BayesianbetaregEst: Bayesian beta regression

In Bayesianbetareg: Bayesian Beta regression: joint mean and precision modeling

Description

Performs the Bayesian Beta Regression for joint modelling of mean and precision

Usage

BayesianbetaregEst(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump, graph1, graph2)

Arguments

Y	object of class matrix, with the dependent variable
X	object of class matrix, with the variables for modelling the mean
Z	object of class matrix, with the variables for modelling the precision
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

Details

The bayesian beta regression allow the joint modelling of mean and precision of a beta distributed variable, as is proposed in Cepeda (2001), with logit link for the mean and logarithmic for the precision.

Value

object of class bayesbetareg with the following:

Bestimado	object of class matrix with the estimated coefficients of beta
Gammaest	object of class matrix with the estimated coefficients of gamma
X	object of class matrix, with the variables for modelling the mean
Z	object of class matrix, with the variables for modelling the precision
DesvBeta	object of class matrix with the estimated desviations of beta
DesvGamma	object of class matrix with the estimated desviations of gamma
B	object of class matrix with the B values
G	object of class matrix with the G values
yestimado	object of class matrix with the fitted values of y
residuales	object of class matrix with the residuals of the regression
phi	object of class matrix with the precision terms of the regression
variance	object of class matrix with the variance terms 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.auto	object of class matrix with the chains for beta after the burned process
gamma.mcmc.auto	object of class matrix with the chains for gamma after the burned process

Author(s)

Daniel Jaimes [e-mail], Margarita Marin [e-mail], Javier Rojas [e-mail], Hugo Andres Gutierrez Rojas [e-mail], Martha Corrales [e-mail], Maria Fernanda Zarate [e-mail], Ricardo Duplat [e-mail], Luis Villaraga [e-mail], Edilberto Cepeda-Cuervo [e-mail]

References

1. Cepeda C. E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matem?ticas. Universidade Federal do R?o do Janeiro. //http://www.docentes.unal.edu.co/ecepedac/docs/MODELAGEM20DA20VARIABILIDADE.pdf. http://www.bdigital.unal.edu.co/9394/. 2.Cepeda, E. C. and Gamerman D. (2005). Bayesian Methodology for modeling parameters in the two-parameter exponential family. Estadistica 57, 93 105. // 3.Cepeda, E. and Garrido, L. (2011). Bayesian beta regression models: joint mean and precision modeling. Universidad Nacional // 4.Cepeda, E. and Migon, H. and Garrido, L. and Achcar, J. (2012) Generalized Linear models with random effects in the two parameter exponential family. Journal of Statistical Computation and Simulation. 1, 1 13.

Examples

# Modelation of the gini coeficient with multiples variables

library(betareg)
data(ReadingSkills)


Y <- as.matrix(ReadingSkills[,1])
n <- length(Y)
X1 <- as.matrix(ReadingSkills[,2])
for(i in 1:length(X1)){
  X1 <- replace(X1,X1=="yes",1)
  X1 <- replace(X1,X1=="no",0)
}
X0 <- rep(1, times=n)
X1 <- as.numeric(X1)
X2 <- as.matrix(ReadingSkills[,3])
X3 <- X1*X2
X <- cbind(X0,X1,X2,X3)
Z0 <-  X0 
Z <- cbind(X0,X1)

burn <- 0.3
jump <- 3
nsim <- 400

bpri <- c(0,0,0,0)
Bpri <- diag(100,nrow=ncol(X),ncol=ncol(X))
gpri <- c(0,0)
Gpri <- diag(10,nrow=ncol(Z),ncol=ncol(Z))

re<-Bayesianbetareg(Y,X,Z,nsim,bpri,Bpri,gpri,Gpri,0.3,3,graph1=FALSE,graph2=FALSE)
summary(re)

Example output

Loading required package: mvtnorm
Loading required package: betareg
 
            ################################################################
            ###                  Bayesian Beta Regression                ###
            ################################################################ 

 Call: 
Bayesianbetareg(Y = Y, X = X, Z = Z, nsim = nsim, bpri = bpri, 
    Bpri = Bpri, gpri = gpri, Gpri = Gpri, burn = 0.3, jump = 3, 
    graph1 = FALSE, graph2 = FALSE)

         Estimate Est.Error L.CredIntv U.CredIntv
beta.X0    2.0329    0.1649     1.7344      2.328
beta.X1   -1.6395    0.1772    -1.9858     -1.334
beta.      0.5332    0.1503     0.3332      0.840
beta.     -0.5921    0.1515    -0.9130     -0.378
gamma.X0   2.0438    0.1414     1.7368      2.215
gamma.X1   1.4817    0.4665     0.5980      2.147

 Deviance: 
[1] 211.8043

 AIC: 
[1] 219.8043

 BIC: 
[1] 226.9411

Bayesianbetareg documentation built on May 30, 2017, 2:35 a.m.