| Type: | Package |
| Title: | Bayesian t Regression for Modeling Mean and Scale Parameters |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Version: | 1.0.1 |
| Date: | 2022-01-18 |
| Author: | Margarita Marin and Edilberto Cepeda-Cuervo. |
| Maintainer: | Margarita Marin <mmarinj@unal.edu.co> |
| Depends: | R (≥ 4.1.0) |
| Imports: | MASS (≥ 7.3), Matrix (≥ 1.2), mvtnorm (≥ 1.1) |
| Description: | Performs Bayesian t Regression where mean and scale parameters are modeling by lineal regression structures, and the degrees of freedom parameters are estimated. |
| Encoding: | UTF-8 |
| Packaged: | 2023-12-14 15:57:19 UTC; hornik |
| NeedsCompilation: | no |
| Repository: | CRAN |
| Date/Publication: | 2023-12-14 16:06:20 UTC |
Function to do Bayesian t Regression: joint mean and variance modeling and estimation of the degrees of freedom
Description
Bayesian t regression package
Details
| Package: | Bayesiantreg |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2020-05-31 |
| License: | GPL-2 |
| LazyLoad: | yes |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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 mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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)
Bayesian t regression
Description
Function to do Bayesian t Regression: joint mean and variance modeling and estimation of the degrees of freedom
Usage
BayesiantregEst(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. |
AIC |
AIC of the model. |
BIC |
BIC of the model. |
DIC |
BIC of the model. |
PseudoDeviance |
a Pseudo Deviance criteria of the model as is proposed in Marin and Cepeda (_). |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
Examples
#library(heavy)
#data(ereturns)
#y <- ereturns[,3]
#x <- cbind(rep(1,nrow(ereturns)),ereturns[,4])
#z <- x
## A priori para Beta
#Bpri <- diag(rep(100,2))
#bpri <- rep(0,2)
## A priori para Gamma
#Gpri <- diag(rep(10,2))
#gpri <- rep(0,2)
##otros parametros
#glpri <- 7
#propuesta <- "unif2"
#apriori <- "unif"
#type <- "D"
#lambda <- 0.1
#p <- 10
#Maxi <- 100
#nsim <- 100
#burn <- 0.1
#jump <- 2
#bini=bpri
#gini=gpri
#glini=glpri
#reg1 <- 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 = T, graph2 = T,
# graph3 = T)
#summary(reg1)
criteria for comparison the bayesian t regression models
Description
Performs the comparison criterias for the Bayesian t Regression
Usage
criteria(object,...)
Arguments
object |
object of class "Bayesiantreg" |
... |
not used. |
Details
This function allows to extract the information criteria from the model AIC, BIC, DIC and pseudo-deviance.
Value
loglik |
the logaritmic of the liklihood of the model |
AIC |
the AiC criteria |
BIC |
the BIC criteria |
DIC |
the DIC criteria |
PseudoDeviance |
the pseudo deviance criteria of the model as is proposed in Marin and Cepeda (_). |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co,
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
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
density of the Jeffrey's distribution
Description
calculates the density of the Jeffrey's distribution
Usage
dJ2(gl.ini, p)
Arguments
gl.ini |
a vector with the number to evaluate in the density. |
p |
a number indicating the parameter value for the Jeffrey's prior an the Jeffrey's proposal |
Details
Calculates the density of the Jeffrey's distribution
Value
J1 |
the value of the density |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
Loglikelihood for every point of the t model
Description
Calculate the loglikelihood for every point of the t model
Usage
devero(y, mu, sigma2, grados)
Arguments
y |
object of class matrix, with the dependent variables. |
mu |
object of class matrix, with the mean of the model. |
sigma2 |
object of class matrix, with the variace of the model. |
grados |
a vector with the degrees of freedom of the model. |
Details
Calculate the loglikelihood for the t model as proposed by Marin and Cepeda (_).
Value
l |
a value with the loglikelihood for the t model |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
Posterior value of beta
Description
Calculate a value for posterior density for beta parameter
Usage
dpostb(y, x, z, betas, gammas, gl, bpri,Bpri)
Arguments
y |
object of class matrix, with the dependen variables. |
x |
object of class matrix, with the variables for modelling the mean. |
z |
object of class matrix, with the variables for modelling the variance. |
betas |
a vector with the proposal beta parameters. |
gammas |
a vector with the proposal gamma parameters. |
gl |
a vector with the proposal degreees of freedom parameters. |
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. |
Details
Generate the posterior density for the beta proposed by Marin and Cepeda (_).
