| Title: | Classic Gamma Regression: Joint Modeling of Mean and Shape Parameters |
|---|---|
| Description: | Performs Gamma regression, where both mean and shape parameters follows lineal regression structures. |
| Authors: | Martha Corrales and Edilberto Cepeda-Cuervo, with the colaboration of Margarita Marin, Maria Fernanda Zarate, Ricardo Duplat and Campo Elias Pardo. |
| Maintainer: | Martha Corrales <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 3.0.1 |
| Built: | 2024-12-09 06:31:13 UTC |
| Source: | CRAN |
Classic gamma regression package
| Package: | Gammareg |
| Type: | Package |
| Version: | 1.1 |
| Date: | 2014-01-23 |
| License: | GPL-2 |
| LazyLoad: | yes |
Martha Corrales and Edilberto Cepeda-Cuervo with the colaboration of Maria Fernanda Zarate, Ricardo Duplat and Campo Elias Pardo.
Performs the Classic Gamma Regression for joint modeling of mean and shape parameters.
gammahetero1(formula1, formula2)gammahetero1(formula1, formula2)
formula1 |
object of class formula. It describes yi and xi for the mean equation of the gamma regression. |
formula2 |
object of class formula. It describes zi for the shape equation of the gamma regression. |
The classic gamma regression allow the joint modeling of mean and shape parameters of a gamma distributed variable, as is proposed in Cepeda (2001), using the Fisher Scoring algorithm, with log link for the mean and log link for the shape.
object of class Gammareg with the following:
X |
object of class matrix, with the variables for modelling the mean. |
Z |
object of class matrix, with the variables for modelling the shape. |
beta |
object of class matrix with the estimated coefficients of beta. |
gamma |
object of class matrix with the estimated coefficients of gamma. |
ICB |
object of class matrix with the estimated confidence intervals of beta. |
ICG |
object of class matrix with the estimated confidence intervals of gamma. |
CovarianceMatrixbeta |
object of class matrix with the estimated covariances of beta. |
CovarianceMatrixgamma |
object of class matrix with the estimated covariances of gamma. |
AIC |
the AIC criteria. |
iteration |
numbers of iterations to convergence. |
convergence |
value of convergence obtained. |
Martha Corrales [email protected] Edilberto Cepeda-Cuervo [email protected]
1. Cepeda-Cuervo, E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matemáticas. Universidade Federal do Río do Janeiro. //http://www.docentes.unal.edu.co/ecepedac/docs/MODELAGEM20DA20VARIABILIDADE.pdf. http://www.bdigital.unal.edu.co/9394/. 2. McCullagh, P. and Nelder, N.A. (1989). Generalized Linear Models. Second Edition. Chapman and Hall.
# Simulation Example X1 <- rep(1,500) X2 <- log(runif(500,0,30)) X3 <- log(runif(500,0,15)) X4 <- log(runif(500,10,20)) mui <- exp(-5 + 0.2*X2 - 0.03*X3) alphai <- exp(0.2 + 0.1*X2 + 0.3*X4) Y <- rgamma(500,shape=alphai,scale=mui/alphai) X <- cbind(X1,X2,X3) Z <- cbind(X1,X2,X4) formula.mean= Y~X2+X3 formula.shape= ~X2+X4 a=gammahetero1(formula.mean,formula.shape) a# Simulation Example X1 <- rep(1,500) X2 <- log(runif(500,0,30)) X3 <- log(runif(500,0,15)) X4 <- log(runif(500,10,20)) mui <- exp(-5 + 0.2*X2 - 0.03*X3) alphai <- exp(0.2 + 0.1*X2 + 0.3*X4) Y <- rgamma(500,shape=alphai,scale=mui/alphai) X <- cbind(X1,X2,X3) Z <- cbind(X1,X2,X4) formula.mean= Y~X2+X3 formula.shape= ~X2+X4 a=gammahetero1(formula.mean,formula.shape) a
Performs the Classic Gamma Regression for joint modeling of mean and shape parameters.
gammahetero2(formula1, formula2)gammahetero2(formula1, formula2)
formula1 |
object of class formula. It describes yi and xi for the mean equation of the gamma regression. |
formula2 |
object of class formula. It describes zi for the shape equation of the gamma regression. |
The classic gamma regression allow the joint modeling of mean and shape parameters of a gamma distributed variable, as is proposed in Cepeda (2001), using the Fisher Scoring algorithm, with log link for the mean and log link for the shape.
