com.numericalmethod.suanshu.stats.regression.linear.glm

Class IWLS

java.lang.Object

com.numericalmethod.suanshu.stats.regression.linear.glm.IWLS

All Implemented Interfaces:

Fitting, java.io.Serializable

public class IWLS
extends java.lang.Object
implements Fitting

We estimate parameters ß in a GLM model using the Iteratively Re-weighted Least Squares algorithm. The idea is that, at each iteration, we regress the adjusted, weighted, dependent variables on the same design matrix.

The R equivalent function is glm.fit.

See Also:

• "P. J. MacCullagh and J. A. Nelder. An algorithm for fitting generalized linear models. Generalized Linear Models. 2nd ed. pp.40. Section 2.5."
• Wikipedia: Maximum likelihood

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
int	maxIterations the maximum number of iterations
double	threshold the convergence threshold

Constructor Summary

Constructors

Constructor and Description
IWLS(double threshold, int maxIterations) Construct an instance to run the Iteratively Re-weighted Least Squares algorithm.

Method Summary

Modifier and Type	Method and Description
ImmutableVector	betaHat() Get the estimates of β, β^, as in
void	fit(GLMProblem probelm, Vector beta0Initial) Fit a Generalized Linear Model.
double	logLikelihood()
ImmutableVector	mu() Get μ as in
ImmutableVector	weights() Get the weights to the observations.

Methods inherited from class java.lang.Object

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

Field Detail

threshold

public final double threshold

the convergence threshold

maxIterations

public final int maxIterations

the maximum number of iterations

Constructor Detail

IWLS

public IWLS(double threshold,
            int maxIterations)

Construct an instance to run the Iteratively Re-weighted Least Squares algorithm.

Parameters:

threshold - the convergence threshold

maxIterations - maximum number of iterations

Method Detail

fit

public void fit(GLMProblem probelm,
                Vector beta0Initial)

Description copied from interface: Fitting

Fit a Generalized Linear Model.

This method must be called before the three get methods.

Specified by:

fit in interface Fitting

Parameters:

probelm - the generalized linear regression problem to be solved

beta0Initial - initial guess for betaHat

mu

public ImmutableVector mu()

Description copied from interface: Fitting

Get μ as in

 E(Y) = μ = g-1(Xβ)
 

Specified by:

mu in interface Fitting

Returns:

μ

betaHat

public ImmutableVector betaHat()

Description copied from interface: Fitting

Get the estimates of β, β^, as in

 E(Y) = μ = g-1(Xβ)
 

Specified by:

betaHat in interface Fitting

Returns:

β^

weights

public ImmutableVector weights()

Description copied from interface: Fitting

Get the weights to the observations.

Specified by:

weights in interface Fitting

Returns:

the weights

logLikelihood

public double logLikelihood()

Specified by:

logLikelihood in interface Fitting