Class GLMBinomial
- java.lang.Object
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- dev.nm.stat.regression.linear.glm.distribution.GLMBinomial
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- All Implemented Interfaces:
GLMExponentialDistribution
- Direct Known Subclasses:
QuasiBinomial
public class GLMBinomial extends Object implements GLMExponentialDistribution
This is the Binomial distribution of the error distribution in GLM model. The R equivalent function isbinomial
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Constructor Summary
Constructors Constructor Description GLMBinomial()
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
AIC(Vector y, Vector mu, Vector weight, double prelogLike, double deviance, int nFactors)
AIC = 2 * #param - 2 * log-likelihooddouble
cumulant(double theta)
The cumulant function of the exponential distribution.double
deviance(double y, double mu)
Deviance D(y;μ^) measures the goodness-of-fit of a model, which is defined as the difference between the maximum log likelihood achievable and that achieved by the model.double
dispersion(Vector y, Vector mu, int nFactors)
Different distribution models have different ways to compute dispersion, Φ.double
overdispersion(Vector y, Vector mu, int nFactors)
Over-dispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on the nominal variance of a given simple statistical model.double
theta(double mu)
The canonical parameter of the distribution in terms of the mean μ.double
variance(double mu)
The variance function of the distribution in terms of the mean μ.
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Method Detail
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variance
public double variance(double mu)
Description copied from interface:GLMExponentialDistribution
The variance function of the distribution in terms of the mean μ.- Specified by:
variance
in interfaceGLMExponentialDistribution
- Parameters:
mu
- the distribution mean, μ- Returns:
- the value of variance function at μ
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theta
public double theta(double mu)
Description copied from interface:GLMExponentialDistribution
The canonical parameter of the distribution in terms of the mean μ.- Specified by:
theta
in interfaceGLMExponentialDistribution
- Parameters:
mu
- the distribution mean, μ- Returns:
- the value of canonical parameter θ at μ
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cumulant
public double cumulant(double theta)
Description copied from interface:GLMExponentialDistribution
The cumulant function of the exponential distribution.- Specified by:
cumulant
in interfaceGLMExponentialDistribution
- Parameters:
theta
- θ- Returns:
- the value of the cumulant function at θ
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deviance
public double deviance(double y, double mu)
Description copied from interface:GLMExponentialDistribution
Deviance D(y;μ^) measures the goodness-of-fit of a model, which is defined as the difference between the maximum log likelihood achievable and that achieved by the model.D(y;μ^) = 2 * [l(y;y) - l(μ^;y)]
where l is the log-likelihood. For an exponential family distribution, this is equivalent to2 * [(y * θ(y) - b(θ(y))) - (y * θ(μ^) - b(θ(μ^)]
where b is the cumulant function of the distribution.- Specified by:
deviance
in interfaceGLMExponentialDistribution
- Parameters:
y
- an observationmu
- the estimated mean, μ^- Returns:
- the deviance
- See Also:
- P. J. MacCullagh and J. A. Nelder, "Section 2.3, pp.34, Measuring the goodness-of-fit," Generalized Linear Models, 2nd ed.
- Wikipedia: Deviance
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overdispersion
public double overdispersion(Vector y, Vector mu, int nFactors)
Description copied from interface:GLMExponentialDistribution
Over-dispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on the nominal variance of a given simple statistical model.
X^2 estimates a(Φ) = Φ, the dispersion parameter (assuming w = 1). For,σ^2 = X^2/(n-p), eq. 4.23 X^2 = sum{(y-μ)^2}/V(μ), p.34 = sum{(y-μ)^2}/b''(θ), p.29
GLMGamma
,GLMGaussian
,GLMInverseGaussian
, over-dispersion is the same as dispersion.- Specified by:
overdispersion
in interfaceGLMExponentialDistribution
- Parameters:
y
- an observationmu
- the distribution mean, μnFactors
- the number of factors- Returns:
- the dispersion
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dispersion
public double dispersion(Vector y, Vector mu, int nFactors)
Description copied from interface:GLMExponentialDistribution
Different distribution models have different ways to compute dispersion, Φ. Note that in R's output, this is called "over-dispersion".- Specified by:
dispersion
in interfaceGLMExponentialDistribution
- Parameters:
y
- an observationmu
- the distribution mean, μnFactors
- the number of factors- Returns:
- the dispersion
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AIC
public double AIC(Vector y, Vector mu, Vector weight, double prelogLike, double deviance, int nFactors)
Description copied from interface:GLMExponentialDistribution
AIC = 2 * #param - 2 * log-likelihood- Specified by:
AIC
in interfaceGLMExponentialDistribution
- Parameters:
y
- an observationmu
- the distribution mean, μweight
- the weights assigned to the observationsprelogLike
- sum of (yi * θi - b(θi))deviance
- the deviancenFactors
- the number of factors- Returns:
- the AIC the Akaike information criterion
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