object of class Gammareg with the following:
X |
object of class matrix, with the variables for modelling the mean. |
Z |
object of class matrix, with the variables for modelling the shape. |
beta |
object of class matrix with the estimated coefficients of beta. |
gamma |
object of class matrix with the estimated coefficients of gamma. |
ICB |
object of class matrix with the estimated confidence intervals of beta. |
ICG |
object of class matrix with the estimated confidence intervals of gamma. |
CovarianceMatrixbeta |
object of class matrix with the estimated covariances of beta. |
CovarianceMatrixgamma |
object of class matrix with the estimated covariances of gamma. |
AIC |
the AIC criteria |
iteration |
numbers of iterations to convergence |
convergence |
value of convergence obtained |
Martha Corrales [email protected] Edilberto Cepeda-Cuervo [email protected],
1. Cepeda-Cuervo, E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matemáticas. Universidade Federal do Río do Janeiro. //http://www.docentes.unal.edu.co/ecepedac/docs/MODELAGEM20DA20VARIABILIDADE.pdf. http://www.bdigital.unal.edu.co/9394/. 2. McCullagh, P. and Nelder, N.A. (1989). Generalized Linear Models. Second Edition. Chapman and Hall.
# Simulation Example X1 <- rep(1,500) X2 <- runif(500,0,30) X3 <- runif(500,0,15) X4 <- runif(500,10,20) mui <- 15 + 2*X2 + 3*X3 alphai <- exp(0.2 + 0.1*X2 + 0.3*X4) Y <- rgamma(500,shape=alphai,scale=mui/alphai) X <- cbind(X1,X2,X3) Z <- cbind(X1,X2,X4) formula.mean= Y~X2+X3 formula.shape= ~X2+X4 a=gammahetero2(formula.mean,formula.shape) a# Simulation Example X1 <- rep(1,500) X2 <- runif(500,0,30) X3 <- runif(500,0,15) X4 <- runif(500,10,20) mui <- 15 + 2*X2 + 3*X3 alphai <- exp(0.2 + 0.1*X2 + 0.3*X4) Y <- rgamma(500,shape=alphai,scale=mui/alphai) X <- cbind(X1,X2,X3) Z <- cbind(X1,X2,X4) formula.mean= Y~X2+X3 formula.shape= ~X2+X4 a=gammahetero2(formula.mean,formula.shape) a
Function to do Classic Gamma Regression: joint mean and shape modeling
Gammareg(formula1,formula2,meanlink)Gammareg(formula1,formula2,meanlink)
formula1 |
object of class matrix, with the dependent variable. |
formula2 |
object of class matrix, with the variables for modelling the mean. |
meanlink |
links for the mean. The default links is the link log. The link identity is also allowed as admisible value. |
The classic gamma regression allow the joint modelling of mean and shape parameters of a gamma distributed variable, as is proposed in Cepeda (2001), using the Fisher Socring algorithm, with two differentes link for the mean: log and identity, and log link for the shape.
object of class bayesbetareg with:
coefficients |
object of class matrix with the estimated coefficients of beta and gamma. |
desvB |
object of class matrix with the estimated covariances of beta. |
desvG |
object of class matrix with the estimated covariances of gamma. |
interv |
object of class matrix with the estimated confidence intervals of beta and gamma. |
AIC |
the AIC criteria. |
iteration |
numbers of iterations to convergence. |
convergence |
value of convergence obtained. |
call |
Call. |
Martha Corrales [email protected] Edilberto Cepeda-Cuervo [email protected]
1. Cepeda-Cuervo, E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matemáticas. Universidade Federal do Río do Janeiro. //http://www.docentes.unal.edu.co/ecepedac/docs/MODELAGEM20DA20VARIABILIDADE.pdf. http://www.bdigital.unal.edu.co/9394/. 2. McCullagh, P. and Nelder, N.A. (1989). Generalized Linear Models. Second Edition. Chapman and Hall.
