Gammareg {Gammareg}

Gammareg

Description

Function to do Classic Gamma Regression: joint mean and shape modeling

Usage

Gammareg(formula1,formula2,meanlink)

Arguments

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.

Details

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.

Value

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.

Author(s)

Martha Corrales [e-mail] Edilberto Cepeda-Cuervo [e-mail]

References

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 Unpublished Ph.D. tesis.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.

Examples

# 

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)