Type: Package
Title: Small Area Estimation using Hierarchical Bayesian under Zero Inflated Binomial Distribution
Version: 0.1.1
Author: Rizqina Rahmati, Azka Ubaidillah
Maintainer: Rizqina Rahmati <221810583@stis.ac.id>
Description: Provides function for area level of small area estimation using hierarchical Bayesian (HB) method with Zero-Inflated Binomial distribution for variables of interest. Some dataset produced by a data generation are also provided. 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.
License: GPL-3
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.1.2
Imports: stringr, coda, rjags, stats, grDevices, graphics
Suggests: rmarkdown, knitr
VignetteBuilder: knitr
Depends: R (≥ 2.10)
NeedsCompilation: no
Packaged: 2022-06-22 08:26:03 UTC; 221810583
Repository: CRAN
Date/Publication: 2022-06-22 08:40:02 UTC

Sample Data for Small Area Estimation using Hierarchical Bayesian Method under Zero-Inflated Binomial Distribution

Description

Dataset to simulate Small Area Estimation using Hierarchical Bayesian Method under Zero-Inflated Binomial distribution

This data is generated by these following steps:

  1. Generate sampling random area effect u.Z and u.nZ with (u.Z ~ N(0,1)) and (u.nZ ~ N(0,1)). The auxilary variabels are generated by Uniform distribution with (x1 ~ U(0,1)) and (x2 ~ U(1,5)). The coefficient parameters \alpha0, \alpha1, \alpha2, \beta0, \beta1, \beta2 are set as 0.

  2. Calculate logit(p)=\alpha0 + \alpha1 * x1+ \alpha2 * x2 + u.Z and logit(\pi)=\beta0 + \beta1 * x1 +\beta2 * x2 + u.nZ

  3. Generate number of sample with n.samp ~ U(10,30)

  4. Generate delta ~ bernoulli(p) and y_star ~ binomial(s, \pi)

  5. calculate y = delta*y_star

  6. Calculate variance of direct estimates (vardir) with var (y) = (1-p)*s*pi*(1-\pi*(1-p*s))

  7. Auxilary variables x1, x2, direct estimation (y), vardir, and s are combined in a dataframe called dataZIB

Usage

data(dataZIB)

Format

A data frame with 64 observations on the following 4 variables:

y

Direct Estimation of y

X1

Auxiliary variable of x1

X2

Auxiliary variable of x2

vardir

sampling variance of y

s

number of sample

Sample Data for Small Area Estimation using Hierarchical Bayesian Method under Zero-Inflated Binomial Distribution

Description

Dataset to simulate Small Area Estimation using Hierarchical Bayesian Method under Zero-Inflated Binomial distribution with non-sampled areas

This data contains NA values that indicates no sampled at one or more small areas. It uses the dataZIB.ns with the direct estimates and the related variances in 3 small areas are missing.

Usage

data(dataZIBns)

Format

A data frame with 30 rows and 4 variables :

y

Direct Estimation of y

X1

Auxiliary variable of x1

X2

Auxiliary variable of x2

vardir

sampling variance of y

s

number of sample

Small Area Estimation using Hierarchical Bayesian under Zero Inflated Binomial Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Zero Inflated Binomial Distribution. The range of data is (0 < y < \infty). This model can be used to handle overdispersion caused by excess zero in data.

Usage

ziBinomial(
  formula,
  n.samp,
  iter.update = 3,
  iter.mcmc = 10000,
  coef.nonzero,
  var.coef.nonzero,
  coef.zero,
  var.coef.zero,
  thin = 2,
  burn.in = 2000,
  tau.u.nZ = 1,
  data
)

Arguments

formula

Formula that describe the fitted model

n.samp

Number of sample in each area

iter.update

Number of updates with default 3

iter.mcmc

Number of total iterations per chain with default 2000

coef.nonzero

Optional argument for mean on coefficient's prior distribution or \beta's prior distribution which value is non-zero

var.coef.nonzero

Optional argument for the variances of the prior distribution of the model coefficients (\beta)

coef.zero

Optional argument for mean on coefficient's prior distribution or \alpha's prior distribution which value is non-zero

var.coef.zero

Optional argument for the variances of the prior distribution of the model coefficients (\alpha)

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.u.nZ

Variance of random effect area for non-zero of variable interest (y) 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

plot_alpha

Trace, Density, Autocorrelation Function Plot of MCMC samples

plot_beta

Trace, Density, Autocorrelation Function Plot of MCMC samples

Examples

#Compute Fitted Model
 y ~ X1 +X2

# For data without any nonsampled area
# Load Dataset
  data(dataZIB)
  saeHB.ZIB <- ziBinomial(formula = y~X1+X2, "s", iter.update=3, iter.mcmc = 1000,
                burn.in = 200,data = dataZIB)
#the setting of iter.update, iter.mcmc, and burn.in in this example
#is considered to make the example execution time be faster.
#Result
saeHB.ZIB$Est                                    #Small Area mean Estimates
saeHB.ZIB$Est$SD                                 #Standard deviation of Small Area Mean Estimates
saeHB.ZIB$refVar                                 #refVar
saeHB.ZIB$coefficient                            #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHB.ZIB$plot_alpha[[3]]) is used to   #ACF Plot for alpha
#autocorr.plot(saeHB.ZIB$plot_beta[[3]]) is used to    #ACF Plot for beta
#plot(saeHB.ZIB$plot_alpha[[3]]) is used to            #Dencity and trace plot for alpha
#plot(saeHB.ZIB$plot_beta[[3]]) is used to             #Dencity and trace plot for beta