Small Area Estimation using Hierarchical Bayesian under Beta Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Beta Distribution. The range of data must be 0<y<1. The data proportion is supposed to be implemented with this function.

Usage

Beta(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 3,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

#Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,0,1)
x3=runif(m,0,1)
x4=runif(m,0,1)
b0=b1=b2=b3=b4=0.5
u=rnorm(m,0,1)
pi=rgamma(1,1,0.5)
Mu <- exp(b0+b1*x1+b2*x2+b3*x3+b4*x4+u)/(1+exp(b0+b1*x1+b2*x2+b3*x3+b4*x4+u))
A=Mu*pi
B=(1-Mu) * pi
y=rbeta(m,A,B)
y <- ifelse(y<1,y,0.99999999)
y <- ifelse(y>0,y,0.00000001)
MU=A/(A+B)
vardir=A*B/((A+B)^2*(A+B+1))
dataBeta = as.data.frame(cbind(y,x1,x2,x3,x4,vardir))
dataBetaNs=dataBeta
dataBetaNs$y[c(3,14,22,29,30)] <- NA
dataBetaNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2


## For data without any nonsampled area

vc = c(1,1,1)
c = c(0,0,0)
formula = y~x1+x2
dat = dataBeta[1:10,]


##Using parameter coef and var.coef
saeHBbeta<-Beta(formula,var.coef=vc,iter.update=10,coef=c,data=dat)

saeHBbeta$Est                                 #Small Area mean Estimates
saeHBbeta$refVar                              #Random effect variance
saeHBbeta$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBbeta$plot[[3]])  # is used to generate ACF Plot
#plot(saeHBbeta$plot[[3]])           # is used to generate Density and trace plot

##Do not use parameter coef and var.coef
saeHBbeta <- Beta(formula,data=dataBeta)

Small Area Estimation using Hierarchical Bayesian under Binomial Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Binomial Distribution using Logit normal model. The data is an accumulation from the Bernoulli process which there are exactly two mutually exclusive outcomes of a case.

Usage

Binomial(
  formula,
  n.samp,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Author(s)

Azka Ubaidillah [aut], Ika Yuni Wulansari [aut], Zaza Yuda Perwira [aut, cre], Jayanti Wulansari [aut, cre], Fauzan Rais Arfizain [aut,cre]

Examples

#Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,0,1)
b0=b1=b2=0.5
u=rnorm(m,0,1)
n.samp1=round(runif(m,10,30))
mu= exp(b0 + b1*x1+b2*x2+u)/(1+exp(b0 + b1*x1+b2*x2+u))
y=rbinom(m,n.samp1,mu)
vardir=n.samp1*mu*(1-mu)
dataBinomial=as.data.frame(cbind(y,x1,x2,n.samp=n.samp1,vardir))
dataBinomialNs = dataBinomial
dataBinomialNs$y[c(3,14,22,29,30)] <- NA
dataBinomialNs$vardir[c(3,14,22,29,30)] <- NA
dataBinomialNs$n.samp[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y~x1+x2


## For data without any nonsampled area
formula = y~x1+x2
n.s = "n.samp"
vc = c(1,1,1)
c = c(0,0,0)
dat = dataBinomial


## Using parameter coef and var.coef
saeHBBinomial<-Binomial(formula,n.samp=n.s,iter.update=10,coef=c,var.coef=vc,data =dat)

saeHBBinomial$Est                                 #Small Area mean Estimates
saeHBBinomial$refVar                              #Random effect variance
saeHBBinomial$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBBinomial$plot[[3]]) is used to generate ACF Plot
#plot(saeHBBinomial$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBBinomial <- Binomial(formula,n.samp ="n.samp",data=dataBinomial)



## For data with nonsampled area use dataBinomialNs

Small Area Estimation using Hierarchical Bayesian under Exponential Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Exponential Distribution. The range of data is y > 0)

Usage

Exponential(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

#Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,0,1)
b0=b1=b2=0.5
u=rnorm(m,0,1)
lambda= exp(b0 + b1*x1 + b2*x2+u)
mu=1/lambda
y=rexp(m,lambda)
vardir=1/lambda^2
hist(y)
dataExp=as.data.frame(cbind(y,x1,x2,vardir))
dataExpNs <- dataExp
dataExpNs$y[c(3,14,22,29,30)] <- NA
dataExpNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2


## For data without any nonsampled area

formula = y ~ x1+x2
v = c(1,1,1)
c = c(0,0,0)


