Package 'saeHB.panel.beta'

Title: Small Area Estimation using HB for Rao Yu Model under Beta Distribution
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).
Authors: Dian Rahmawati Salis [aut, cre], Azka Ubaidillah [aut]
Maintainer: Dian Rahmawati Salis <[email protected]>
License: GPL-3
Version: 0.1.5
Built: 2025-03-04 07:01:32 UTC
Source: CRAN

Help Index

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 ϵ\epsilon, variance of ydi vardir, sampling error e, auxiliary xdi1 and xdi2

    • Set coefficient β0=β1=β2=2\beta_{0}=\beta_{1}=\beta_{2}=2 and ρ=−0,5\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 ϵij\epsilon_{ij}~N(0,1)

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

    • Generate ϕij\phi_{ij}~Gamma(1,0.5)

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

    • Calculate μij=(exp⁡β0+β1xdi1ij+β2xdi2ij+vi+ϵij)(1+exp⁡β0+β1xdi1ij+β2xdi2ij+vi+ϵij)\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 Aij=μij∗ϕijA_{ij}=\mu_{ij}*\phi_{ij}

    • Calculate Bij=(1−μij)∗ϕijB_{ij}=(1-\mu_{ij})*\phi_{ij}

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

    • Calculate variance of ydi with vardirij=(Aij)(Bij)(Aij+Bij)2(Aij+Bij+1)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 ϵ\epsilon, variance of ydi vardir, sampling error e, auxiliary xdi1 and xdi2

    • Set coefficient β0=β1=β2=2\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 ϵij\epsilon_{ij}~N(0,1)

    • Generate ϕij\phi_{ij}~Gamma(1,0.5)

    • Calculate μij=exp⁡β0+β1xdi1ij+β2xdi2ij+vi+ϵij(1+exp⁡β0+β1xdi1ij+β2xdi2ij+vi+ϵij)\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 Aij=μij∗ϕijA_{ij}=\mu_{ij}*\phi_{ij}

    • Calculate Bij=(1−μij)∗ϕijB_{ij}=(1-\mu_{ij})*\phi_{ij}

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

    • Calculate variance of ydi with vardirij=(Aij)(Bij)(Aij+Bij)2(Aij+Bij+1)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

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