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

java.lang.Object
  com.numericalmethod.suanshu.stats.regression.linear.glm.IWLS

All Implemented Interfaces:

GLMFitting

public class IWLS
extends java.lang.Object
implements GLMFitting

This implementation estimates parameters β 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

Constructor Summary

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

Method Summary

ImmutableVector	betaHat() Get the estimates of β, β^, as in E(Y) = μ = g-1(Xβ)
void	fit(GLMProblem probelm, Vector beta0Initial) Fit a Generalized Linear Model.
double	logLikelihood()
ImmutableVector	mu() Get μ as in E(Y) = μ = g-1(Xβ)
ImmutableVector	weights() Get the weights assigned to the observations.

Methods inherited from class java.lang.Object

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

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: GLMFitting

Fit a Generalized Linear Model.

This method must be called before the three get methods.

Specified by:

fit in interface GLMFitting

Parameters:

probelm - the generalized linear regression problem to be solved

beta0Initial - initial guess for β^

mu

public ImmutableVector mu()

Description copied from interface: GLMFitting

Get μ as in

E(Y) = μ = g^-1(Xβ)

Specified by:

mu in interface GLMFitting

Returns:

μ

betaHat

public ImmutableVector betaHat()

Description copied from interface: GLMFitting

Get the estimates of β, β^, as in

E(Y) = μ = g^-1(Xβ)

Specified by:

betaHat in interface GLMFitting

Returns:

β^

weights

public ImmutableVector weights()

Description copied from interface: GLMFitting

Get the weights assigned to the observations.

Specified by:

weights in interface GLMFitting

Returns:

the weights

logLikelihood

public double logLikelihood()

Specified by:

logLikelihood in interface GLMFitting