Type: Package
Title: Small Area Estimation using HB for Rao Yu Model under Beta Distribution
Version: 0.1.5
Maintainer: Dian Rahmawati Salis <dianrahmawatisalis03@gmail.com>
Description: Several functions are provided for small area estimation at the area level using the hierarchical bayesian (HB) method with panel data under beta distribution for variable interest. This package also provides a dataset produced by data generation. The 'rjags' package is employed to obtain parameter estimates. Model-based estimators involve the HB estimators, which include the mean and the variation of the mean. For the reference, see Rao and Molina (2015, ISBN: 978-1-118-73578-7).
License: GPL-3
URL: https://github.com/DianRahmawatiSalis/saeHB.panel.beta
BugReports: https://github.com/DianRahmawatiSalis/saeHB.panel.beta/issues
Depends: R(≥ 2.10)
Imports: coda, dplyr, graphics, grDevices, rjags, stats, stringr
Suggests: knitr, R.rsp, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder: knitr, R.rsp
Config/testthat/edition: 3
Encoding: UTF-8
LazyData: true
NeedsCompilation: no
RoxygenNote: 7.3.1
SystemRequirements: JAGS (http://mcmc-jags.sourceforge.net)
Packaged: 2024-09-04 10:38:04 UTC; LenovO
Author: Dian Rahmawati Salis [aut, cre], Azka Ubaidillah [aut]
Repository: CRAN
Date/Publication: 2024-09-04 11:00:02 UTC

Small Area Estimation using Hierarchical Bayesian for Rao-Yu Model under Beta Distribution with rho=0

Description

This function is implemented to variable of interest ydi

Usage

Panel.beta(
  formula,
  area,
  period,
  iter.update = 3,
  iter.mcmc = 2000,
  thin = 1,
  burn.in = 1000,
  tau.e = 1,
  tau.v = 1,
  data
)

Arguments

formula

Formula that describe the fitted model

area

Number of areas (domain) of the data

period

Number of periods (subdomains) for each area of the data

iter.update

Number of updates with default 3

iter.mcmc

Number of total iterations per chain with default 2000

thin

Thinning rate, must be a positive integer with default 1

burn.in

Number of iterations to discard at the beginning with default 1000

tau.e

Variance of area-by-time effect of variable interest with default 1

tau.v

Variance of random area effect of variable interest with default 1

data

The data frame

Value

This function returns a list of the following objects:

Est

A vector with the values of Small Area mean Estimates using Hierarchical bayesian method

refVar

Estimated random effect variances

coef

A dataframe with the estimated model coefficient

plot

Trace, Density, Autocorrelation Function Plot of MCMC samples

convergence.test

Convergence diagnostic for Markov chains based on Geweke test

Examples

##For data without any non-sampled area
data(dataPanelbeta)     # Load dataset
dataPanelbeta = dataPanelbeta[1:25,] #for the example only use part of the dataset
formula = ydi ~ xdi1 + xdi2
area = max(dataPanelbeta[, "area"])
period = max(dataPanelbeta[,"period"])

result <- Panel.beta(formula, area, period, data = dataPanelbeta)

result$Est
result$refVar
result$coef
result$plot


## For data with non-sampled area use dataPanelbetaNs

Small Area Estimation using Hierarchical Bayesian for Rao-Yu Model under Beta Distribution

Description

This function is implemented to variable of interest ydi

Usage

RaoYuAr1.beta(
  formula,
  area,
  period,
  iter.update = 3,
  iter.mcmc = 2000,
  thin = 1,
  burn.in = 1000,
  tau.e = 1,
  tau.v = 1,
  data
)

Arguments

formula

Formula that describe the fitted model

area

Number of areas (domain) of the data

period

Number of periods (subdomains) for each area of the data

iter.update

Number of updates with default 3

iter.mcmc

Number of total iterations per chain with default 2000

thin

Thinning rate, must be a positive integer with default 1

burn.in

Number of iterations to discard at the beginning with default 1000

tau.e

Variance of area-by-time effect of variable interest with default 1

tau.v

Variance of random area effect of variable interest with default 1

data

The data frame

Value

This function returns a list of the following objects:

Est

A vector with the values of Small Area mean Estimates using Hierarchical bayesian method

refVar

Estimated random effect variances

coefficient

A dataframe with the estimated model coefficient

alpha

Parameter dispersion of Generalized Poisson distribution

plot

Trace, Density, Autocorrelation Function Plot of MCMC samples

convergence.test

Convergence diagnostic for Markov chains based on Geweke test

Examples

##For data without any non-sampled area
data(dataBetaAr1)     # Load dataset
dataBetaAr1 = dataBetaAr1[1:25,] #for the example only use part of the dataset
formula = ydi ~ xdi1 + xdi2
area = max(dataBetaAr1[, "area"])
period = max(dataBetaAr1[,"period"])

result <- RaoYuAr1.beta(formula, area, period, data = dataBetaAr1)
result$Est
result$refVar
result$coefficient
result$plot
## For data with non-sampled area use dataBetaAr1Ns

Sample Data under Beta Distribution for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model

