Poisson-Inverse_Gaussian Regression

Description

The function fits a mixed Poisson regression, in which the random parameter follows inverse_Gaussian distribution. As the method of estimation Expectation-maximization algorithm is used. In M-step the GLM is applied.

Usage

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pig.reg.glm(variable, regressors, lambda.start, delta.start, epsylon, n)

Arguments

variable

The count dependent variable in the regression

regressors

The independent variables in the regression. Could be numerical as well as factors.

lambda.start

The starting value of lambda parameter of Poisson distribution. Default to 1.

delta.start

The starting value of delta parameter of inverse?Gaussian distribution. Default to 1.

epsylon

Default to epsylon = 10^(-8)

n

The integer value for the Laguerre quadrature. Default to 100.

Details

This function provides estimated parameters of the model N|θ \sim Poisson(λ_i θ) where θ is a latent variable comes from inverse-gaussian distribution with one parameter γ. The pdf of inverse-Gaussian is of the form f_θ(θ)=\frac{δ}{2π}\exp(δ^2)θ^{-\frac{3}{2}} \exp(-\frac{δ^2}{2}(\frac{1}{θ}+θ)) . The parameter λ_i is determined by regressors X_1,...,X_k through log-link λ_i=\mathbf{x}_i'\mathbf{\boldsymbol β}.

Value

lambda

fitted values of parameter lambda

delta

the parameter of mixing inverse-Gaussian distribution

regression.coefficients

beta vector

n.iter

n

likelihood.values

values of log-likelihood

References

Ghitany, M. E., Karlis, D., Al-Mutairi, D. K., & Al-Awadhi, F. A. (2012). An EM algorithm for multivariate mixed Poisson regression models and its application. Applied Mathematical Sciences, 6(137), 6843-6856.

Examples

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library(MASS)	
index = which(quine$Days<11)
reg = quine[index, -which(names(quine)=="Days")]
poisig = pig.reg.glm(variable=quine$Days[index], regressors=reg)	
print(poisig)