MillerUpdatingRegression (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.stat.regression.MillerUpdatingRegression

All Implemented Interfaces:: UpdatingMultipleLinearRegression

public class MillerUpdatingRegression
extends Object
implements UpdatingMultipleLinearRegression

This class is a concrete implementation of the UpdatingMultipleLinearRegression interface.

The algorithm is described in:

 Algorithm AS 274: Least Squares Routines to Supplement Those of Gentleman
 Author(s): Alan J. Miller
 Source: Journal of the Royal Statistical Society.
 Series C (Applied Statistics), Vol. 41, No. 2
 (1992), pp. 458-478
 Published by: Blackwell Publishing for the Royal Statistical Society
 Stable URL: http://www.jstor.org/stable/2347583

This method for multiple regression forms the solution to the OLS problem by updating the QR decomposition as described by Gentleman.

Since:: 3.0

Constructor Summary

Constructors
Constructor and Description
`MillerUpdatingRegression(int numberOfVariables, boolean includeConstant)` Primary constructor for the MillerUpdatingRegression.
`MillerUpdatingRegression(int numberOfVariables, boolean includeConstant, double errorTolerance)` This is the augmented constructor for the MillerUpdatingRegression class.

Method Summary

Methods
Modifier and Type	Method and Description
`void`	`addObservation(double[] x, double y)` Adds an observation to the regression model.
`void`	`addObservations(double[][] x, double[] y)` Adds multiple observations to the model.
`void`	`clear()` As the name suggests, clear wipes the internals and reorders everything in the canonical order.
`double`	`getDiagonalOfHatMatrix(double[] row_data)` Gets the diagonal of the Hat matrix also known as the leverage matrix.
`long`	`getN()` Gets the number of observations added to the regression model.
`int[]`	`getOrderOfRegressors()` Gets the order of the regressors, useful if some type of reordering has been called.
`double[]`	`getPartialCorrelations(int in)` In the original algorithm only the partial correlations of the regressors is returned to the user.
`boolean`	`hasIntercept()` A getter method which determines whether a constant is included.
`RegressionResults`	`regress()` Conducts a regression on the data in the model, using all regressors.
`RegressionResults`	`regress(int numberOfRegressors)` Conducts a regression on the data in the model, using a subset of regressors.
`RegressionResults`	`regress(int[] variablesToInclude)` Conducts a regression on the data in the model, using regressors in array Calling this method will change the internal order of the regressors and care is required in interpreting the hatmatrix.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - MillerUpdatingRegression
```
public MillerUpdatingRegression(int numberOfVariables,
                        boolean includeConstant,
                        double errorTolerance)
                         throws ModelSpecificationException
```
    This is the augmented constructor for the MillerUpdatingRegression class.
    
    Parameters:
    numberOfVariables - number of regressors to expect, not including constant
    includeConstant - include a constant automatically
    errorTolerance - zero tolerance, how machine zero is determined
    
    Throws:
    
    ModelSpecificationException - if numberOfVariables is less than 1
  - MillerUpdatingRegression
```
public MillerUpdatingRegression(int numberOfVariables,
                        boolean includeConstant)
                         throws ModelSpecificationException
```
    Primary constructor for the MillerUpdatingRegression.
    
    Parameters:
    numberOfVariables - maximum number of potential regressors
    includeConstant - include a constant automatically
    
    Throws:
    
    ModelSpecificationException - if numberOfVariables is less than 1
- Method Detail
  - hasIntercept
```
public boolean hasIntercept()
```
    A getter method which determines whether a constant is included.
    
    Specified by:
    
    hasIntercept in interface UpdatingMultipleLinearRegression
    
    Returns:
    true regression has an intercept, false no intercept
  - getN
```
public long getN()
```
    Gets the number of observations added to the regression model.
    
    Specified by:
    
    getN in interface UpdatingMultipleLinearRegression
    
    Returns:
    number of observations
  - addObservation
```
public void addObservation(double[] x,
                  double y)
                    throws ModelSpecificationException
```
    Adds an observation to the regression model.
    
    Specified by:
    
    addObservation in interface UpdatingMultipleLinearRegression
    
    Parameters:
    x - the array with regressor values
    y - the value of dependent variable given these regressors
    
    Throws:
    
    ModelSpecificationException - if the length of x does not equal the number of independent variables in the model
  - addObservations
```
public void addObservations(double[][] x,
                   double[] y)
                     throws ModelSpecificationException
```
    Adds multiple observations to the model.
    