## Using parameter coef and var.coef
saeHBExponential <- Exponential(formula,coef=c,var.coef=v,iter.update=10,data=dataExp)

saeHBExponential$Est                                 #Small Area mean Estimates
saeHBExponential$refVar                              #Random effect variance
saeHBExponential$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBExponential$plot[[3]]) is used to generate ACF Plot
#plot(saeHBExponential$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBExponential <- Exponential(formula,data=dataExp[1:10,])



## For data with nonsampled area use dataExpNs

Small Area Estimation using Hierarchical Bayesian under Double Exponential Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Double Exponential Distribution or Laplace Distribution. The range of data is (-\infty < y < \infty)

Usage

ExponentialDouble(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
library(nimble)
m=30
x1=runif(m,10,20)
x2=runif(m,1,10)
b0=b1=b2=0.5
u=rnorm(m,0,1)
tau=rgamma(m,1,1)
sd=1/sqrt(tau)
mu=b0 + b1*x1+b2*x2+u
y=rdexp(m,mu,sd)
vardir=sqrt(2)*sd^2
dataExpDouble=as.data.frame(cbind(y,x1,x2,vardir))
dataExpDoubleNs=dataExpDouble
dataExpDoubleNs$y[c(3,14,22,29,30)] <- NA
dataExpDoubleNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2


## For data without any nonsampled area
formula = y ~ x1+x2
vc = c(1,1,1)
c = c(0,0,0)
dat = dataExpDouble[1:10,]


## Using parameter coef and var.coef

saeHBExpDouble<-ExponentialDouble(formula,coef=c,var.coef=vc,iter.update=10,data=dat)

saeHBExpDouble$Est                                 #Small Area mean Estimates
saeHBExpDouble$refVar                              #Random effect variance
saeHBExpDouble$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBExpDouble$plot[[3]]) is used to generate ACF Plot
#plot(saeHBExpDouble$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBExpDouble <- ExponentialDouble(formula,data=dataExpDouble)



## For data with nonsampled area use dataExpDoubleNs

Small Area Estimation using Hierarchical Bayesian under Gamma Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Gamma Distribution. The range of data is ( y > 0)

Usage

Gamma(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,0,1)
b0=b1=b2=0.5
u=rnorm(m,0,1)
phi=rgamma(m,0.5,0.5)
vardir=1/phi
mu= exp(b0 + b1*x1+b2*x2+u)
A=mu^2*phi
B=mu*phi
y=rgamma(m,A,B)

dataGamma=as.data.frame(cbind(y,x1,x2,vardir))
dataGammaNs <- dataGamma
dataGammaNs$y[c(3,14,22,29,30)] <- NA
dataGammaNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2


## For data without any nonsampled area
#formula = y ~ x1 +x2
v = c(1,1,1)
c = c(0,0,0)


## Using parameter coef and var.coef
saeHBGamma <- Gamma(formula,coef=c,var.coef=v,iter.update=10,data =dataGamma)

saeHBGamma$Est                                 #Small Area mean Estimates
saeHBGamma$refVar                              #Random effect variance
saeHBGamma$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBGamma$plot[[3]]) is used to generate ACF Plot
#plot(saeHBGamma$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBGamma <- Gamma(formula, data =  dataGamma)#'


## For data with nonsampled area use dataGammaNs

Small Area Estimation using Hierarchical Bayesian under Logistic Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Logistic Distribution

Usage

Logistic(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,1,2)
x3=runif(m,2,3)
b0=b1=b2=b3=0.5
u=rnorm(m,0,1)
Mu=b0 + b1*x1+b2*x2+b3*x3+u
sig=sqrt(1/rgamma(m,1,1))
y=rlogis(m,Mu,sig)
vardir=1/3*pi*sig^2
dataLogistic=as.data.frame(cbind(y,x1,x2,x3,vardir))
dataLogisticNs=dataLogistic
dataLogisticNs$y[c(3,14,22,29,30)] <- NA
dataLogisticNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2 +x3


## For data without any nonsampled area
formula = y ~ x1 +x2 +x3
v = c(1,1,1,1)
c = c(0,0,0,0)


## Using parameter coef and var.coef
saeHBLogistic <- Logistic(formula,coef=c,var.coef=v,iter.update=10,data =dataLogistic)

saeHBLogistic$Est                                 #Small Area mean Estimates
saeHBLogistic$refVar                              #Random effect variance
saeHBLogistic$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBLogistic$plot[[3]]) is used to generate ACF Plot
#plot(saeHBLogistic$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBLogistic <- Logistic(formula,data =dataLogistic)



