| Title: | Bayesian Gamma Regression: Joint Mean and Shape Modeling |
|---|---|
| Description: | Adjust the Gamma regression models from a Bayesian perspective described by Cepeda and Urdinola (2012) <doi:10.1080/03610918.2011.600500>, modeling the parameters of mean and shape and using different link functions for the parameter associated to the mean. And calculates different adjustment statistics such as the Akaike information criterion and Bayesian information criterion. |
| Authors: | Arturo Camargo Lozano [aut, cre], Edilberto Cepeda Cuervo [aut] |
| Maintainer: | Arturo Camargo Lozano <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1.0 |
| Built: | 2025-02-19 03:58:26 UTC |
| Source: | https://github.com/cran/Bayesiangammareg |
Function to do Bayesian Gamma Regression: Joint Mean and Shape Modeling
Bayesiangammareg(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump, graph1, graph2, meanlink = "log")Bayesiangammareg(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump, graph1, graph2, meanlink = "log")
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. |
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).
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. |
Arturo Camargo Lozano [email protected], Edilberto Cepeda-Cuervo [email protected]
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.
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")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")
Performs the comparison criterias for the Bayesian Gamma regression
criteria(X, gammaresiduals)criteria(X, gammaresiduals)
X |
object of class matrix, with the independent variable for the mean. |
gammaresiduals |
object of class bayesiangammareg, with the residuals of the Bayesian Gamma regression, that can be calculated by the function gammaresiduals |
This function calculate the residuals of a Bayesian Gamma regression.
deviance |
the deviance criteria |
AIC |
the AIC criteria |
BIC |
the BIC criteria |
Arturo Camargo Lozano [email protected], Edilberto Cepeda-Cuervo [email protected]
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. 3. Espinheira, P. L., Ferrari, S. L., and Cribari-Neto, F. On beta regression residuals. Journal of Applied Statistics 4. Cepeda-Cuervo E., Corrales, M., Cifuentes, M. V., and Zarate, H. (2016). On Gamma Regression Residuals.
Function to do Bayesian Gamma Regression link Identity: Joint Mean and Shape modeling with Identity link for Mean.
GammaIdentity(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump, graph1, graph2)GammaIdentity(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump, graph1, graph2)
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. |
object of class bayesiangammareg 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 |
residuals |
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 |
Arturo Camargo Lozano [email protected], Edilberto Cepeda-Cuervo [email protected]
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. 3. Cepeda Cuervo E. and Gamerman D. (2001). Bayesian Modeling of Variance Heterogeneity in Normal Regression Models. Brazilian Journal of Probability and Statistics. 14, 207-221.
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")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")
Function to do Bayesian Gamma Regression: Joint Mean and Shape modeling with Log link for Mean.
GammaLog(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump, graph1, graph2)GammaLog(Y, X, Z, nsim, bpri, Bpri, gpri, Gpri, burn, jump, graph1, graph2)
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 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. |
object of class bayesiangammareg 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 |
residuals |
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 |
Arturo Camargo Lozano [email protected], Edilberto Cepeda-Cuervo [email protected]
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. 3. Cepeda Cuervo E. and Gamerman D. (2001). Bayesian Modeling of Variance Heterogeneity in Normal Regression Models. Brazilian Journal of Probability and Statistics. 14, 207-221.
X1 <- rep(1,50) X2 <- runif(50,0,30) X3 <- runif(50,0,20) X4 <- runif(50,10,20) mui<-exp(1 + 0.14*X2 + 0.05*X3) alphai<-exp(0.1 + 0.01*X2 + 0.03*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,"log")X1 <- rep(1,50) X2 <- runif(50,0,30) X3 <- runif(50,0,20) X4 <- runif(50,10,20) mui<-exp(1 + 0.14*X2 + 0.05*X3) alphai<-exp(0.1 + 0.01*X2 + 0.03*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,"log")
This function calculates the Gamma regression residuals
gammaresiduals(Y, X, model)gammaresiduals(Y, X, model)
Y |
object of class matrix, with the dependent variable. |
X |
object of class matrix, with the independent variable. |
model |
object of class Bayesiangammareg. |
rabs |
Pearson absolute residuals |
rp |
Pearson residuals |
rd |
deviance residuals |
rast |
Asteric residuals |
Arturo Camargo Lozano [email protected], Edilberto Cepeda Cuervo [email protected]
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. 3. Cepeda Cuervo E., Corrales, M., Cifuentes, M. V., and Zarate, H. (2016). On Gamma Regression Residuals.
Print the Bayesian Gamma Regression for Joint modeling of Mean and Shape
## S3 method for class 'Bayesiangammareg' print(x,...)## S3 method for class 'Bayesiangammareg' print(x,...)
x |
object of class Bayesiangammareg |
... |
not used. |
print the Bayesian Gamma regression
Arturo Camargo Lozano [email protected], Edilberto Cepeda Cuervo [email protected]
1. Cepeda-Cuervo E. (2001) Modelagem da variabilidade em modelos lineares generalizados. Ph.D. tesis. Instituto de Matematicas. Universidade Federal do Rio do Janeiro.
Print the summary Bayesian Gamma regression for Joint modeling of Mean and Shape parameters
## S3 method for class 'summary.Bayesiangammareg' print(x, ...)## S3 method for class 'summary.Bayesiangammareg' print(x, ...)
x |
object of class Bayesiangammareg |
... |
not used. |
Print the summary Bayesian Gamma Regression for Joint modeling of Mean and Shape parameters
Arturo Camargo [email protected], Edilberto Cepeda-Cuervo [email protected]
1. Cepeda-Cuervo E. (2001) Modelagem da variabilidade em modelos lineares generalizados. Ph.D. tesis. Instituto de Matematicas. Universidade Federal do Rio do Janeiro.
Summarized the Bayesian Gamma Regression for joint modeling of mean and variance
## S3 method for class 'Bayesiangammareg' summary(object, ...)## S3 method for class 'Bayesiangammareg' summary(object, ...)
object |
an object of class Bayesiangammareg |
... |
not used. |
call |
Call |
coefficients |
Coefficients |
deviance |
deviance |
AIC |
AIC |
BIC |
BIC |
Brayan Arturo Camargo [email protected], Edilberto Cepeda Cuervo [email protected]
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. 3. Cepeda Cuervo E. and Gamerman D. (2001). Bayesian Modeling of Variance Heterogeneity in Normal Regression Models. Brazilian Journal of Probability and Statistics. 14, 207-221.