    Specified by:
    
    addObservations in interface UpdatingMultipleLinearRegression
    
    Parameters:
    x - observations on the regressors
    y - observations on the regressand
    
    Throws:
    
    ModelSpecificationException - if x is not rectangular, does not match the length of y or does not contain sufficient data to estimate the model
  - clear
```
public void clear()
```
    As the name suggests, clear wipes the internals and reorders everything in the canonical order.
    
    Specified by:
    
    clear in interface UpdatingMultipleLinearRegression
  - getPartialCorrelations
```
public double[] getPartialCorrelations(int in)
```
    In the original algorithm only the partial correlations of the regressors is returned to the user. In this implementation, we have
```
 corr =
 {
   corrxx - lower triangular
   corrxy - bottom row of the matrix
 }
 Replaces subroutines PCORR and COR of:
 ALGORITHM AS274  APPL. STATIST. (1992) VOL.41, NO. 2 
```
    Calculate partial correlations after the variables in rows 1, 2, ..., IN have been forced into the regression. If IN = 1, and the first row of R represents a constant in the model, then the usual simple correlations are returned.
    
    If IN = 0, the value returned in array CORMAT for the correlation of variables Xi & Xj is:
```
 sum ( Xi.Xj ) / Sqrt ( sum (Xi^2) . sum (Xj^2) )
```
    On return, array CORMAT contains the upper triangle of the matrix of partial correlations stored by rows, excluding the 1's on the diagonal. e.g. if IN = 2, the consecutive elements returned are: (3,4) (3,5) ... (3,ncol), (4,5) (4,6) ... (4,ncol), etc. Array YCORR stores the partial correlations with the Y-variable starting with YCORR(IN+1) = partial correlation with the variable in position (IN+1).
    Parameters:
    in - how many of the regressors to include (either in canonical order, or in the current reordered state)
    
    Returns:
    an array with the partial correlations of the remainder of regressors with each other and the regressand, in lower triangular form
  - getDiagonalOfHatMatrix
```
public double getDiagonalOfHatMatrix(double[] row_data)
```
    Gets the diagonal of the Hat matrix also known as the leverage matrix.
    
    Parameters:
    row_data - returns the diagonal of the hat matrix for this observation
    
    Returns:
    the diagonal element of the hatmatrix
  - getOrderOfRegressors
```
public int[] getOrderOfRegressors()
```
    Gets the order of the regressors, useful if some type of reordering has been called. Calling regress with int[]{} args will trigger a reordering.
    
    Returns:
    int[] with the current order of the regressors
  - regress
```
public RegressionResults regress()
                          throws ModelSpecificationException
```
    Conducts a regression on the data in the model, using all regressors.
    
    Specified by:
    
    regress in interface UpdatingMultipleLinearRegression
    
    Returns:
    RegressionResults the structure holding all regression results
    
    Throws:
    
    ModelSpecificationException - - thrown if number of observations is less than the number of variables
  - regress
```
public RegressionResults regress(int numberOfRegressors)
                          throws ModelSpecificationException
```
    Conducts a regression on the data in the model, using a subset of regressors.
    
    Parameters:
    numberOfRegressors - many of the regressors to include (either in canonical order, or in the current reordered state)
    
    Returns:
    RegressionResults the structure holding all regression results
    
    Throws:
    
    ModelSpecificationException - - thrown if number of observations is less than the number of variables or number of regressors requested is greater than the regressors in the model
  - regress
```
public RegressionResults regress(int[] variablesToInclude)
                          throws ModelSpecificationException
```
    Conducts a regression on the data in the model, using regressors in array Calling this method will change the internal order of the regressors and care is required in interpreting the hatmatrix.
    
    Specified by:
    
    regress in interface UpdatingMultipleLinearRegression
    
    Parameters:
    variablesToInclude - array of variables to include in regression
    
    Returns:
    RegressionResults the structure holding all regression results
    
    Throws:
    
    ModelSpecificationException - - thrown if number of observations is less than the number of variables, the number of regressors requested is greater than the regressors in the model or a regressor index in regressor array does not exist

Class MillerUpdatingRegression

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MillerUpdatingRegression

MillerUpdatingRegression

Method Detail

hasIntercept

getN

addObservation

addObservations

clear

getPartialCorrelations

getDiagonalOfHatMatrix

getOrderOfRegressors

regress

regress

regress