org.hipparchus.stat.regression

Class AbstractMultipleLinearRegression

java.lang.Object

org.hipparchus.stat.regression.AbstractMultipleLinearRegression

All Implemented Interfaces:

MultipleLinearRegression

Direct Known Subclasses:

GLSMultipleLinearRegression, OLSMultipleLinearRegression

public abstract class AbstractMultipleLinearRegression
extends Object
implements MultipleLinearRegression

Abstract base class for implementations of MultipleLinearRegression.

Constructor Summary

Constructors

Constructor and Description
AbstractMultipleLinearRegression()

Method Summary

Modifier and Type	Method and Description
protected abstract RealVector	calculateBeta() Calculates the beta of multiple linear regression in matrix notation.
protected abstract RealMatrix	calculateBetaVariance() Calculates the beta variance of multiple linear regression in matrix notation.
protected double	calculateErrorVariance() Calculates the variance of the error term.
protected RealVector	calculateResiduals() Calculates the residuals of multiple linear regression in matrix notation.
protected double	calculateYVariance() Calculates the variance of the y values.
double	estimateErrorVariance() Estimates the variance of the error.
double	estimateRegressandVariance() Returns the variance of the regressand, ie Var(y).
double[]	estimateRegressionParameters() Estimates the regression parameters b.
double[]	estimateRegressionParametersStandardErrors() Returns the standard errors of the regression parameters.
double[][]	estimateRegressionParametersVariance() Estimates the variance of the regression parameters, ie Var(b).
double	estimateRegressionStandardError() Estimates the standard error of the regression.
double[]	estimateResiduals() Estimates the residuals, ie u = y - X*b.
protected RealMatrix	getX()
protected RealVector	getY()
boolean	isNoIntercept()
void	newSampleData(double[] data, int nobs, int nvars) Loads model x and y sample data from a flat input array, overriding any previous sample.
protected void	newXSampleData(double[][] x) Loads new x sample data, overriding any previous data.
protected void	newYSampleData(double[] y) Loads new y sample data, overriding any previous data.
void	setNoIntercept(boolean noIntercept)
protected void	validateCovarianceData(double[][] x, double[][] covariance) Validates that the x data and covariance matrix have the same number of rows and that the covariance matrix is square.
protected void	validateSampleData(double[][] x, double[] y) Validates sample data.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

AbstractMultipleLinearRegression

public AbstractMultipleLinearRegression()

Method Detail

getX

protected RealMatrix getX()

Returns:

the X sample data.

getY

protected RealVector getY()

Returns:

the Y sample data.

isNoIntercept

public boolean isNoIntercept()

Returns:

true if the model has no intercept term; false otherwise

setNoIntercept

public void setNoIntercept(boolean noIntercept)

Parameters:

noIntercept - true means the model is to be estimated without an intercept term

newSampleData

public void newSampleData(double[] data,
                          int nobs,
                          int nvars)

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 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 null
• data.length = nobs * (nvars + 1)
• nobs > nvars

Parameters:

data - input data array

nobs - number of observations (rows)

nvars - number of independent variables (columns, not counting y)

Throws:

NullArgumentException - if the data array is null

MathIllegalArgumentException - if the length of the data array is not equal to nobs * (nvars + 1)

MathIllegalArgumentException - if nobs is less than nvars + 1

newYSampleData

protected void newYSampleData(double[] y)

Loads new y sample data, overriding any previous data.

Parameters:

y - the array representing the y sample

Throws:

NullArgumentException - if y is null

MathIllegalArgumentException - if y is empty

newXSampleData

protected void newXSampleData(double[][] x)

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.

Parameters:

x - the rectangular array representing the x sample

Throws:

NullArgumentException - if x is null

MathIllegalArgumentException - if x is empty

MathIllegalArgumentException - if x is not rectangular

validateSampleData

protected void validateSampleData(double[][] x,
                                  double[] y)
                           throws MathIllegalArgumentException

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.

Parameters:

x - the [n,k] array representing the x data

y - the [n,1] array representing the y data

Throws:

NullArgumentException - if x or y is null

MathIllegalArgumentException - if x and y do not have the same length

MathIllegalArgumentException - if x or y are zero-length

MathIllegalArgumentException - if the number of rows of 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

validateCovarianceData

protected void validateCovarianceData(double[][] x,
                                      double[][] covariance)

Validates that the x data and covariance matrix have the same number of rows and that the covariance matrix is square.

Parameters:

x - the [n,k] array representing the x sample

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

MathIllegalArgumentException - if the covariance matrix is not square

estimateRegressionParameters

public double[] estimateRegressionParameters()

Estimates the regression parameters b.

Specified by:

estimateRegressionParameters in interface MultipleLinearRegression

Returns:

The [k,1] array representing b

estimateResiduals

public double[] estimateResiduals()

Estimates the residuals, ie u = y - X*b.

Specified by:

estimateResiduals in interface MultipleLinearRegression

Returns:

The [n,1] array representing the residuals

estimateRegressionParametersVariance

public double[][] estimateRegressionParametersVariance()

Estimates the variance of the regression parameters, ie Var(b).

Specified by:

estimateRegressionParametersVariance in interface MultipleLinearRegression

Returns:

The [k,k] array representing the variance of b

estimateRegressionParametersStandardErrors

public double[] estimateRegressionParametersStandardErrors()

Returns the standard errors of the regression parameters.

Specified by:

estimateRegressionParametersStandardErrors in interface MultipleLinearRegression

Returns:

standard errors of estimated regression parameters

estimateRegressandVariance

public double estimateRegressandVariance()

Returns the variance of the regressand, ie Var(y).

Specified by:

estimateRegressandVariance in interface MultipleLinearRegression

Returns:

The double representing the variance of y

estimateErrorVariance

public double estimateErrorVariance()

Estimates the variance of the error.

Returns:

estimate of the error variance

estimateRegressionStandardError

public double estimateRegressionStandardError()

Estimates the standard error of the regression.

Returns:

regression standard error

calculateBeta

protected abstract RealVector calculateBeta()

Calculates the beta of multiple linear regression in matrix notation.

Returns:

beta

calculateBetaVariance

protected abstract RealMatrix calculateBetaVariance()

Calculates the beta variance of multiple linear regression in matrix notation.

Returns:

beta variance

calculateYVariance

protected double calculateYVariance()

Calculates the variance of the y values.

Returns:

Y variance

calculateErrorVariance

protected double calculateErrorVariance()

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.

Returns:

error variance estimate

calculateResiduals

protected RealVector calculateResiduals()

Calculates the residuals of multiple linear regression in matrix notation.

 u = y - X * b
 

Returns:

The residuals [n,1] matrix