Value
value |
a value with the posterior denity for beta |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
Posterior density of gamma
Description
Propose a value for posterior density of the gamma parameter
Usage
dpostg(y, x, z, betas, gammas, gl, gpri, Gpri)
Arguments
y |
object of class matrix, with the dependent variables. |
x |
object of class matrix, with the variables for modelling the mean. |
z |
object of class matrix, with the variables for modelling the variance. |
betas |
a vector with the proposal beta parameters. |
gammas |
a vector with the proposal gamma parameters. |
gl |
a vector with the proposal degrees of freedom parameter. |
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. |
Details
Generate the posterior density for the gamma proposed by Marin and Cepeda (_).
Value
value |
a value with the posterior denity for gamma |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
the probability of a gamma parameter from the probability density funcion defined by old parameters.
Description
evaluate the probability of a gamma parameter from the probability density function defined by old parameters.
Usage
gammakernel(y, x, z, betas.ini, gammas.now, gammas.old, gl.ini, gpri, Gpri)
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 variance |
betas.ini |
a vector with the beta parameters that define the old p.d.f |
gammas.now |
a vector with the gamma parameters - new parameters - to evaluate in the old p.d.f |
gammas.old |
a vector with the gamma parameters that define the old p.d.f |
gl.ini |
a vector with the degrees of freedom parameters that define the old p.d.f |
gpri |
a vector with the initial values of gamma |
Gpri |
a matrix with the initial values of the variance of gamma |
Details
Evaluate the probability of a gamma parameter from the probability density function defined by old parameters, according with the model proposed by Marin and Cepeda-Cuervo (_).
Value
value |
a vector with the probability for the gamma parameter from the probability density function defined by old parameters. |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
A proposal for gamma parameters
Description
Propose a value for the gamma parameters
Usage
gammaproposal(y, x, z, betas.ini, gammas.ini, gl.ini, gpri, Gpri)
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 variance |
betas.ini |
a vector with the previous proposal beta parameters |
gammas.ini |
a vector with the previous proposal gamma parameters |
gl.ini |
a vector with the previous proposal degrees of freedom parameter |
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. |
Details
Generate a proposal for the gamma parameters according to the model proposed by Marin and Cepeda-Cuervo (_).
Value
gammas.pro |
a number with the proposal for the gamma parameters. |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
Posterior value of the degrees of freedom
Description
Calculate a value for posterior density of the degrees of freedom parameter
Usage
glpost(y, x, z, betas.ini, gammas.ini, gl.ini, Maxi, lambda, p, prior, type)
Arguments
y |
object of class matrix, with the dependent variables. |
x |
object of class matrix, with the variables for modelling the mean. |
z |
object of class matrix, with the variables for modelling the variance. |
betas.ini |
a vector with the proposal beta parameters. |
gammas.ini |
a vector with the proposal gamma parameters. |
gl.ini |
a vector with the proposal degrees of freedom parameter. |
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 |
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. |
prior |
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. |
Details
Generate the posterior density for the degrees of freedom proposed by Marin and Cepeda (_).
Value
value |
a value with the posterior denity for the degrees of freedom |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
A proposal for degrees of freedom parameter
Description
Propose a value for the degrees of freedom parameter
Usage
glproposal(gl.ini, lambda, p, Maxi, matriz, propuesta, type)
Arguments
gl.ini |
a vector with the previous proposal degrees of freedom parameter |
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. |
Maxi |
a number indicating the maximum value for the uniform prior an the uniforme proposal. |
matriz |
a matrix generate by the function tabla of the bayesiantreg package. |
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 (_). |
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. |
Details
Generate a proposal for the gamma parameter according to the model proposed by Marin and Cepeda-Cuervo (_).
