Package 'saeHB.ZIB'

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

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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

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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

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