## For data with nonsampled area use dataLogisticNs

Small Area Estimation using Hierarchical Bayesian under Lognormal Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Lognormal Distribution. The range of data is (y > 0

Usage

Lognormal(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,1,2)
x3=runif(m,2,3)
b0=b1=b2=b3=0.5
u=rnorm(m,0,1)
mu=b0 + b1*x1+b2*x2+b3*x3+u
sig=1
y=rlnorm(m,mu,sig)
E=exp(mu+1/2*sig^2)
vardir=exp(2*mu+sig^2)*(exp(sig^2)-1)
dataLognormal=as.data.frame(cbind(y,x1,x2,x3,vardir))
dataLognormalNs=dataLognormal
dataLognormalNs$y[c(3,14,22,29,30)] <- NA
dataLognormalNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2 +x3


## For data without any nonsampled area

formula = y ~ x1 +x2 +x3
v = c(1,1,1,1)
c= c(0,0,0,0)


## Using parameter coef and var.coef
saeHBLognormal <- Lognormal(formula,coef=c,var.coef=v,iter.update=10,data=dataLognormal)

saeHBLognormal$Est                                 #Small Area mean Estimates
saeHBLognormal$refVar                              #Random effect variance
saeHBLognormal$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBLognormal$plot[[3]]) is used to generate ACF Plot
#plot(saeHBLognormal$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBLognormal <- Lognormal(formula,data=dataLognormal)


## For data with nonsampled area use dataLognormalNs

Small Area Estimation using Hierarchical Bayesian under Negative Binomial Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Negative Binomial Distribution. The data is a number of the Bernoulli process. The negative binomial is used to overcome an over dispersion from the discrete model.

Usage

NegativeBinomial(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
library(MASS)
m=30
x=runif(m,0,1)
b0=b1=0.5
u=rnorm(m,0,1)
Mu=exp(b0+b1*x+u)
theta=1
y=rnegbin(m,Mu,theta)
vardir=Mu+Mu^2/theta
dataNegativeBinomial=as.data.frame(cbind(y,x,vardir))
dataNegativeBinomialNs=dataNegativeBinomial
dataNegativeBinomialNs$y[c(3,14,22,29,30)] <- NA
dataNegativeBinomialNs$vardir[c(3,14,22,29,30)] <- NA


## Compute Fitted Model
## y ~ x


## For data without any nonsampled area

formula = y ~ x
v= c(1,1)
c= c(0,0)
dat = dataNegativeBinomial

## Using parameter coef and var.coef
saeHBNegbin <- NegativeBinomial(formula,coef=c,var.coef=v,iter.update=10,data =dat)

saeHBNegbin$Est                                 #Small Area mean Estimates
saeHBNegbin$refVar                              #Random effect variance
saeHBNegbin$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBNegbin$plot[[3]]) is used to generate ACF Plot
#plot(saeHBNegbin$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBNegbin <- NegativeBinomial(formula,data =dat)



## For data with nonsampled area use dataNegativeBinomialNs

Small Area Estimation using Hierarchical Bayesian under Normal Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Normal Distribution. The range of data is (-\infty < y < \infty)

Usage

Normal(
  formula,
  vardir,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

#Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,1,5)
x3=runif(m,10,15)
x4=runif(m,10,20)
b0=b1=b2=b3=b4=0.5
u=rnorm(m,0,1)
vardir=1/rgamma(m,1,1)
Mu <- b0+b1*x1+b2*x2+b3*x3+b4*x4+u
y=rnorm(m,Mu,sqrt(vardir))
dataNormal=as.data.frame(cbind(y,x1,x2,x3,x4,vardir))
dataNormalNs=dataNormal
dataNormalNs$y[c(3,10,15,29,30)] <- NA
dataNormalNs$vardir[c(3,10,15,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2 +x3 +x4


## For data without any nonsampled area
formula=y~x1+x2+x3+x4
var= "vardir"
v = c(1,1,1,1,1)
c= c(0,0,0,0,0)


## Using parameter coef and var.coef
saeHBnormal<-Normal(formula,vardir=var,coef=c,var.coef=v,data=dataNormal)

saeHBnormal$Est                                 #Small Area mean Estimates
saeHBnormal$refVar                              #Random effect variance
saeHBnormal$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBnormal$plot[[3]]) is used to generate ACF Plot
#plot(saeHBnormal$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBnormal<-Normal(formula,vardir ="vardir",data=dataNormal)



## For data with nonsampled area use dataNormalNs

Small Area Estimation using Hierarchical Bayesian under Poisson Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Poisson Distribution. The data is a count data, y = 1,2,3,...