Value
gl.pro |
a number with the proposal for the degrees of freedom parameter. |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
the probability of a beta parameter from the probability density funcion defined by old parameters
Description
evaluate the probability of a beta parameter from the probability density function defined by old parameters
Usage
mukernel(y, x, z, betas.now, betas.old, gammas.ini, gl.ini, bpri, Bpri)
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 variance |
betas.now |
a vector with the beta parameters - new parameters - to evaluate in the old p.d.f |
betas.old |
a vector with the beta parameters that define the old p.d.f |
gammas.ini |
a vector with the gammas parameters that define the old p.d.f |
gl.ini |
a vector with the degrees of freedom parameter that define the old p.d.f |
bpri |
a vector with the initial values of beta |
Bpri |
a matrix with the initial values of the variance of beta |
Details
Evaluate the probability of a beta parameter from the probability density function defined by old parameters, according with the model proposed by Cepeda(2001) and Cepeda and Gamerman(2005).
Value
value |
a matrix with the probability for the beta parameter from the probability density function defined by old parameters |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
A proposal for beta parameter
Description
Propose a value for the beta parameter
Usage
muproposal(y, x, z, betas.ini, gammas.ini, gl.ini, bpri, Bpri)
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 variance |
betas.ini |
a vector with the previous proposal beta parameters |
gammas.ini |
a vector with the previous proposal gamma parameters |
gl.ini |
a vector with the previous proposal degrees of freedom parameter |
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. |
Details
Generate a proposal for the beta parameters according to the model proposed by Marin and Cepeda-Cuervo (_).
Value
betas.pro |
a number with the proposal for the beta parameters. |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
density of the Jeffrey's distribution
Description
calculates the probability of the Jeffrey's distribution
Usage
pJ2(gl.ini, p)
Arguments
gl.ini |
a vector with the number to evaluate in the density. |
p |
a number indicating the parameter value for the Jeffrey's prior an the Jeffrey's proposal |
Details
Calculates the probability of the Jeffrey's distribution
Value
J1I |
the value of the probability |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
print the summary of the Bayesian t regression
Description
Print the summary BBayesian t Regression: joint mean and variance modeling and estimation of the degrees of freedom
Usage
## S3 method for class 'summary.Bayesiantreg'
print(x, ...)
Arguments
x |
object of class Bayesiantreg |
... |
not used. |
Value
Print the summary Bayesian t Regression: joint mean and variance modeling and estimation of the degrees of freedom
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
random number from the Jeffrey's distribution
Description
generates random numbers from the Jeffrey's distribution
Usage
rJ2(n, matriz, min, max)
Arguments
n |
a number that indicates the number of random values that will by generate from the Jeffrey's distribution. |
matriz |
a matrix generate by the function tabla of the bayesiantreg package. |
min |
a number indicatein the minimum number that can be generated from the Jeffrey's distribution. |
max |
a number indicatein the maximum number that can be generated from the Jeffrey's distribution. |
Details
generates random numbers from the Jeffrey's distribution
Value
grados |
the random number |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
summary of the Bayesian t regression
Description
Summarized the Bayesian Bayesian t Regression: joint mean and variance modeling and estimation of the degrees of freedom
Usage
## S3 method for class 'Bayesiantreg'
summary(object, ...)
Arguments
object |
an object of class Bayesiantreg |
... |
not used. |
Value
call |
Call |
coefficients |
Coefficients. |
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 (_). |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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
probabilities and numbers from the Jeffrey's distribution
Description
generates a table with diferente probabilities and associated numbers from the Jeffrey's distribution
Usage
tabla(min, max, p)
Arguments
min |
a number indicatein the minimum number that can be generated from the Jeffrey's distribution. |
max |
a number indicatein the maximum number that can be generated from the Jeffrey's distribution. |
p |
a number indicating the parameter value for the Jeffrey's prior an the Jeffrey's proposal. |
Details
generates a table with diferente probabilities and associated numbers from the Jeffrey's distribution
Value
matriz |
a matrix with the generated probabilities and associated numbers from the Jeffrey's distribution |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
Loglikelihood for the t model
Description
Calculate the loglikelihood for the t model
Usage
vero(y, mu, sigma2, grados)
Arguments
y |
object of class matrix, with the dependent variables. |
mu |
object of class matrix, with the mean of the model. |
sigma2 |
object of class matrix, with the variace of the model. |
grados |
a vector with the degrees of freedom of the model. |
Details
Calculate the loglikelihood for the t model as proposed by Marin and Cepeda (_).
Value
l |
a value with the loglikelihood for the t model |
Author(s)
Margarita Marin mmarinj@unal.edu.co, Edilberto Cepeda-Cuervo ecepedac@unal.edu.co
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
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