dev.nm.stat.regression.linear.glm.quasi

Class QuasiGLMNewtonRaphson

java.lang.Object

dev.nm.stat.regression.linear.glm.quasi.QuasiGLMNewtonRaphson

All Implemented Interfaces:

GLMFitting

public class QuasiGLMNewtonRaphson
extends Object
implements GLMFitting

The Newton-Raphson method is an iterative algorithm to estimate the β of the quasi GLM regression. It is a maximum likelihood method.

See Also:

• "P. J. MacCullagh and J. A. Nelder, "pp.327, An algorithm for fitting generalized linear models," in Generalized Linear Models, 2nd ed."
• Wikipedia: Fitting

Constructor Summary

Constructors

Constructor and Description
QuasiGLMNewtonRaphson(double epsilon, int maxIterations) Constructs an instance to run the Newton-Raphson method.

Method Summary

Modifier and Type	Method and Description
ImmutableVector	betaHat() Gets the estimates of β, β^, as in \[ E(Y) = \mu = g^{-1}(X\beta ) \]
ImmutableMatrix	D() Computes D. \[ D = d(\mu )/d(\beta ) = (d\mu /d\eta ) \cdot (d\eta /d\beta ) \]
ImmutableMatrix	DVInv() Computes D / V(μ).
void	fit(GLMProblem problem, Vector beta0Initial) Fits a Generalized Linear Model.
double	logLikelihood()
ImmutableVector	mu() Gets μ as in \[ E(Y) = \mu = g^{-1}(X\beta ) \]
ImmutableVector	weights() Gets 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

QuasiGLMNewtonRaphson

public QuasiGLMNewtonRaphson(double epsilon,
                             int maxIterations)

Constructs an instance to run the Newton-Raphson method.

Parameters:

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

maxIterations - the maximum number of iterations

Method Detail

fit

public void fit(GLMProblem problem,
                Vector beta0Initial)

Description copied from interface: GLMFitting

Fits a Generalized Linear Model.

This method must be called before the three get methods.

Specified by:

fit in interface GLMFitting

Parameters:

problem - the generalized linear regression problem to be solved

beta0Initial - initial guess for \(\hat{\beta}\)

mu

public ImmutableVector mu()

Description copied from interface: GLMFitting

Gets μ as in \[ E(Y) = \mu = g^{-1}(X\beta ) \]

Specified by:

mu in interface GLMFitting

Returns:

μ

betaHat

public ImmutableVector betaHat()

Description copied from interface: GLMFitting

Gets the estimates of β, β^, as in \[ E(Y) = \mu = g^{-1}(X\beta ) \]

Specified by:

betaHat in interface GLMFitting

Returns:

\(\hat{\beta}\)

logLikelihood

public double logLikelihood()

Specified by:

logLikelihood in interface GLMFitting

weights

public ImmutableVector weights()

Description copied from interface: GLMFitting

Gets the weights assigned to the observations.

Specified by:

weights in interface GLMFitting

Returns:

the weights

D

public ImmutableMatrix D()

Computes D. \[ D = d(\mu )/d(\beta ) = (d\mu /d\eta ) \cdot (d\eta /d\beta ) \]

Returns:

D

DVInv

public ImmutableMatrix DVInv()

Computes D / V(μ).

Returns:

D / V(μ)