Usage

Poisson(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Author(s)

Azka Ubaidillah [aut], Ika Yuni Wulansari [aut], Zaza Yuda Perwira [aut, cre], Jayanti Wulansari [aut, cre], Fauzan Rais Arfizain [aut,cre]

Examples

##Load Dataset
library(CARBayesdata)
data(lipdata)
dataPoisson <- lipdata
dataPoissonNs <- lipdata
dataPoissonNs$observed[c(2,9,15,23,40)] <- NA


##Compute Fitted Model
#observed ~ pcaff


## For data without any nonsampled area

formula = observed ~ pcaff
v = c(1,1)
c = c(0,0)


## Using parameter coef and var.coef
saeHBPoisson <- Poisson(formula, coef=c,var.coef=v,iter.update=10,data=dataPoisson)

saeHBPoisson$Est                                 #Small Area mean Estimates
saeHBPoisson$refVar                              #Random effect variance
saeHBPoisson$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBPoisson$plot[[3]]) is used to generate ACF Plot
#plot(saeHBPoisson$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBPoisson <- Poisson(formula,data=dataPoisson)



## For data with nonsampled area use dataPoissonNs

Small Area Estimation using Hierarchical Bayesian under Poisson Gamma Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Poisson Distribution which it is parameter (\lambda) is assumed to be a Gamma distribution. The data is a count data, y = 1,2,3,...

Usage

PoissonGamma(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Load Dataset
library(CARBayesdata)
data(lipdata)
dataPoissonGamma <- lipdata
dataPoissonGammaNs <- lipdata
dataPoissonGammaNs$observed[c(2,9,15,23,40)] <- NA


##Compute Fitted Model
##observed ~ pcaff


## For data without any nonsampled area

formula = observed ~ pcaff
v= c(1,1)
c = c(0,0)
dat = dataPoissonGamma


## Using parameter coef and var.coef
saeHBPoissonGamma <- PoissonGamma(formula,coef=c,var.coef=v,iter.update=10,data=dat)

saeHBPoissonGamma$Est                                 #Small Area mean Estimates
saeHBPoissonGamma$refVar                              #Random effect variance
saeHBPoissonGamma$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBPoissonGamma$plot[[3]]) is used to generate ACF Plot
#plot(saeHBPoissonGamma$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBPoissonGamma <- PoissonGamma(formula,data=dataPoissonGamma)



## For data with nonsampled area use dataPoissonGammaNs

Small Area Estimation using Hierarchical Bayesian under Student-t Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Student-t Distribution. The range of data is (-\infty < y < \infty)

Usage

Student_t(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
m=30
x1=runif(m,10,20)
x2=runif(m,30,50)
b0=b1=b2=0.5
u=rnorm(m,0,1)
MU=b0+b1*x1+b2*x2+u
k=rgamma(1,10,1)
y=rt(m,k,MU)
vardir=k/(k-1)
vardir=sd(y)^2
datat=as.data.frame(cbind(y,x1,x2,vardir))
datatNs=datat
datatNs$y[c(3,14,22,29,30)] <- NA
datatNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2


## For data without any nonsampled area

formula =  y ~ x1+x2
var.coef = c(1,1,1)
coef = c(0,0,0)


## Using parameter coef and var.coef
saeHBt <- Student_t(formula,coef=coef,var.coef=var.coef,iter.update=10,data = datat)

saeHBt$Est                                 #Small Area mean Estimates
saeHBt$refVar                              #Random effect variance
saeHBt$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBt$plot[[3]]) is used to generate ACF Plot
#plot(saeHBt$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBt <- Student_t(formula,data = datat)



## For data with nonsampled area use datatNs

Small Area Estimation using Hierarchical Bayesian under Student-t (non central) Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Student-t (non central) Distribution. The range of data is (-\infty < y < \infty)

Usage

Student_tnc(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
m=30
x1=runif(m,1,100)
x2=runif(m,10,15)
b0=b1=b2=0.5
u=rnorm(m,0,1)
MU=b0+b1*x1+b2*x2+u
k=rgamma(1,10,1)
y=rt(m,k,MU)
vardir=k/(k-1)
vardir=sd(y)^2
datatnc=as.data.frame(cbind(y,x1,x2,vardir))
datatncNs=datatnc
datatncNs$y[c(3,14,22,29,30)] <- NA
datatncNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x1 +x2


