Bayesiangammareg {Bayesiangammareg}

Bayesian Gamma Regression: Joint Mean and Shape Modeling

Description

Function to do Bayesian Gamma Regression: Joint Mean and Shape Modeling

Usage

Bayesiangammareg(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump,
graph1, graph2, meanlink = "log")

Arguments

Y

object of class matrix, with the dependent variable.

X

object of class matrix, with the variables for modeling the mean.

Z

object of class matrix, with the variables for modeling the shape.

nsim

a number that indicate the number of iterations.

bpri

a vector with the initial values of beta.

Bpri

a matrix with the initial values of the variance of beta.

gpri

a vector with the initial values of gamma.

Gpri

a matrix with the initial values of the variance of gamma.

burn

a proportion that indicate the number of iterations to be burn at the beginning of the chain.

jump

a number that indicate the distance between samples of the autocorrelated the chain, to be excluded from the final chain.

graph1

if it is TRUE present the graph of the chains without jump and burn.

graph2

if it is TRUE present the graph of the chains with jump and burn.

meanlink

represent the link function, logarithm or identity.

Details

The Bayesian Gamma regression allows the joint modeling of the mean and the shape of a gamma distributed variable, using a Bayesian estimation algorithm proposed by Cepeda-Cuervo (2001).

Value

object of class bayesiangammareg with:

coefficients

object of class matrix with the estimated coefficients of beta and gamma.

desv

object of class matrix with the estimated desviations of beta and gamma.

interv

object of class matrix with the estimated confidence intervals of beta and gamma.

fitted.values

object of class matrix with the fitted values of y.

residuals

object of class matrix with the residuals of the regression.

beta.mcmc

object of class matrix with the complete chains for beta.

gamma.mcmc

object of class matrix with the complete chains for gamma.

beta.mcmc.short

object of class matrix with the chains for beta after the burned process.

gamma.mcmc.short

object of class matrix with the chains for gamma after the burned process.

call

Call.

Author(s)

Arturo Camargo Lozano [e-mail], Edilberto Cepeda-Cuervo [e-mail]

References

1. Cepeda-Cuervo E. (2001) Modelagem da variabilidade em modelos lineares generalizados. Ph.D. tesis. Instituto de Matematicas. Universidade Federal do Rio do Janeiro. 2. Cepeda-Cuervo E. and Gamerman D. (2005). Bayesian Methodology for modeling parameters in the two-parameter exponential family. Estadistica 57, 93 105.

Examples

X1 <- rep(1,50)
X2 <- runif(50,0,30)
X3 <- runif(50,0,20)
X4 <- runif(50,10,20)
mui <- 15 + 3*X2 + 2*X3
alphai <- exp(3 + 0.15*X2 + 0.15*X4)
Y <- rgamma(50,shape=alphai,scale=mui/alphai)
X <- cbind(X1,X2,X3)
Z <- cbind(X1,X2,X4)
bpri <- c(1,1,1)
Bpri <- diag(10^(3),nrow=ncol(X),ncol=ncol(X))
gpri <- c(0,0,0)
Gpri <- diag(10^(3),nrow=ncol(Z),ncol=ncol(Z))
burn <- 0
jump <- 1
nsim <- 300
graph1=FALSE
graph2=FALSE
Bayesiangammareg(Y,X,Z,nsim,bpri,Bpri,gpri,Gpri,burn,jump,graph1,graph2,"ide")