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The Hipparchus statistics module
/*
* 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.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.stat.regression;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.NullArgumentException;
import org.hipparchus.linear.Array2DRowRealMatrix;
import org.hipparchus.linear.ArrayRealVector;
import org.hipparchus.linear.RealMatrix;
import org.hipparchus.linear.RealVector;
import org.hipparchus.stat.LocalizedStatFormats;
import org.hipparchus.stat.descriptive.moment.Variance;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathUtils;
/**
* Abstract base class for implementations of MultipleLinearRegression.
*/
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;
/**
* @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
*/
public boolean isNoIntercept() {
return noIntercept;
}
/**
* @param noIntercept true means the model is to be estimated without an intercept term
*/
public void setNoIntercept(boolean noIntercept) {
this.noIntercept = noIntercept;
}
/**
* Loads model x and y sample data from a flat input array, overriding any previous sample.
*
* Assumes that rows are concatenated with y values first in each row. For example, an input
* data array containing the sequence of values (1, 2, 3, 4, 5, 6, 7, 8, 9) with
* nobs = 3 and nvars = 2 creates a regression dataset with two
* independent variables, as below:
*
* y x[0] x[1]
* --------------
* 1 2 3
* 4 5 6
* 7 8 9
*
*
* 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 true,
* the X matrix will be created without an initial column of "1"s; otherwise this column will
* be added.
*
* Throws IllegalArgumentException if any of the following preconditions fail:
*
data cannot be nulldata.length = nobs * (nvars + 1)nobs > nvars
*
*
* @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 MathIllegalArgumentException if the length of the data array is not equal
* to nobs * (nvars + 1)
* @throws MathIllegalArgumentException if nobs is less than
* nvars + 1
*/
public void newSampleData(double[] data, int nobs, int nvars) {
MathUtils.checkNotNull(data, LocalizedCoreFormats.INPUT_ARRAY);
MathUtils.checkDimension(data.length, nobs * (nvars + 1));
if (nobs <= nvars) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.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 MathIllegalArgumentException if y is empty
*/
protected void newYSampleData(double[] y) {
if (y == null) {
throw new NullArgumentException();
}
if (y.length == 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NO_DATA);
}
this.yVector = new ArrayRealVector(y);
}
/**
* Loads new x sample data, overriding any previous data.
*
* The input x array should have one row for each sample
* observation, with columns corresponding to independent variables.
* For example, if
* x = new double[][] {{1, 2}, {3, 4}, {5, 6}}
* then setXSampleData(x) results in a model with two independent
* variables and 3 observations:
*
* x[0] x[1]
* ----------
* 1 2
* 3 4
* 5 6
*
*
* Note that there is no need to add an initial unitary column (column of 1's) when
* specifying a model including an intercept term.
*
* @param x the rectangular array representing the x sample
* @throws NullArgumentException if x is null
* @throws MathIllegalArgumentException if x is empty
* @throws MathIllegalArgumentException if x is not rectangular
*/
protected void newXSampleData(double[][] x) {
if (x == null) {
throw new NullArgumentException();
}
if (x.length == 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NO_DATA);
}
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++) {
MathUtils.checkDimension(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
* - Neither x nor y is null or empty;
* - The length (i.e. number of rows) of x equals the length of y
* - 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.
*
*
* @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 MathIllegalArgumentException if {@code x} and {@code y} do not
* have the same length
* @throws MathIllegalArgumentException 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 if the model has an intercept;
* or the number of columns if there is no intercept term
*/
protected void validateSampleData(double[][] x, double[] y) throws MathIllegalArgumentException {
if ((x == null) || (y == null)) {
throw new NullArgumentException();
}
MathUtils.checkDimension(x.length, y.length);
if (x.length == 0) { // Must be no y data either
throw new MathIllegalArgumentException(LocalizedCoreFormats.NO_DATA);
}
if (x[0].length + (noIntercept ? 0 : 1) > x.length) {
throw new MathIllegalArgumentException(
LocalizedStatFormats.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 MathIllegalArgumentException if the number of rows in x is not equal
* to the number of rows in covariance
* @throws MathIllegalArgumentException if the covariance matrix is not square
*/
protected void validateCovarianceData(double[][] x, double[][] covariance) {
MathUtils.checkDimension(x.length, covariance.length);
if (covariance.length > 0 && covariance.length != covariance[0].length) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NON_SQUARE_MATRIX,
covariance.length, covariance[0].length);
}
}
/**
* {@inheritDoc}
*/
@Override
public double[] estimateRegressionParameters() {
RealVector b = calculateBeta();
return b.toArray();
}
/**
* {@inheritDoc}
*/
@Override
public double[] estimateResiduals() {
RealVector b = calculateBeta();
RealVector e = yVector.subtract(xMatrix.operate(b));
return e.toArray();
}
/**
* {@inheritDoc}
*/
@Override
public double[][] estimateRegressionParametersVariance() {
return calculateBetaVariance().getData();
}
/**
* {@inheritDoc}
*/
@Override
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] = FastMath.sqrt(sigma * betaVariance[i][i]);
}
return result;
}
/**
* {@inheritDoc}
*/
@Override
public double estimateRegressandVariance() {
return calculateYVariance();
}
/**
* Estimates the variance of the error.
*
* @return estimate of the error variance
*/
public double estimateErrorVariance() {
return calculateErrorVariance();
}
/**
* Estimates the standard error of the regression.
*
* @return regression standard error
*/
public double estimateRegressionStandardError() {
return FastMath.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());
}
/**
* Calculates the variance of the error term.
* Uses the formula
* var(u) = u · u / (n - k)
*
* where n and k are the row and column dimensions of the design
* matrix X.
*
* @return error variance estimate
*/
protected double calculateErrorVariance() {
RealVector residuals = calculateResiduals();
return residuals.dotProduct(residuals) /
(xMatrix.getRowDimension() - xMatrix.getColumnDimension());
}
/**
* Calculates the residuals of multiple linear regression in matrix
* notation.
*
*
* u = y - X * b
*
*
* @return The residuals [n,1] matrix
*/
protected RealVector calculateResiduals() {
RealVector b = calculateBeta();
return yVector.subtract(xMatrix.operate(b));
}
}