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 doubleAIC(Vector y, Vector mu, Vector weight, double prelogLike, double deviance, int nFactors)AIC = 2 * #param - 2 * log-likelihooddoublecumulant(double theta)The cumulant function of the exponential distribution.doubledeviance(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.doubledispersion(Vector y, Vector mu, int nFactors)Different distribution models have different ways to compute dispersion, Φ.doubleoverdispersion(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.doubletheta(double mu)The canonical parameter of the distribution in terms of the mean μ.doublevariance(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:GLMExponentialDistributionThe variance function of the distribution in terms of the mean μ.- Specified by:
variancein 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:GLMExponentialDistributionThe canonical parameter of the distribution in terms of the mean μ.- Specified by:
thetain 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:GLMExponentialDistributionThe cumulant function of the exponential distribution.- Specified by:
cumulantin 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:GLMExponentialDistributionDeviance 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:
deviancein 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:GLMExponentialDistributionOver-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.29GLMGamma,GLMGaussian,GLMInverseGaussian, over-dispersion is the same as dispersion.- Specified by:
overdispersionin 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:GLMExponentialDistributionDifferent distribution models have different ways to compute dispersion, Φ. Note that in R's output, this is called "over-dispersion".- Specified by:
dispersionin 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:GLMExponentialDistributionAIC = 2 * #param - 2 * log-likelihood- Specified by:
AICin 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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