com.numericalmethod.suanshu.stats.regression.linear

Class LMProblem

java.lang.Object

com.numericalmethod.suanshu.stats.regression.linear.LMProblem

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

GLMProblem, LogisticProblem

public class LMProblem
extends java.lang.Object
implements java.io.Serializable

This class represents a linear regression or a linear model (LM) problem.

Linear regression models the relationship between a scalar variable y and one or more variables denoted X. In linear regression, models of the unknown parameters are estimated from the data using linear functions. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of y is an affine function of y.

See Also:

Wikipedia: Linear regression, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
ImmutableMatrix	A the design matrix, the regressors, including the intercept if any; each column corresponds to one regressor
boolean	addIntercept true iff to add an intercept term to the linear regression
ImmutableMatrix	wA the weighted design matrix, w
ImmutableVector	weights the weights to each observation
ImmutableVector	wy the weighted response vector
ImmutableVector	y the response vector; the regressands; the dependent variables

Constructor Summary

Constructors

Constructor and Description
LMProblem(LMProblem that) Copy constructor.
LMProblem(Vector y, Matrix X) Construct a linear regression problem, assuming a constant term (the intercept) equal weights to all observations
LMProblem(Vector y, Matrix X, boolean addIntercept) Construct a linear regression problem, assuming equal weights to all observations.
LMProblem(Vector y, Matrix X, boolean addIntercept, Vector weights) Construct a linear regression problem.
LMProblem(Vector y, Matrix X, Vector weights) Construct a linear regression problem, assuming a constant term (the intercept).

Method Summary

Modifier and Type	Method and Description
protected void	checkInputs() Check whether this LMProblem instance is valid.
ImmutableMatrix	invOfwAtwA() (wA' %*% wA)-1
int	nExogenousFactors() the number of factors, excluding the intercept
int	nFactors() the number of factors, including the intercept if any
int	nObs() the number of observations
ImmutableMatrix	X() Get a copy of the factor matrix.

Methods inherited from class java.lang.Object

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

Field Detail

y

public final ImmutableVector y

the response vector; the regressands; the dependent variables

a vector of length n

wy

public final ImmutableVector wy

the weighted response vector

A

public final ImmutableMatrix A

the design matrix, the regressors, including the intercept if any; each column corresponds to one regressor

a n x m matrix

wA

public final ImmutableMatrix wA

the weighted design matrix, w

addIntercept

public final boolean addIntercept

true iff to add an intercept term to the linear regression

weights

public final ImmutableVector weights

the weights to each observation

Constructor Detail

LMProblem

public LMProblem(Vector y,
                 Matrix X,
                 boolean addIntercept,
                 Vector weights)

Construct a linear regression problem.

Parameters:

y - the dependent variables

X - the factors

addIntercept - true iff to add an intercept term to the linear regression

weights - the weights to each observation

LMProblem

public LMProblem(Vector y,
                 Matrix X,
                 Vector weights)

Construct a linear regression problem, assuming a constant term (the intercept).

Parameters:

y - the dependent variables

X - the factors

weights - the weights to each observation

LMProblem

public LMProblem(Vector y,
                 Matrix X,
                 boolean addIntercept)

Construct a linear regression problem, assuming equal weights to all observations.

Parameters:

y - the dependent variables

X - the factors

addIntercept - true iff to add an intercept term to the linear regression

LMProblem

public LMProblem(Vector y,
                 Matrix X)

Construct a linear regression problem, assuming

• a constant term (the intercept)
• equal weights to all observations

Parameters:

y - the dependent variables

X - the factors

LMProblem

public LMProblem(LMProblem that)

Copy constructor.

Parameters:

that - another LMProblem

Method Detail

nObs

public int nObs()

the number of observations

Returns:

the number of observations

nFactors

public int nFactors()

the number of factors, including the intercept if any

Returns:

the number of factors, including the intercept if any

nExogenousFactors

public int nExogenousFactors()

the number of factors, excluding the intercept

Returns:

the number of factors, excluding the intercept

X

public ImmutableMatrix X()

Get a copy of the factor matrix.

The automatically appended intercept is not included.

Returns:

a copy of the factor matrix.

invOfwAtwA

public ImmutableMatrix invOfwAtwA()

(wA' %*% wA)^-1

Returns:

(wA' %*% wA)^-1

checkInputs

protected void checkInputs()

Check whether this LMProblem instance is valid.

Throws:

java.lang.IllegalArgumentException - if this problem is invalid