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

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

public class GeneralizedLinearModel
extends java.lang.Object

The Generalized Linear Model (GLM) is a flexible generalization of the Ordinary Least Squares regression. GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. In GLM, each outcome of the dependent variables, Y, is assumed to be generated from a particular distribution in the exponential family, a large range of probability distributions that includes the normal, binomial and Poisson distributions, among others. The mean, μ, of the distribution depends on the independent variables, X, through

E(Y) = μ = g^-1(Xβ)

where E(Y) is the expected value of Y; Xβ is the linear predictor, a linear combination of unknown parameters, β; g is the link function.

The R equivalent function is glm.

See Also:

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

Constructor Summary

GeneralizedLinearModel(GLMProblem problem)
Solve a generalized linear problem using the Iterative Re-weighted Least Squares algorithm.

GeneralizedLinearModel(GLMProblem problem, GLMFitting fitting)
Construct a GeneralizedLinearModel instance.

Method Summary

double	AIC() Get the Akaike information criterion (AIC).
GLMBeta	beta() Get the GLM coefficients estimator, β^.
GLMProblem	getProblem() Get the generalized linear regression problem.
GLMResiduals	residuals() Get the residual analysis of this GLM regression.

Methods inherited from class java.lang.Object

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

Constructor Detail

GeneralizedLinearModel

public GeneralizedLinearModel(GLMProblem problem,
                              GLMFitting fitting)

Construct a GeneralizedLinearModel instance.

Parameters:

problem - the generalized linear regression problem to be solved

fitting - the fitting method, c.f., GLMFitting

GeneralizedLinearModel

public GeneralizedLinearModel(GLMProblem problem)

Solve a generalized linear problem using the Iterative Re-weighted Least Squares algorithm.

Parameters:

problem - the generalized linear regression problem to be solved

See Also:

IWLS

Method Detail

getProblem

public GLMProblem getProblem()

Get the generalized linear regression problem.

Returns:

the generalized linear regression problem

beta

public GLMBeta beta()

Get the GLM coefficients estimator, β^.

Returns:

the GLM coefficients estimator, β^

residuals

public GLMResiduals residuals()

Get the residual analysis of this GLM regression.

Returns:

the residual analysis of this GLM regression

AIC

public double AIC()

Get the Akaike information criterion (AIC).

Returns:

the Akaike information criterion (AIC)