# SuanShu, a Java numerical and statistical library

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

## Class GeneralizedLinearModelQuasiFamily

• java.lang.Object
• com.numericalmethod.suanshu.stats.regression.linear.glm.quasi.GeneralizedLinearModelQuasiFamily
• All Implemented Interfaces:
LinearModel

public class GeneralizedLinearModelQuasiFamily
extends Object
implements LinearModel
GLM for the quasi-families. In order to construct a likelihood function it is usually necessary to posit a probabilistic mechanism specifying, for a range of parameter values, the probabilities of all relevant samples that might possibly have been observed. Such a specification implies the knowledge of the mechanism by which the data were generated or substantial experience of similar data from previous experiments. Often, this knowledge is not available. We may, however, be able to specify the range of possible response values and past experience with similar data is usually sufficient to specify, in a qualitative fashion, a few additional characteristic features of the data. From these characteristics, we may construct a quasi-likelihood function.

Note that AIC is not computed for the quasi-GLM because there is no 'real' likelihood function.

"P. J. MacCullagh and J. A. Nelder, "Chapter 9, An algorithm for fitting generalized linear models," in Generalized Linear Models, 2nd ed."
• ### Constructor Summary

Constructors
Constructor and Description
GeneralizedLinearModelQuasiFamily(QuasiGLMProblem problem)
Constructs a GeneralizedLinearModelQuasiFamily instance.
• ### Method Summary

All Methods
Modifier and Type Method and Description
QuasiGLMBeta beta()
Gets the GLM coefficient estimator, β^.
double Ey(Vector x)
Computes the expectation $$E(y(x))$$ given an input.
QuasiGLMResiduals residuals()
Gets the residual analysis.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### GeneralizedLinearModelQuasiFamily

public GeneralizedLinearModelQuasiFamily(QuasiGLMProblem problem)
Constructs a GeneralizedLinearModelQuasiFamily instance.
Parameters:
problem - the quasi generalized linear regression problem to be solved
• ### Method Detail

• #### Ey

public double Ey(Vector x)
Description copied from interface: LinearModel
Computes the expectation $$E(y(x))$$ given an input.
Specified by:
Ey in interface LinearModel
Parameters:
x - an input
Returns:
$$E(y(x))$$
• #### beta

public QuasiGLMBeta beta()
Gets the GLM coefficient estimator, β^.
Specified by:
beta in interface LinearModel
Returns:
the GLM coefficient estimator, β^
• #### residuals

public QuasiGLMResiduals residuals()
Gets the residual analysis.
Specified by:
residuals in interface LinearModel
Returns:
the residual analysis