Repository Mirror for your Cloud Server and Webhosting

Type:

Package

Title:

Negative Binomial and Beta Binomial Bayesian Regression Models

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Version:

1.0

Date:

2016-11-15

Author:

Edilberto Cepeda-Cuervo, Maria Victoria Cifuentes-Amado and Margarita Marin

Maintainer:

Edilberto Cepeda <ecepedac@unal.edu.co>

Depends:

R (≥ 3.1.1), mvtnorm, Matrix, boot

Description:

The Negative Binomial regression with mean and shape modeling and mean and variance modeling and Beta Binomial regression with mean and dispersion modeling.

NeedsCompilation:

Packaged:

2016-11-15 20:15:15 UTC; margarita

Repository:

CRAN

Date/Publication:

2016-11-17 08:27:30

NegBinBetaBinreg

Description

Function to estimate a Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Details

Package:	NegBinBetaBinreg
Type:	Package
Version:	1.0
Date:	2016-10-8
License:	GPL-2
LazyLoad:	yes

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

NegBinBetaBinreg

Description

Function to estimate a Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Usage

NegBinBetaBinreg(y,x,z,nsim,bpri,Bpri,
gpri,Gpri,burn,jump,bini,gini,model,m,ni,graph1,graph2)

Arguments

y

object of class matrix or vector, 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, variance or dispersion.

nsim

a number that indicate the number of iterations.

bpri

a vector with the prior values of beta.

Bpri

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

gpri

a vector with the prior values of gamma.

Gpri

a matrix with the prior 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.

bini

a vector with the initial values of beta.

gini

a vector with the initial values of gamma.

model

it indicates the model that will be used. By default, is the Beta Binomial model (BB), but it could also be the Negative Binomial with mean and shape (NB1) or the Negative Binomial with mean and variance (NB2).

m

Is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

ni

Is a vector of positive integer that In the Beta Binomial model indicates the number of trials to each individual. By default, is a vector of m

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 Negative Binomial regression allow the joint modelling of mean and shape or variance of a negative binomial distributed variable, as is proposed in Cepeda (2001), with exponential link for the mean and the shape or variance. The Bayesian Beta Binomial regression allow the joint modelling of mean and precision of a beta binomial distributed variable, as is proposed in Cepeda (2001), with logit link for the mean and exponential link for the precision.

Value

object of class NegBinBetaBinreg 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.

estresiduals

object of class matrix with the standardized 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.

aceptbeta

object of class integer with the acceptance rate for the beta values.

aceptgamma

object of class integer with the acceptance rate for the gamma values.

call

Call.

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

1. Cepeda C. E. (2001). Modelagem da variabilidade em modelos lineares generalizados. Unpublished Ph.D. tesis. Instituto de Matematicas. Universidade Federal do Rio 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. // 5.Cepeda-Cuervo, E. and Cifuentes-Amado, V. (2016) Double generalized beta-binomial and negative binomial regression. To appear.

Examples


rm(list=ls(all=TRUE))

Y<-c(6,6,9,13,23,25,32,53,54,5,5,11,17,19,2,8,13,14,20,47,
     48,60,81,6,17,67,0,0,2,7,11,12,0,0,5,5,5,11,17,3,4,22,
     30,36,0,1,5,7,8,16,27,25,10,11,20,33,0,1,5,5,5,5,5,7,7,11,15,5,6,6,7,14
)
y <- Y <- Y[1:68]

x0<-rep(1,times=68)
x2<-c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,
      1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
      1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
)
x3<-c(0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,
      0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,1,1,1,
      0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1
)
x<-cbind(x0,x2,x3)
z0<-rep(1,times=68)
z<-cbind(z0,x2)

Bpri=diag(rep(1,3))
bpri=rep(0,3)
Gpri=diag(rep(1,2))
gpri=rep(0,2)

Bini=diag(rep(1,3))
bini=c(3,-1,-0.5)
Gini=diag(rep(1,2))
gini=c(3,-1)

nsim = 300
burn <- 0.1
jump <- 5
model <- "NB1"
m <- 360
ni <- NULL
re<- NegBinBetaBinregEst (y,x,z,nsim,bpri,
	Bpri,gpri,Gpri,burn,jump,bini,gini,
	model,m,ni,graph1=FALSE,graph2=FALSE)
summary(re)

Negative Binomial and Beta Binomial regression

Description

Function to estimate a Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Usage

NegBinBetaBinregEst(y,x,z,nsim,bpri,Bpri,
gpri,Gpri,burn,jump,bini,gini,model,m,ni,graph1,graph2)

Arguments

y

object of class matrix or vector, 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, variance or dispersion.

nsim

a number that indicate the number of iterations.

bpri

a vector with the prior values of beta.

Bpri

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

gpri

a vector with the prior values of gamma.

Gpri

a matrix with the prior 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.

bini

a vector with the initial values of beta.

gini

a vector with the initial values of gamma.

model

m

Is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

ni

Is a vector of positive integer that In the Beta Binomial model indicates the number of trials to each individual. By default, is a vector of m

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

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 shape, variance or dispersion.

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 of the confidence intervals for beta

G

object of class matrix with the G values of the confidence intervals for gamma

yestimado

object of class matrix with the fitted values of y

residuales

object of class matrix with the residuals of the regression

residuales

object of class matrix with the standardized 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.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

aceptbeta

object of class matrix with the acceptance rate for the betas

aceptgamma

object of class matrix with the acceptance rate for the gammas

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

criteria for comparison the Bayesian Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Description

Performs the comparison criterias for the Bayesian Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Usage

criteria(objeto)

Arguments

objeto

object of class NegBinBetaBinreg

Details

This function calculate the information criteria for a Bayesian Negative Binomial regression with mean and shape modeling and mean and variance modeling and Beta Binomial regression with mean and dispersion modeling.

