Bayesiantreg {Bayesiantreg}

Bayesiantreg

Description

Function to do Bayesian t Regression: joint mean and variance modeling and estimation of the degrees of freedom

Usage

Bayesiantreg(y, x, z, nsim, bini, bpri, Bpri, gini, gpri,Gpri, glini, glpri, 
           type, apriori, propuesta, Maxi=NULL,
           lambda = NULL, p = NULL, burn, jump, graph1 = TRUE, graph2 = TRUE,
           graph3 = TRUE)

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.

bini

a vector with the initial values of beta.

bpri

a vector with the values of the mean of the prior of beta.

Bpri

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

gini

a vector with the initial values of gamma.

gpri

a vector with the values of the mean of the prior of gamma.

Gpri

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

glini

a vector with the initial value of the degrees of freedom.

glpri

a vector with the value of the the prior of the degrees of freedom.

type

a vector that can take the value "D" if the prior for the degrees of freedom considered as discrete or "C" if it is continuous.

apriori

when type is "D", it is a vector that can take the values of "poi" for a Poisson prior or "unif" for a uniform prior. When type is "C", it is a vector that can take the values of "exp" for the exponential prior, "unif" for the uniform prior or "J2" for the Jeffrey's prior.

propuesta

when type is "D", it is a vector that can take the values of "poi" for a Poisson proposal, "unif" for a uniform proposal or by default the proposal made by Marin and Cepeda (_). When type is "C", it is a vector that can take the values of "exp" for the exponential proposal, "unif" for the uniform proposal, "J2" for the Jeffrey's proposal or by default the proposal made by Marin and Cepeda (_).

Maxi

a number indicating the maximum value for the uniform prior an the uniforme proposal.

lambda

a number indicating the mean parameter value for the Poisson prior an the Poisson proposal.

p

a number indicating the parameter value for the Jeffrey's prior an the Jeffrey's proposal.

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.

graph3

if it is TRUE present the graph of the standardized residuals, the the standardized residuals against the lineal predictor, the pseudo deviance residuals and the pseudo deviance residuals against the lineal predictor.

Details

The bayesian t regression allows the joint modelling of mean and variance and the estimation of the degrees of freedom of a t distributed variable, as is proposed in Marin and Cepeda (_), with identical link for the mean and logarithmic for the variance, and differents discrete and continuous aproach for the degrees of freedom.

Value

object of class bayesbetareg with:

coefficients

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

interv

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

fitted.values

object of class matrix with the fitted values of y.

residuals

object of class matrix with the residuals of the regression.

residualsstd

object of class matrix with the standardized residuals of the regression.

residualsdev

object of class matrix with the pseudo deviance residuals 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.

gl.mcmc

object of class matrix with the complete chains for the degrees of freedom.

beta.mcmc.burn

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

gamma.mcmc.burn

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

gl.mcmc.burn

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

loglik

the logaritmic of the liklihood of the model.

AIC

AIC of the model.

BIC

BIC of the model.

DIC

BIC of the model.

PseudoDeviance

Pseudo deviance criteria of the model as is proposed by Marin and Cepeda (_).

arb

acceptance percentage for beta.

arg

acceptance percentage for gamma.

argl

acceptance percentage for the degrees of freedom.

call

Call.

Author(s)

Margarita Marin [e-mail], Edilberto Cepeda-Cuervo [e-mail]

2. Cepeda-Cuervo E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matematicas. Universidade Federal do Rio do Janeiro.

3. Cepeda C., E. and Gamerman D. (2001). Bayesian Modeling of Variance Heterogeneity in Normal Regression Models. Brazilian Journal of Probability and Statistics. 14, 207-221

References

1. Marin and Cepeda-Cuervo (_). A Bayesian regression model for the non-standardized t distribution with location, scale and degrees of freedom parameters. Unpublished

Examples

n <- 10
X1 <- runif(n,0,10)
X2 <- runif(n,5,10)
X3 <- runif(n,10,15)


y1 <- c(0.09, 1.68, -2.43, 0.23, 2.94, 1.50, 3.40, 2.22, 0.28, -0.17)

betas <- c(0,0,0,0)
gammas <- c(0,0,0)
gl <- 3

x <- cbind(rep(1,n),X1,X2,X3)
z <- cbind(rep(1,n),X2,X3)
y <- y1

Bpri <- diag(rep(100,4))
bpri <- rep(0,4)

Gpri <- diag(rep(10,3))
gpri <- rep(0,3)

glpri <- 7

propuesta <- "unif2"
apriori <- "unif"
tipo <- "D"

Maxi <- 100
nsim <- 50

bini=bpri
gini=gpri
glini=glpri

reg1 <- Bayesiantreg(y, x, z, nsim=nsim, bini, bpri, 
                     Bpri, gini, 
                     gpri,Gpri, glini, glpri, 
                     type=tipo, apriori=apriori, 
                     propuesta=propuesta, 
                     Maxi=Maxi,burn=0.3, jump=3, 
                    graph1 = TRUE, graph2 = TRUE, graph3 = TRUE)