Small Area Estimation Using Hierarchical Bayesian Method under Twofold Subarea Level Model with 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

• This function gives estimation of subarea and area means simultaneously under Twofold Subarea Level Small Area Estimation Model Using Hierarchical Bayesian Method with Normal distribution

Usage

NormalTF(
  formula,
  vardir,
  area,
  weight,
  iter.update = 3,
  iter.mcmc = 2000,
  thin = 1,
  burn.in = 1000,
  data,
  coef,
  var.coef
)

Arguments

Value

This function returns a list with following objects:

Est_sub

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

Est_area

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

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

##load dataset for data without any nonsampled subarea
data(dataTwofold)

#formula of fitted model
formula=y~x1+x2

#model fitting
mod=NormalTF(formula,vardir="vardir",area="codearea",weight="w",data=dataTwofold)

#estimate
mod$Est_sub #Subarea mean estimate
mod$Est_area #area mean estimate
mod$coefficient #coefficient estimate
mod$refVar #random effect subarea and area estimates

#Load Library 'coda' to execute the plot
#autocorr.plot(mod$plot[[3]]) is used to generate ACF Plot
#plot(mod$plot[[3]]) is used to generate Density and trace plot

##for dataset with nonsampled subarea use dataTwofoldNS

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

Description

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

This data is generated by these following steps:

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

   • Generate subarea random effect u_{ij}~N(0,8)

   • Generate area random effect v_{i} ~ N(0,8)

   • Generate auxilary variabel on subarea level x_{ij1}~ U(0,1)

   • Generate auxilary variabel on subarea level x_{ij2}~N(10,1)

   • Generate unit proportion on each subarea w_{ij}~U(10,20)

   • Generate sampling error e_{ij}~N(0,\sigma^{2}_{e}) where \sigma^{2}_{e}~IG(1,1) is a variance of direct estimator

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

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

   • Calculate direct estimator y_{ij}=\mu_{ij}+e_{ij}

2. Auxiliary variables x_{ij1},x_{ij2}, direct estimation (y_{ij}) ,vardir, and weight w_{ij} are combined in a dataframe called dataTwofold

Usage

dataTwofold

Format

A data frame with 90 rows and 6 columns:

y

Direct estimation of subarea mean y_{ij}

x1

Auxiliary variabel of x_{ij1}

x2

Auxiliary variabel of x_{ij2}

codearea

Index that describes the code relating to warea 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 Normal 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 Normal distribution and Non-sampled subarea

2. This data contains NA values that indicates no sampled at one or more Subareas. It uses the dataTwofold with the direct estimates and the related variances in 10 subareas are missing.

Usage

dataTwofoldNS

Format

A data frame with 90 rows and 6 columns:

y

Direct estimation of subarea mean y_{ij}

x1

Auxiliary variabel of x_{ij1}

x2

Auxiliary variabel 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}

saeHB.twofold : Small Area Estimation Under Twofold Subarea Level Model Using Hierarchical Bayesian Method

Description

Provides several functions for area and subarea level of small area estimation under Twofold Subarea Level Model using hierarchical Bayesian (HB) method with Univariate Normal distribution for variables of interest. Some dataset simulated by a data generation are also provided. The 'rjags' package is employed to obtain parameter estimates using Gibbs Sampling algorithm. Model-based estimators involves the HB estimators which include the mean, the variation of mean, and the quantile. For the reference, see Rao and Molina (2015), Torabi (2014), Leyla Mohadjer et.al(2007)

Author(s)

Reyhan Saadi, Azka Ubaidillah

Maintaner: Reyhan Saadi reyhansaadi335@gmail.com

Functions

NormalTF

This function gives estimation of subarea and area means simultaneously under Twofold Subarea Small Area Estimation Model Using Hierarchical Bayesian Method with Normal distribution based on model in Torabi (2014) amd Erciulescu et al. (2018)

Reference

• Mohadjer, L.K., Rao, J.N., Liu, B., Krenzke, T., & Kerckhove, W.V. (2007). Hierarchical Bayes Small Area Estimates of Adult Literacy Using Unmatched Sampling and Linking Models.

• Torabi, M., & Rao, J.N. (2014). On small area estimation under a sub-area level model. J. Multivar. Anal., 127, 36-55. DOI:10.1016/j.jmva.2014.02.001

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

• Erciulescu, A.L., Cruze, N.B. and Nandram, B. (2019), Model-based county level crop estimates incorporating auxiliary sources of information. J. R. Stat. Soc. A, 182: 283-303. DOI:10.1111/rssa.12390