Value

AIC

the AiC criteria

BIC

the BIC criteria

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

Posterior value of beta

Description

Propose a value for posterior distribution of the beta parameter

Usage

dpostb(y,x,z,betas,gammas,bpri,Bpri,model,m)

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

a vector with the previous proposal beta parameters

gammas

a vector with the previous proposal gamma parameters

bpri

a vector with the initial values of beta

Bpri

a matrix with the initial values of the variance of beta

model

m

It is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

Details

Generate a proposal for the beta parameter according to the model proposed by Cepeda and Gamerman(2005).

Value

value

a matrix with the proposal for beta

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

Posterior value of gamma

Description

Propose a value for posterior distribution of the gamma parameter

Usage

dpostg(y,x,z,betas,gammas,gpri,Gpri,model,m)

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

a vector with the previous proposal beta parameters

gammas

a vector with the previous proposal gamma parameters

gpri

a vector with the initial values of gamma

Gpri

a matrix with the initial values of the variance of gamma

model

m

It is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

Details

Generate a proposal for the beta parameter according to the model proposed by Cepeda(2001) and Cepeda and Gamerman(2005).

Value

value

a integer with the value of the posterior density for gamma

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

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,gpri,Gpri,model,m,ni)

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 that define the old p.d.f

gammas.now

a vector with the gamma parameter - new parameters - to evaluate in the old p.d.f

gammas.old

a vector with the gamma 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

model

m

It is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

ni

It is a vector of positive integer that In the Beta Binomial model indicates the number of trials to each individual. By default, is a vector of m

Details

Evaluate the probability of a gamma 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 vector with the probability for the gamma parameter from the probability density function defined by old parameters

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

A proposal for gamma parameter

Description

Propose a value for the gamma parameter

Usage

gammaproposal(y, x, z, betas.ini,gammas.ini,gpri,Gpri,model,m,ni)

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

gpri

a vector with the initial values of gamma

Gpri

a matrix with the initial values of the variance of gamma

model

m

It is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

ni

It is a vector of positive integer that In the Beta Binomial model indicates the number of trials to each individual. By default, is a vector of m

Details

Generate a proposal for the gamma parameter according to the model proposed by Cepeda(2001) and Cepeda and Gamerman(2005).

Value

value

a number with the proposal for the gamma parameter

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

the probability of a beta parameter from the probability density function 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,bpri,Bpri,model,m,ni)

Arguments

y

object of class matrix or vector, 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, variance or dispersion.

betas.now

a vector with the beta parameter, new parameter, to evaluate in the old p.d.f

betas.old

a vector with the beta that define the old p.d.f

gammas.ini

a vector with the gamma that define the old p.d.f

bpri

a vector with the prior values of beta.

Bpri

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

model

m

It is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

ni

It is a vector of positive integer that In the Beta Binomial model indicates the number of trials to each individual. By default, is a vector of m

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)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

A proposal for beta parameter

Description

Propose a value for the beta parameter

Usage

muproposal(y, x, z, betas.ini,gammas.ini,bpri,Bpri,model,m,ni)

Arguments

y

object of class matrix or vector, 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, variance or dispersion.

betas.ini

a vector with the beta that define the old p.d.f

gammas.ini

a vector with the gamma that define the old p.d.f

bpri

a vector with the prior values of beta.

Bpri

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

model

m

It is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

ni

It is a vector of positive integer that In the Beta Binomial model indicates the number of trials to each individual. By default, is a vector of m

Details

Generate a proposal for the beta parameter according to the model proposed by Cepeda(2001) and Cepeda and Gamerman(2005).

Value

value

a matrix with the proposal for beta

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

print.NegBinBetaBinreg

Description

Print the Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Usage

## S3 method for class 'NegBinBetaBinreg'
print(x,...)

Arguments

x

object of class NegBinBetaBinreg

...

not used.

Value

print the Negative Binomial regression with mean and shape modeling and mean and variance modeling and Beta Binomial regression with mean and dispersion modeling

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

print the summary of the NegBinBetaBinreg

Description

Print the summary for a Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Usage

## S3 method for class 'summary.NegBinBetaBinreg'
print(x, ...)

Arguments

x

object of class NegBinBetaBinreg

...

not used.

Value

Print the summary for a Negative Binomial regression with mean and shape modeling and mean and variance modeling and Beta Binomial regression with mean and dispersion modeling

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

summary.NegBinBetaBinreg

Description

Print the Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Usage

## S3 method for class 'NegBinBetaBinreg'
summary(object, ...)

Arguments

object

an object of class NegBinBetaBinreg

...

not used.

Value

call

Call

coefficients

Coefficients

AIC

AIC

BIC

BIC

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co

References

Likelihood

Description

calculate the likelihood value for the Negative Binomial regression models with mean and shape (or variance) regression structures, and Beta Binomial regression with mean and dispersion regression structures.

Usage

veros(y,x,z,betas,gammas,model,m)

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

a vector with the previous proposal beta parameters

gammas

a vector with the previous proposal gamma parameters

model

m

It is positive integer that In the Beta Binomial model indicates the number of trials. By default, is the number of data

Details

calculate the likelihood value for the Negative Binomial regression with mean and shape modeling and mean and variance modeling and Beta Binomial regression with mean and dispersion modeling.

Value

value

a integer with the likelihood

Author(s)

Edilberto Cepeda-Cuervo ecepedac@unal.edu.co, Maria Victoria Cifuentes-Amado mvcifuentesa@unal.edu.co, Margarita Marin mmarinj@unal.edu.co