Description

Dataset under Beta Distribution to simulate Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model This data is generated by these following steps:

  1. Generate random effect area v, random effect for area i at time point j u, epsilon \epsilon, variance of ydi vardir, sampling error e, auxiliary xdi1 and xdi2

    • Set coefficient \beta_{0}=\beta_{1}=\beta_{2}=2 and \rho = -0,5

    • Generate random effect area v_{i}~N(0,1)

    • Generate auxiliary variable xdi1_{ij}~U(0,1)

    • Generate auxiliary variable xdi2_{ij}~U(0,1)

    • Generate epsilon \epsilon_{ij}~N(0,1)

    • Generate sampling error e_{ij}~N(0,vardir_{ij})

    • Generate \phi_{ij}~Gamma(1,0.5)

    • Calculate random effect for area i at time point j u_{ij}=\rho*u_{ij-1}+\epsilon_{ij}

    • Calculate \mu_{ij}=\frac{(\exp{\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+\epsilon_{ij}})}{(1+\exp{\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+\epsilon_{ij}}})

    • Calculate A_{ij}=\mu_{ij}*\phi_{ij}

    • Calculate B_{ij}=(1-\mu_{ij})*\phi_{ij}

    • Generate ydi y_{ij}~Beta(A_{ij},B_{ij})

    • Calculate variance of ydi with vardir_{ij}=\frac{(A_{ij})(B_{ij})}{(A_{ij}+B_{ij})^2(A_{ij}+B_{ij}+1)}

    • Set area=20 and period=5

  2. Auxiliary variables xdi1,xdi2, direct estimation y, area, period, and vardir are combined in a dataframe called dataAr1

Usage

dataBetaAr1

Format

A data frame with 100 rows and 6 variables:

ydi

Direct Estimation of y

area

Area (domain) of the data

period

Period (subdomain) of the data

vardir

Sampling Variance of y

xdi1

Auxiliary variable of xdi1

xdi2

Auxiliary variable of xdi2

Sample Data under Beta Distribution for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model with Non Sampled Area

Description

  1. A dataset under Beta Distribution to simulate Small Area Estimation using Hierarchical Bayesian method for Rao-Yu Model with Non-sampled Area

  2. This data contains NA values that indicates no sampled in at least one area.

Usage

dataBetaAr1Ns

Format

A data frame with 100 row and 6 column:

ydi

Direct Estimation of y

area

Area (domain) of the data

period

Period (subdomain) of the data

vardir

Sampling Variance of y

xdi1

Auxiliary variable of xdi1

xdi2

Auxiliary variable of xdi2

Sample Data under Beta Distribution for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model when rho = 0

Description

Dataset under Beta Distribution to simulate Small Area Estimation using Hierarchical Bayesian Method for Rao-Yu Model with rho = 0 This data is generated by these following steps:

  1. Generate random effect area v, random effect for area i at time point j u, epsilon \epsilon, variance of ydi vardir, sampling error e, auxiliary xdi1 and xdi2

    • Set coefficient \beta_{0}=\beta_{1}=\beta_{2}=2

    • Generate random effect area v_{i}~N(0,1)

    • Generate auxiliary variable xdi1_{ij}~U(0,1)

    • Generate auxiliary variable xdi2_{ij}~U(0,1)

    • Generate epsilon \epsilon_{ij}~N(0,1)

    • Generate \phi_{ij}~Gamma(1,0.5)

    • Calculate \mu_{ij}=\frac{\exp{\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+\epsilon_{ij}}}{(1+\exp{\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+\epsilon_{ij}})}

    • Calculate A_{ij}=\mu_{ij}*\phi_{ij}

    • Calculate B_{ij}=(1-\mu_{ij})*\phi_{ij}

    • Generate ydi y_{ij}~Beta(A_{ij},B_{ij})

    • Calculate variance of ydi with vardir_{ij}=\frac{(A_{ij})(B_{ij})}{(A_{ij}+B_{ij})^2(A_{ij}+B_{ij}+1)}

    • Set area=20 and period=5

  2. Auxiliary variables xdi1,xdi2, direct estimation y, area, period, and vardir are combined in a dataframe called dataPanel

Usage

dataPanelbeta

Format

A data frame with 100 rows and 6 variables:

ydi

Direct Estimation of y

area

Area (domain) of the data

period

Period (subdomain) of the data

vardir

Sampling Variance of y

xdi1

Auxiliary variable of xdi1

xdi2

Auxiliary variable of xdi2

Sample Data under Beta Distribution for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model when rho = 0 with Non Sampled Area

Description

  1. A dataset under Beta Distribution to simulate Small Area Estimation using Hierarchical Bayesian method for Rao-Yu Model with Non-sampled area

  2. This data contains NA values that indicates no sampled in at least one area.

Usage

dataPanelbetaNs

Format

A data frame with 100 row and 6 column:

ydi

Direct Estimation of y

area

Area (domain) of the data

period

Period (subdomain) of the data

vardir

Sampling Variance of y

xdi1

Auxiliary variable of xdi1

xdi2

Auxiliary variable of xdi2