Package 'saeHB.panel'

Title: Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model
Description: We designed this package to provide several functions for area level of small area estimation using hierarchical Bayesian (HB) method. This package provides model using panel data for variable interest.This package also provides a dataset produced by a data generation. 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).
Authors: Velia Tri Marliana [aut, cre], Azka Ubaidillah [aut]
Maintainer: Velia Tri Marliana <[email protected]>
License: GPL-3
Version: 0.1.1
Built: 2024-10-18 06:27:42 UTC
Source: CRAN

Help Index

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

Description

Dataset 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(1,2)

    • Generate auxiliary variable xdi2_{ij}~U(1,3)

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

    • Calculate variance of ydi with vardir_{ij}~IG(10,6)

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

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

    • Calculate μij=β0+β1xdi1ij+β2xdi2ij+vi+uij+eij\mu_{ij}=\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+u_{ij}+e_{ij}

    • Set area=50 and period=10

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

Usage

dataAr1

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 for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model with Non Sampled Area

Description

  1. A dataset 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

dataAr1Ns

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 for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model when rho = 0

Description

Dataset 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 and ρ=−0,5\rho = -0,5

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

    • Generate auxiliary variable xdi1_{ij}~U(1,2)

    • Generate auxiliary variable xdi2_{ij}~U(1,3)

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

    • Calculate variance of ydi with vardir_{ij}~IG(10,6)

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

    • Calculate μij=β0+β1xdi1ij+β2xdi2ij+vi+ϵij+eij\mu_{ij}=\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+\epsilon_{ij}+e_{ij}

    • Set area=50 and period=10

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

Usage

dataPanel

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 for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model when rho = 0 with Non Sampled Area

Description

  1. A dataset 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

dataPanelNs

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 under Rao-Yu Model with rho=0

Description

This function is implemented to variable of interest ydi

Usage

Panel(
  formula,
  area,
  period,
  vardir,
  iter.update = 3,
  iter.mcmc = 2000,
  thin = 2,
  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
vardir

Sampling variances of direct estimations
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

Examples

##For data without any non-sampled area
data(dataPanel)     # Load dataset
formula = ydi ~ xdi1 + xdi2
area = max(dataPanel[, "area"])
period = max(dataPanel[,"period"])
vardir = dataPanel[,"vardir"]

result <- Panel(formula, area, period, vardir, data = dataPanel)

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


## For data with non-sampled area use dataPanelNs

Small Area Estimation using Hierarchical Bayesian under Rao-Yu Model

Description

This function is implemented to variable of interest ydi

Usage

RaoYuAr1(
  formula,
  area,
  period,
  vardir,
  iter.update = 3,
  iter.mcmc = 2000,
  thin = 2,
  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
vardir

Sampling variances of direct estimations
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

Examples

##For data without any non-sampled area
data(dataAr1)     # Load dataset
formula = ydi ~ xdi1 + xdi2
area = max(dataAr1[, "area"])
period = max(dataAr1[,"period"])
vardir = dataAr1[,"vardir"]

result <- RaoYuAr1(formula, area, period, vardir, data = dataAr1)
result$Est
result$refVar
result$coefficient
result$plot
## For data with non-sampled area use dataAr1Ns