dev.nm.stat.regression.linear

Class LMProblem

java.lang.Object

dev.nm.stat.regression.linear.LMProblem

Direct Known Subclasses:

ConstrainedLASSOProblem, GLMProblem, LARSProblem, LogisticProblem, UnconstrainedLASSOProblem

public class LMProblem
extends Object

This is 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 as 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 X is an affine function of X.

Arranging observations and the intercept

Each row of X is one observation; each column is one predictor. The length of y must equal the number of rows. When intercept == true, a column of ones is appended as the last column; do not also put that constant column into X. Coefficients therefore follow predictor-column order, with the intercept last.

Weights, when supplied, have one nonnegative entry per observation; null selects equal weights. Avoid rank-deficient designs. For meaningful residual-variance estimates, use more observations than fitted coefficients. Inputs are exposed through read-only wrappers, not necessarily copied: do not mutate their underlying data after constructing the problem.

See Also:

OLSRegression, Wikipedia: Linear regression

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
ImmutableMatrix	A() Gets the regressor matrix.
protected void	checkInputs() Checks whether this LMProblem instance is valid.
boolean	intercept() Checks if an intercept term is added to the linear regression.
ImmutableMatrix	invOfwAtwA() (wA' * wA)-1
int	nExogenousFactors() Gets the number of factors, excluding the intercept.
int	nFactors() Gets the number of factors, including the intercept if any.
int	nObs() Gets the number of observations.
ImmutableMatrix	wA() Gets the weighted regressor matrix.
ImmutableVector	weights() Gets the weights assigned to each observation.
ImmutableVector	wy() Gets the weighted response vector.
ImmutableMatrix	X() Gets the factor matrix.
ImmutableVector	y() Gets the response vector, the regressands, the dependent variables.

Methods inherited from class java.lang.Object

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

Constructor Detail

LMProblem

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

Constructs a linear regression problem.

Parameters:

y - the dependent variables

X - the factors

intercept - true if to additionally add an intercept term to the linear regression

weights - the weights assigned to each observation

LMProblem

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

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

Parameters:

y - the dependent variables

X - the factors

weights - the weights assigned to each observation

LMProblem

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

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

Parameters:

y - the dependent variables

X - the factors

intercept - true if to additionally add an intercept term to the linear regression

LMProblem

public LMProblem(Vector y,
                 Matrix X)

Constructs a linear regression problem, assuming

• a constant term (the intercept)
• equal weights assigned 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()

Gets the number of observations.

Returns:

the number of observations

nFactors

public int nFactors()

Gets the number of factors, including the intercept if any.

Returns:

the number of factors, including the intercept if any

y

public ImmutableVector y()

Gets the response vector, the regressands, the dependent variables.

Returns:

the response vector

wy

public ImmutableVector wy()

Gets the weighted response vector.

Returns:

the weighted response vector

A

public ImmutableMatrix A()

Gets the regressor matrix.

Returns:

the regressor matrix

wA

public ImmutableMatrix wA()

Gets the weighted regressor matrix.

Returns:

the weighted regressor matrix

intercept

public boolean intercept()

Checks if an intercept term is added to the linear regression.

Returns:

true if an intercept term is added

weights

public ImmutableVector weights()

Gets the weights assigned to each observation.

Returns:

the weights assigned to each observation

nExogenousFactors

public int nExogenousFactors()

Gets the number of factors, excluding the intercept.

Returns:

the number of factors, excluding the intercept

X

public ImmutableMatrix X()

Gets the factor matrix.

Note: the automatically appended intercept is not included.

Returns:

the factor matrix.

invOfwAtwA

public ImmutableMatrix invOfwAtwA()

(wA' * wA)^-1

Returns:

(wA' * wA)^-1

checkInputs

protected void checkInputs()

Checks whether this LMProblem instance is valid.

Throws:

IllegalArgumentException - if this problem is invalid