dev.nm.stat.regression.linear.glm

Interface GLMFitting

All Known Implementing Classes:

IWLS, QuasiGLMNewtonRaphson

public interface GLMFitting

This interface represents a fitting method for estimating β in a Generalized Linear Model (GLM). John Nelder and Robert Wedderburn proposed an iteratively re-weighted least squares method for maximum likelihood estimation of the model parameters, β. Maximum-likelihood estimation remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian approaches and least squares fits to variance stabilized responses, have been developed.

See Also:

Wikipedia: Generalized linear model, IWLS

Method Summary

Modifier and Type	Method and Description
ImmutableVector	betaHat() Gets the estimates of β, β^, as in \[ E(Y) = \mu = g^{-1}(X\beta ) \]
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.

Method Detail

fit

void fit(GLMProblem problem,
         Vector beta0Initial)

Fits a Generalized Linear Model.

This method must be called before the three get methods.

Parameters:

problem - the generalized linear regression problem to be solved

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

mu

ImmutableVector mu()

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

Returns:

μ

betaHat

ImmutableVector betaHat()

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

Returns:

\(\hat{\beta}\)

weights

ImmutableVector weights()

Gets the weights assigned to the observations.

Returns:

the weights

logLikelihood

double logLikelihood()