Bayesiangammareg {Bayesiangammareg} R Documentation

## 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 bacamargol@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co

### 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")
```

[Package Bayesiangammareg version 0.1.0 Index]