Title: SAE using HB Twofold Subarea Model under Beta Distribution
Version: 0.1.0
Maintainer: Nasya Zahira Putri <nasyazp28@gmail.com>
Description: Estimates area and subarea level proportions using the Small Area Estimation (SAE) Twofold Subarea Model with a hierarchical Bayesian (HB) approach under Beta distribution. A number of simulated datasets generated for illustration purposes are also included. The 'rstan' package is employed to estimate parameters via the Hamiltonian Monte Carlo and No U-Turn Sampler algorithm. The model-based estimators include the HB mean, the variation of the mean, and quantiles. For references, see Rao and Molina (2015) <doi:10.1002/9781118735855>, Torabi and Rao (2014) <doi:10.1016/j.jmva.2014.02.001>, Leyla Mohadjer et al.(2007) http://www.asasrms.org/Proceedings/y2007/Files/JSM2007-000559.pdf, and Erciulescu et al.(2019) <doi:10.1111/rssa.12390>.
License: GPL (≥ 3)
Encoding: UTF-8
RoxygenNote: 7.3.2
Biarch: true
Depends: R (≥ 3.5)
Imports: methods, Rcpp (≥ 0.12.0), RcppParallel (≥ 5.0.1), rstan (≥ 2.18.1), rstantools (≥ 2.4.0), bayesplot, stringr
LinkingTo: BH (≥ 1.66.0), Rcpp (≥ 0.12.0), RcppEigen (≥ 0.3.3.3.0), RcppParallel (≥ 5.0.1), rstan (≥ 2.18.1), StanHeaders (≥ 2.18.0)
SystemRequirements: GNU make
URL: https://github.com/Nasyazahira/saeHB.TF.beta
BugReports: https://github.com/Nasyazahira/saeHB.TF.beta/issues
LazyData: true
Suggests: knitr, rmarkdown
VignetteBuilder: knitr
NeedsCompilation: yes
Packaged: 2025-07-09 12:09:22 UTC; User
Author: Nasya Zahira Putri [aut, cre], Cucu Sumarni [aut]
Repository: CRAN
Date/Publication: 2025-07-14 17:00:06 UTC

The 'saeHB.TF.beta' package.

Description

Small Area Estimation using Hierarchical Bayes Twofold Subarea Level Model under Beta Distribution

References

Stan Development Team (NA). RStan: the R interface to Stan. R package version 2.36.0.9000. https://mc-stan.org

Small Area Estimation using Hierarchical Bayes Twofold Subarea Level Model under Beta Distribution

Description

Function betaTF used for estimation of subarea and area means simultaneously under Twofold Subarea Level Small Area Estimation Model Using Hierarchical Bayesian Method with Beta distribution The range of data must be 0<y<1.

Usage

betaTF(
  formula,
  area,
  weight,
  iter.update = 3,
  iter.mcmc = 1000,
  coef = NULL,
  var.coef = NULL,
  thin = 1,
  burn.in = floor(iter.mcmc/2),
  sigma2.u = 1,
  sigma2.v = 1,
  data
)

Arguments

formula

Formula that describe the fitted model

area

Index that describes the code relating to area in each subarea.This should be defined for aggregation to get area estimator. Index start from 1 until m

weight

Vector contain proportion units or proportion of population on each subarea. w_{ij}

iter.update

Number of updates perform ( default = 3)

iter.mcmc

Number of total iterations per chain (default = 1000)

coef

Vector contains prior initial value of Coefficient of Regression Model for fixed effect with default vector of 0 with the length of the number of regression coefficients

var.coef

Vector contains prior initial value of variance of Coefficient of Regression Model for fixed effect with default vector of 1 with the length of the number of regression coefficients

thin

Thinning rate, must be a positive integer

burn.in

Number of iterations to discard at the beginning

sigma2.u

Number of prior initial value of variance of subarea random effect

sigma2.v

Number of prior initial value of variance of area random effect

data

The data frame

Value

This function returns a list with following objects:

Est_sub

A dataframe contains the values, standard deviation, and quantile of Subarea mean Estimates using Twofold Subarea level model under Hierarchical Bayes method

Est_area

A dataframe contains the values, standard deviation, and quantile of Area mean Estimates using Twofold Subarea level model under Hierarchical Bayes method

area_randeff

A dataframe contains area random effect

sub_randeff

A dataframe contains subarea random effect

refVar

A dataframe that contains estimated subarea and area random effect variance (\sigma_{u}^{2} and \sigma_{v}^{2})

coefficient

A dataframe that contains the estimated model coefficient \beta

plot

Trace, Density, Autocorrelation Function Plot of coefficient

Examples

fit <- betaTF(y~X1+X2,area="codearea",weight="w",data=dataBeta, iter.mcmc = 500)

Simulated dataset Under Two Fold Subarea level model with Beta distribution.

Description

A dataset to simulate Small Area Estimation using Hierarchical Bayesian method under Two Fold Subarea level model with Beta distribution on variable interest.

This data is generated by these following steps:

  1. Generate auxiliary variable X_{ij1},X_{ij2}, sampling error e_{ij},subarea random effect u_{ij}, area random effect v_{i}, and weight or proportions of unit w_{ij}

    • Generate auxiliary variable on subarea level X_{ij1}~ U(0,1)

    • Generate auxiliary variable on subarea level X_{ij2}~N(0,1)

    • Setting coefficient \beta_{0}=\beta_{1}=\beta_{2} =0.5

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

    • Generate subarea random effect u_{ij}~N(0,1)

    • Calculate target parameter \mu_{ij}=\beta_{0} +\beta_{1}x_{ij1} +\beta_{2}x_{ij2}+v_{i}+u_{ij}

    • Generate constant for Beta parameter \pi_{ij}~ Gamma(1,0.5)

    • Calculate Beta parameter A=\mu_{ij}\pi_{ij} and A=(1-\mu_{ij})\pi_{ij}

    • Generate direct estimator y_{ij}~ Beta(A,B)

    • Generate weight on each subarea w_{ij}~U(0.2,0.7)

  2. Direct estimation (y_{ij}), Auxiliary variables X_{ij1},X_{ij2}, vardir, codearea, and weight w_{ij} are combined in a dataframe called dataBeta

Usage

dataBeta

Format

A data frame with 90 rows and 6 columns:

y

Direct estimation of subarea mean y_{ij}

X1

Auxiliary variable of X_{ij1}

X2

Auxiliary variable of X_{ij2}

codearea

Index that describes the code relating to area for each subarea

w

Unit proportion on each subarea or weight w_{ij}

vardir

Sampling variance of direct estimator y_{ij}

Simulated dataset Under Two Fold Subarea level model with Beta distribution and Non-Sampled subarea.

Description

  1. A dataset to simulate Small Area Estimation using Hierarchical Bayesian method under Two Fold Subarea level model with Beta distribution and Non-sampled subarea

  2. This data contains NA values that indicates no sampled at one or more Subareas. It uses the dataBeta with the direct estimates and the related variances in 5 subareas are missing.

Usage

dataBetaNS

Format

A data frame with 90 rows and 6 columns:

y

Direct estimation of subarea mean y_{ij}

X1

Auxiliary variable of X_{ij1}

X2

Auxiliary variable of X_{ij2}

codearea

Index that describes the code relating to area for each subarea

w

Unit proportion on each subarea or weight w_{ij}

vardir

Sampling variance of direct estimator y_{ij}