org.yamcs.external.SimpleRegression Maven / Gradle / Ivy
package org.yamcs.external;
/*
* This class has been copied from apache math in order not to include the whole package into Yamcs.
* Methods we do not use have been removed.
*/
/*
* 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.
*/
/**
* Estimates an ordinary least squares regression model
* with one independent variable.
*
* y = intercept + slope * x
*
* Standard errors for intercept and slope are
* available as well as ANOVA, r-square and Pearson's r statistics.
*
* Observations (x,y pairs) can be added to the model one at a time or they
* can be provided in a 2-dimensional array. The observations are not stored
* in memory, so there is no limit to the number of observations that can be
* added to the model.
*
* Usage Notes:
* - When there are fewer than two observations in the model, or when
* there is no variation in the x values (i.e. all x values are the same)
* all statistics return
NaN. At least two observations with
* different x coordinates are required to estimate a bivariate regression
* model.
*
* - Getters for the statistics always compute values based on the current
* set of observations -- i.e., you can get statistics, then add more data
* and get updated statistics without using a new instance. There is no
* "compute" method that updates all statistics. Each of the getters performs
* the necessary computations to return the requested statistic.
*
* - The intercept term may be suppressed by passing {@code false} to
* the {@link #SimpleRegression(boolean)} constructor. When the
* {@code hasIntercept} property is false, the model is estimated without a
* constant term and {@link #getIntercept()} returns {@code 0}.
*
*
*/
public class SimpleRegression {
/** sum of x values */
private double sumX = 0d;
/** total variation in x (sum of squared deviations from xbar) */
private double sumXX = 0d;
/** sum of y values */
private double sumY = 0d;
/** total variation in y (sum of squared deviations from ybar) */
private double sumYY = 0d;
/** sum of products */
private double sumXY = 0d;
/** number of observations */
private long n = 0;
/** mean of accumulated x values, used in updating formulas */
private double xbar = 0;
/** mean of accumulated y values, used in updating formulas */
private double ybar = 0;
/** include an intercept or not */
private final boolean hasIntercept;
// ---------------------Public methods--------------------------------------
/**
* Create an empty SimpleRegression instance
*/
public SimpleRegression() {
this(true);
}
/**
* Create a SimpleRegression instance, specifying whether or not to estimate
* an intercept.
*
* Use {@code false} to estimate a model with no intercept. When the
* {@code hasIntercept} property is false, the model is estimated without a
* constant term and {@link #getIntercept()} returns {@code 0}.
*
* @param includeIntercept whether or not to include an intercept term in
* the regression model
*/
public SimpleRegression(boolean includeIntercept) {
super();
hasIntercept = includeIntercept;
}
/**
* Adds the observation (x,y) to the regression data set.
*
* Uses updating formulas for means and sums of squares defined in
* "Algorithms for Computing the Sample Variance: Analysis and
* Recommendations", Chan, T.F., Golub, G.H., and LeVeque, R.J.
* 1983, American Statistician, vol. 37, pp. 242-247, referenced in
* Weisberg, S. "Applied Linear Regression". 2nd Ed. 1985.
*
*
* @param x independent variable value
* @param y dependent variable value
*/
public void addData(final double x,final double y) {
if (n == 0) {
xbar = x;
ybar = y;
} else {
if( hasIntercept ){
final double fact1 = 1.0 + n;
final double fact2 = n / (1.0 + n);
final double dx = x - xbar;
final double dy = y - ybar;
sumXX += dx * dx * fact2;
sumYY += dy * dy * fact2;
sumXY += dx * dy * fact2;
xbar += dx / fact1;
ybar += dy / fact1;
}
}
if( !hasIntercept ){
sumXX += x * x ;
sumYY += y * y ;
sumXY += x * y ;
}
sumX += x;
sumY += y;
n++;
}
/**
* Appends data from another regression calculation to this one.
*
* The mean update formulae are based on a paper written by Philippe
* Pébay:
*
* Formulas for Robust, One-Pass Parallel Computation of Covariances and
* Arbitrary-Order Statistical Moments, 2008, Technical Report
* SAND2008-6212, Sandia National Laboratories.
*
* @param reg model to append data from
* @since 3.3
*/
public void append(SimpleRegression reg) {
if (n == 0) {
xbar = reg.xbar;
ybar = reg.ybar;
sumXX = reg.sumXX;
sumYY = reg.sumYY;
sumXY = reg.sumXY;
} else {
if (hasIntercept) {
final double fact1 = reg.n / (double) (reg.n + n);
final double fact2 = n * reg.n / (double) (reg.n + n);
final double dx = reg.xbar - xbar;
final double dy = reg.ybar - ybar;
sumXX += reg.sumXX + dx * dx * fact2;
sumYY += reg.sumYY + dy * dy * fact2;
sumXY += reg.sumXY + dx * dy * fact2;
xbar += dx * fact1;
ybar += dy * fact1;
}else{
sumXX += reg.sumXX;
sumYY += reg.sumYY;
sumXY += reg.sumXY;
}
}
sumX += reg.sumX;
sumY += reg.sumY;
n += reg.n;
}
/**
* Removes the observation (x,y) from the regression data set.