# num.killed <- c(7,59,115,149,178,229,5,43,76,4,57,83,6,57,84) size.sam <- c(1,2,3,3,3,3,rep(1,9))*100 insecticide <- c(4,5,8,10,15,20,2,5,10,2,5,10,2,5,10) insecticide.2 <- insecticide^2 synergist <- c(rep(0,6),rep(3.9,3),rep(19.5,3),rep(39,3)) par(mfrow=c(2,2)) plot(density(num.killed/size.sam),main="") boxplot(num.killed/size.sam) plot(insecticide,num.killed/size.sam) plot(synergist,num.killed/size.sam) mean.for <- (num.killed/size.sam) ~ insecticide + insecticide.2 dis.for <- ~ synergist + insecticide res=Gammareg(mean.for,dis.for,meanlink="ide") summary(glm((num.killed/size.sam) ~ insecticide + insecticide.2,family=Gamma("log"))) summary(res) # Simulation Example X1 <- rep(1,500) X2 <- runif(500,0,30) X3 <- runif(500,0,15) X4 <- runif(500,10,20) mui <- 15 + 2*X2 + 3*X3 alphai <- exp(0.2 + 0.1*X2 + 0.3*X4) Y <- rgamma(500,shape=alphai,scale=mui/alphai) X <- cbind(X1,X2,X3) Z <- cbind(X1,X2,X4) formula.mean= Y~X2+X3 formula.shape= ~X2+X4 a=Gammareg(formula.mean,formula.shape,meanlink="ide") summary(a)# num.killed <- c(7,59,115,149,178,229,5,43,76,4,57,83,6,57,84) size.sam <- c(1,2,3,3,3,3,rep(1,9))*100 insecticide <- c(4,5,8,10,15,20,2,5,10,2,5,10,2,5,10) insecticide.2 <- insecticide^2 synergist <- c(rep(0,6),rep(3.9,3),rep(19.5,3),rep(39,3)) par(mfrow=c(2,2)) plot(density(num.killed/size.sam),main="") boxplot(num.killed/size.sam) plot(insecticide,num.killed/size.sam) plot(synergist,num.killed/size.sam) mean.for <- (num.killed/size.sam) ~ insecticide + insecticide.2 dis.for <- ~ synergist + insecticide res=Gammareg(mean.for,dis.for,meanlink="ide") summary(glm((num.killed/size.sam) ~ insecticide + insecticide.2,family=Gamma("log"))) summary(res) # Simulation Example X1 <- rep(1,500) X2 <- runif(500,0,30) X3 <- runif(500,0,15) X4 <- runif(500,10,20) mui <- 15 + 2*X2 + 3*X3 alphai <- exp(0.2 + 0.1*X2 + 0.3*X4) Y <- rgamma(500,shape=alphai,scale=mui/alphai) X <- cbind(X1,X2,X3) Z <- cbind(X1,X2,X4) formula.mean= Y~X2+X3 formula.shape= ~X2+X4 a=Gammareg(formula.mean,formula.shape,meanlink="ide") summary(a)
Print the Classic Gamma Regression for joint modeling of mean and shape parameters.
## S3 method for class 'Gammareg' print(x,...)## S3 method for class 'Gammareg' print(x,...)
x |
object of class Gammareg |
... |
not used. |
print the Classic gamma regression
Martha Corrales [email protected] Edilberto Cepeda-Cuervo [email protected]
1. Cepeda-Cuervo, E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matemáticas. Universidade Federal do Río do Janeiro. //http://www.docentes.unal.edu.co/ecepedac/docs/MODELAGEM20DA20VARIABILIDADE.pdf. http://www.bdigital.unal.edu.co/9394/. 2. McCullagh, P. and Nelder, N.A. (1989). Generalized Linear Models. Second Edition. Chapman and Hall.
Print the summary Classic Gamma Regression for joint modelling of mean and shape parameters.
## S3 method for class 'summary.Gammareg' print(x, ...)## S3 method for class 'summary.Gammareg' print(x, ...)
x |
object of class Gammareg |
... |
not used. |
Print the summary Classic Gamma Regression for joint modelling of mean and shape parameters.
Martha Corrales [email protected] Edilberto Cepeda-Cuervo [email protected]
1. Cepeda-Cuervo E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matemáticas. Universidade Federal do Río do Janeiro. //http://www.docentes.unal.edu.co/ecepedac/docs/MODELAGEM20DA20VARIABILIDADE.pdf. http://www.bdigital.unal.edu.co/9394/. 2. McCullagh, P. and Nelder, N.A. (1989). Generalized Linear Models. Second Edition. Chapman and Hall.
Summarized the Classic gamma regression for joint modelling of mean and shape parameters.
## S3 method for class 'Gammareg' summary(object, ...)## S3 method for class 'Gammareg' summary(object, ...)
object |
an object of class Gammareg |
... |
not used. |
call |
Call |
coefficients |
Coefficients |
covB |
object of class matrix with the estimated covariances of beta. |
covG |
object of class matrix with the estimated covariances of gamma. |
AIC |
AIC |
iteration |
number of iterations |
convergence |
convergence obtained |
Martha Corrales [email protected] Edilberto Cepeda-Cuervo [email protected]
1. Cepeda-Cuervo, E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matemáticas. Universidade Federal do Río do Janeiro. //http://www.docentes.unal.edu.co/ecepedac/docs/MODELAGEM20DA20VARIABILIDADE.pdf. http://www.bdigital.unal.edu.co/9394/. 2. McCullagh, P. and Nelder, N.A. (1989). Generalized Linear Models. Second Edition. Chapman and Hall.