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

Class GeneralizedLinearModel

java.lang.Object

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

All Implemented Interfaces:

java.io.Serializable

public class GeneralizedLinearModel
extends java.lang.Object
implements java.io.Serializable

The Generalized Linear Model (GLM) is a flexible generalization of ordinary least squares regression. The 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 a 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."

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	AIC
Beta	beta the GLM coefficients β^ statistics
GLMProblem	problem the generalized linear regression problem to be solved
Residuals	residuals the residual analysis of this GLM regression

Constructor Summary

Constructors

Constructor and Description
GeneralizedLinearModel(GLMProblem problem) Solve a generalized linear problem using the Iterative Re-weighted Least Squares algorithm.
GeneralizedLinearModel(GLMProblem problem, Fitting fitting) Construct a GeneralizedLinearModel instance.

Method Summary

Methods inherited from class java.lang.Object

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

Field Detail

problem

public final GLMProblem problem

the generalized linear regression problem to be solved

beta

public final Beta beta

the GLM coefficients β^ statistics

residuals

public final Residuals residuals

the residual analysis of this GLM regression

AIC

public final double AIC

Constructor Detail

GeneralizedLinearModel

public GeneralizedLinearModel(GLMProblem problem,
                              Fitting fitting)

Construct a GeneralizedLinearModel instance.

Parameters:

problem - the generalized linear regression problem to be solved

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

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