*
* Mirrors the addData method. This method permits the use of
* SimpleRegression instances in streaming mode where the regression
* is applied to a sliding "window" of observations, however the caller is
* responsible for maintaining the set of observations in the window.
*
* The method has no effect if there are no points of data (i.e. n=0)
*
* @param x independent variable value
* @param y dependent variable value
*/
public void removeData(final double x,final double y) {
if (n > 0) {
if (hasIntercept) {
final double fact1 = n - 1.0;
final double fact2 = n / (n - 1.0);
final double dx = x - xbar;
final double dy = y - ybar;
sumXX -= dx * dx * fact2;
sumYY -= dy * dy * fact2;
sumXY -= dx * dy * fact2;
xbar -= dx / fact1;
ybar -= dy / fact1;
} else {
final double fact1 = n - 1.0;
sumXX -= x * x;
sumYY -= y * y;
sumXY -= x * y;
xbar -= x / fact1;
ybar -= y / fact1;
}
sumX -= x;
sumY -= y;
n--;
}
}
/**
* Removes observations represented by the elements in data.
*
* If the array is larger than the current n, only the first n elements are
* processed. This method permits the use of SimpleRegression instances in
* streaming mode where the regression is applied to a sliding "window" of
* observations, however the caller is responsible for maintaining the set
* of observations in the window.
*
* To remove all data, use clear().
*
* @param data array of observations to be removed
*/
public void removeData(double[][] data) {
for (int i = 0; i < data.length && n > 0; i++) {
removeData(data[i][0], data[i][1]);
}
}
/**
* Clears all data from the model.
*/
public void clear() {
sumX = 0d;
sumXX = 0d;
sumY = 0d;
sumYY = 0d;
sumXY = 0d;
n = 0;
}
/**
* Returns the number of observations that have been added to the model.
*
* @return n number of observations that have been added.
*/
public long getN() {
return n;
}
/**
* Returns the "predicted" y value associated with the
* supplied x value, based on the data that has been
* added to the model when this method is activated.
*
* predict(x) = intercept + slope * x
*
* Preconditions:
* - At least two observations (with at least two different x values)
* must have been added before invoking this method. If this method is
* invoked before a model can be estimated,
Double,NaN is
* returned.
*
*
* @param x input x value
* @return predicted y value
*/
public double predict(final double x) {
final double b1 = getSlope();
if (hasIntercept) {
return getIntercept(b1) + b1 * x;
}
return b1 * x;
}
/**
* Returns the intercept of the estimated regression line, if
* {@link #hasIntercept()} is true; otherwise 0.
*
* The least squares estimate of the intercept is computed using the
* normal equations.
* The intercept is sometimes denoted b0.
*
* Preconditions:
* - At least two observations (with at least two different x values)
* must have been added before invoking this method. If this method is
* invoked before a model can be estimated,
Double,NaN is
* returned.
*
*
* @return the intercept of the regression line if the model includes an
* intercept; 0 otherwise
* @see #SimpleRegression(boolean)
*/
public double getIntercept() {
return hasIntercept ? getIntercept(getSlope()) : 0.0;
}
/**
* Returns true if the model includes an intercept term.
*
* @return true if the regression includes an intercept; false otherwise
* @see #SimpleRegression(boolean)
*/
public boolean hasIntercept() {
return hasIntercept;
}
/**
* Returns the slope of the estimated regression line.
*
* The least squares estimate of the slope is computed using the
* normal equations.
* The slope is sometimes denoted b1.
*
* Preconditions:
* - At least two observations (with at least two different x values)
* must have been added before invoking this method. If this method is
* invoked before a model can be estimated,
Double.NaN is
* returned.
*
*
* @return the slope of the regression line
*/
public double getSlope() {
if (n < 2) {
return Double.NaN; //not enough data
}
if (Math.abs(sumXX) < 10 * Double.MIN_VALUE) {
return Double.NaN; //not enough variation in x
}
return sumXY / sumXX;
}
/**
* Returns the
* sum of squared errors (SSE) associated with the regression
* model.
*
* The sum is computed using the computational formula
*
* SSE = SYY - (SXY * SXY / SXX)
*
* where SYY is the sum of the squared deviations of the y
* values about their mean, SXX is similarly defined and
* SXY is the sum of the products of x and y mean deviations.
