variables and 3 observations:
* <pre>
* x[0] x[1]
* ----------
* 1 2
* 3 4
* 5 6
* </pre>
* </p>
* <p>Note that there is no need to add an initial unitary column (column of 1's) when
* specifying a model including an intercept term.
* </p>
* @param x the rectangular array representing the x sample
* @throws NullArgumentException if x is null
* @throws NoDataException if x is empty
* @throws DimensionMismatchException if x is not rectangular
*/
protected void newXSampleData(double[][] x) {
if (x == null) {
throw new NullArgumentException();
}
if (x.length == 0) {
throw new NoDataException();
}
if (noIntercept) {
this.xMatrix = new Array2DRowRealMatrix(x, true);
} else { // Augment design matrix with initial unitary column
final int nVars = x[0].length;
final double[][] xAug = new double[x.length][nVars + 1];
for (int i = 0; i < x.length; i++) {
if (x[i].length != nVars) {
throw new DimensionMismatchException(x[i].length, nVars);
}
xAug[i][0] = 1.0d;
System.arraycopy(x[i], 0, xAug[i], 1, nVars);
}
this.xMatrix = new Array2DRowRealMatrix(xAug, false);
}
}
/**
* Validates sample data. Checks that
* <ul><li>Neither x nor y is null or empty;</li>
* <li>The length (i.e. number of rows) of x equals the length of y</li>
* <li>x has at least one more row than it has columns (i.e. there is
* sufficient data to estimate regression coefficients for each of the
* columns in x plus an intercept.</li>
* </ul>
*
* @param x the [n,k] array representing the x data
* @param y the [n,1] array representing the y data
* @throws NullArgumentException if {@code x} or {@code y} is null
* @throws DimensionMismatchException if {@code x} and {@code y} do not
* have the same length
* @throws NoDataException if {@code x} or {@code y} are zero-length
* @throws MathIllegalArgumentException if the number of rows of {@code x}
* is not larger than the number of columns + 1
*/
protected void validateSampleData(double[][] x, double[] y) throws MathIllegalArgumentException {
if ((x == null) || (y == null)) {
throw new NullArgumentException();
}
if (x.length != y.length) {
throw new DimensionMismatchException(y.length, x.length);
}
if (x.length == 0) { // Must be no y data either
throw new NoDataException();
}
if (x[0].length + 1 > x.length) {
throw new MathIllegalArgumentException(
LocalizedFormats.NOT_ENOUGH_DATA_FOR_NUMBER_OF_PREDICTORS,
x.length, x[0].length);
}
}
/**
* Validates that the x data and covariance matrix have the same
* number of rows and that the covariance matrix is square.
*
* @param x the [n,k] array representing the x sample
* @param covariance the [n,n] array representing the covariance matrix
* @throws DimensionMismatchException if the number of rows in x is not equal
* to the number of rows in covariance
* @throws NonSquareMatrixException if the covariance matrix is not square
*/
protected void validateCovarianceData(double[][] x, double[][] covariance) {
if (x.length != covariance.length) {
throw new DimensionMismatchException(x.length, covariance.length);
}
if (covariance.length > 0 && covariance.length != covariance[0].length) {
throw new NonSquareMatrixException(covariance.length, covariance[0].length);
}
}
/**
* {@inheritDoc}
*/
public double[] estimateRegressionParameters() {
RealVector b = calculateBeta();
return b.toArray();
}
/**
* {@inheritDoc}
*/
public double[] estimateResiduals() {
RealVector b = calculateBeta();
RealVector e = yVector.subtract(xMatrix.operate(b));
return e.toArray();
}
/**
* {@inheritDoc}
*/
public double[][] estimateRegressionParametersVariance() {
return calculateBetaVariance().getData();
}
/**
* {@inheritDoc}
*/
public double[] estimateRegressionParametersStandardErrors() {
double[][] betaVariance = estimateRegressionParametersVariance();
double sigma = calculateErrorVariance();
int length = betaVariance[0].length;
double[] result = new double[length];
for (int i = 0; i < length; i++) {
result[i] = Math.sqrt(sigma * betaVariance[i][i]);
}
return result;
}
/**
* {@inheritDoc}
*/
public double estimateRegressandVariance() {
return calculateYVariance();
}
/**
* Estimates the variance of the error.
*
* @return estimate of the error variance
* @since 2.2
*/
public double estimateErrorVariance() {
return calculateErrorVariance();
}
/**
* Estimates the standard error of the regression.
*
* @return regression standard error
* @since 2.2
*/
public double estimateRegressionStandardError() {
return Math.sqrt(estimateErrorVariance());
}
/**
* Calculates the beta of multiple linear regression in matrix notation.
*
* @return beta
*/
protected abstract RealVector calculateBeta();
/**
* Calculates the beta variance of multiple linear regression in matrix
* notation.
*
* @return beta variance
*/
protected abstract RealMatrix calculateBetaVariance();
/**
* Calculates the variance of the y values.
*
* @return Y variance
*/
protected double calculateYVariance() {
return new Variance().evaluate(yVector.toArray());
}
/**
* <p>Calculates the variance of the error term.</p>
* Uses the formula <pre>
* var(u) = u · u / (n - k)
* </pre>
* where n and k are the row and column dimensions of the design
* matrix X.
*
* @return error variance estimate
* @since 2.2
*/
protected double calculateErrorVariance() {
RealVector residuals = calculateResiduals();
return residuals.dotProduct(residuals) /
(xMatrix.getRowDimension() - xMatrix.getColumnDimension());
}
/**
* Calculates the residuals of multiple linear regression in matrix
* notation.
*
* <pre>
* u = y - X * b
* </pre>
*
* @return The residuals [n,1] matrix
*/
protected RealVector calculateResiduals() {
RealVector b = calculateBeta();
return yVector.subtract(xMatrix.operate(b));
}
}