## For data without any nonsampled area

#formula =  y ~ x1+x2
v = c(1,1,1)
c = c(0,0,0)
dat =   datatnc


## Using parameter coef and var.coef
saeHBtnc <- Student_tnc(formula,coef=c, var.coef=v,iter.update=10, data = dat)

saeHBtnc$Est                                 #Small Area mean Estimates
saeHBtnc$refVar                              #Random effect variance
saeHBtnc$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBtnc$plot[[3]]) is used to generate ACF Plot
#plot(saeHBtnc$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBtnc <- Student_tnc(formula,data =  datatnc)



## For data with nonsampled area use datatncNs

Small Area Estimation using Hierarchical Bayesian under Weibull Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Weibull Distribution. The range of data is (y > 0

Usage

Weibull(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

Value

This function returns a list of the following objects:

Examples

##Data Generation
set.seed(123)
m=30
x=runif(m,0,1)
b0=b1=0.5
u=rnorm(m,0,1)
Mu=exp(b0+b1*x+u)
k=rgamma(m,2,1)
lambda=Mu/gamma(1+1/k)
y=rweibull(m,k,lambda)
MU=lambda*gamma(1+1/k)
vardir=lambda^2*(gamma(1+2/k)-(gamma(1+1/k))^2)
dataWeibull=as.data.frame(cbind(y,x,vardir))
dataWeibullNs=dataWeibull
dataWeibullNs$y[c(3,14,22,29,30)] <- NA
dataWeibullNs$vardir[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y ~ x


## For data without any nonsampled area

formula = y ~ x
var.coef = c(1,1)
coef = c(0,0)


## Using parameter coef and var.coef
saeHBWeibull <- Weibull(formula,coef=coef,var.coef=var.coef,iter.update=10,data=dataWeibull)

saeHBWeibull$Est                                 #Small Area mean Estimates
saeHBWeibull$refVar                              #Random effect variance
saeHBWeibull$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBWeibull$plot[[3]]) is used to generate ACF Plot
#plot(saeHBWeibull$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBWeibull <- Weibull(formula, data=dataWeibull)



## For data with nonsampled area use dataWeibullNs

saeHB : Small Area Estimation using Hierarchical Bayesian Method

Description

Provides several functions for area level of small area estimation using hierarchical Bayesian (HB) method with several univariate distributions for variable of interest. The dataset that used in every function is generated accordingly in the Example. The 'rjags' package is employed to obtain parameter estimates. Model-based estimators involves the HB estimators which include the mean and the variation of mean. For the reference, see Rao and Molina (2015) <doi:10.1002/9781118735855>.

Author(s)

Azka Ubaidillah azka@stis.ac.id, Ika Yuni Wulansari ikayuni@stis.ac.id, Zaza Yuda Perwira 221710086@stis.ac.id

Maintainer: Zaza Yuda Perwira 221710086@stis.ac.id

Functions

Beta

Produces HB estimators, standard error, random effect variance, coefficient and plot under beta distribution

Binomial

Produces HB estimators, standard error, random effect variance, coefficient and plot under binomial distribution

Exponential

Produces HB estimators, standard error, random effect variance, coefficient and plot under exponential distribution

ExponentialDouble

Produces HB estimators, standard error, random effect variance, coefficient and plot double exponential distribution

Gamma

Produces HB estimators, standard error, random effect variance, coefficient and plot under Gamma distribution

Logistic

Produces HB estimators, standard error, random effect variance, coefficient and plot under logistic distribution

Lognormal

Produces HB estimators, standard error, random effect variance, coefficient and plot under lognormal distribution

NegativeBinomial

Produces HB estimators, standard error, random effect variance, coefficient and plot under negative binomial distribution

Normal

Produces HB estimators, standard error, random effect variance, coefficient and plot under normal distribution

Poisson

Produces HB estimators, standard error, random effect variance, coefficient and plot under poisson distribution

PoissonGamma

Produces HB estimators, standard error, random effect variance, coefficient and plot under poisson gamma distribution

Student_t

Produces HB estimators, standard error, random effect variance, coefficient and plot under student-t distribution

Student_tnc

Produces HB estimators, standard error, random effect variance, coefficient and plot under student-t (not central) distribution

Weibull

Produces HB estimators, standard error, random effect variance, coefficient and plot under weibull distribution

Reference

• Rao, J.N.K & Molina. (2015). Small Area Estimation 2nd Edition. New York: John Wiley and Sons, Inc. <doi:10.1002/9781118735855>.