*
* The sums are accumulated using the updating algorithm referenced in
* {@link #addData}.
*
* The return value is constrained to be non-negative - i.e., if due to
* rounding errors the computational formula returns a negative result,
* 0 is returned.
*
* Preconditions:
* - At least two observations (with at least two different x values)
* must have been added before invoking this method. If this method is
* invoked before a model can be estimated,
Double,NaN is
* returned.
*
*
* @return sum of squared errors associated with the regression model
*/
public double getSumSquaredErrors() {
return Math.max(0d, sumYY - sumXY * sumXY / sumXX);
}
/**
* Returns the sum of squared deviations of the y values about their mean.
*
* This is defined as SSTO
* here.
*
* If {@code n < 2}, this returns Double.NaN.
*
* @return sum of squared deviations of y values
*/
public double getTotalSumSquares() {
if (n < 2) {
return Double.NaN;
}
return sumYY;
}
/**
* Returns the sum of squared deviations of the x values about their mean.
*
* If n < 2, this returns Double.NaN.
*
* @return sum of squared deviations of x values
*/
public double getXSumSquares() {
if (n < 2) {
return Double.NaN;
}
return sumXX;
}
/**
* Returns the sum of crossproducts, xi*yi.
*
* @return sum of cross products
*/
public double getSumOfCrossProducts() {
return sumXY;
}
/**
* Returns the sum of squared deviations of the predicted y values about
* their mean (which equals the mean of y).
*
* This is usually abbreviated SSR or SSM. It is defined as SSM
* here
*
* Preconditions:
* - At least two observations (with at least two different x values)
* must have been added before invoking this method. If this method is
* invoked before a model can be estimated,
Double.NaN is
* returned.
*
*
* @return sum of squared deviations of predicted y values
*/
public double getRegressionSumSquares() {
return getRegressionSumSquares(getSlope());
}
/**
* Returns the sum of squared errors divided by the degrees of freedom,
* usually abbreviated MSE.
*
* If there are fewer than three data pairs in the model,
* or if there is no variation in x, this returns
* Double.NaN.
*
* @return sum of squared deviations of y values
*/
public double getMeanSquareError() {
if (n < 3) {
return Double.NaN;
}
return hasIntercept ? (getSumSquaredErrors() / (n - 2)) : (getSumSquaredErrors() / (n - 1));
}
/**
* Returns
* Pearson's product moment correlation coefficient,
* usually denoted r.
*
* Preconditions:
* - At least two observations (with at least two different x values)
* must have been added before invoking this method. If this method is
* invoked before a model can be estimated,
Double,NaN is
* returned.
*
*
* @return Pearson's r
*/
public double getR() {
double b1 = getSlope();
double result = Math.sqrt(getRSquare());
if (b1 < 0) {
result = -result;
}
return result;
}
/**
* Returns the
* coefficient of determination,
* usually denoted r-square.
*
* Preconditions:
* - At least two observations (with at least two different x values)
* must have been added before invoking this method. If this method is
* invoked before a model can be estimated,
Double,NaN is
* returned.
*
*
* @return r-square
*/
public double getRSquare() {
double ssto = getTotalSumSquares();
return (ssto - getSumSquaredErrors()) / ssto;
}
/**
* Returns the
* standard error of the intercept estimate,
* usually denoted s(b0).
*
* If there are fewer that three observations in the
* model, or if there is no variation in x, this returns
* Double.NaN.
Additionally, a Double.NaN is
* returned when the intercept is constrained to be zero
*
* @return standard error associated with intercept estimate
*/
public double getInterceptStdErr() {
if( !hasIntercept ){
return Double.NaN;
}
return Math.sqrt(
getMeanSquareError() * ((1d / n) + (xbar * xbar) / sumXX));
}
/**
* Returns the standard
* error of the slope estimate,
* usually denoted s(b1).
*
* If there are fewer that three data pairs in the model,
* or if there is no variation in x, this returns Double.NaN.
*
*
* @return standard error associated with slope estimate
*/
public double getSlopeStdErr() {
return Math.sqrt(getMeanSquareError() / sumXX);
}
// ---------------------Private methods-----------------------------------
/**
* Returns the intercept of the estimated regression line, given the slope.
*
* Will return NaN if slope is NaN.
*
* @param slope current slope
* @return the intercept of the regression line
*/
private double getIntercept(final double slope) {
if( hasIntercept){
return (sumY - slope * sumX) / n;
}
return 0.0;
}
/**
* Computes SSR from b1.
*
* @param slope regression slope estimate
* @return sum of squared deviations of predicted y values
*/
private double getRegressionSumSquares(final double slope) {
return slope * slope * sumXX;
}
}