Binomial {saeHB}

Small Area Estimation using Hierarchical Bayesian under Binomial Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Binomial Distribution using Logit normal model. The data is an accumulation from the Bernoulli process which there are exactly two mutually exclusive outcomes of a case.

Usage

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

Arguments

formula

Formula that describe the fitted model

n.samp

number of sample

iter.update

Number of updates with default 3

iter.mcmc

Number of total iterations per chain with default 10000

coef

a 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

a vector contains prior initial value of variance of Coefficient of Regression Model with default vector of 1 with the length of the number of regression coefficients

thin

Thinning rate, must be a positive integer with default 2

burn.in

Number of iterations to discard at the beginning with default 2000

tau.u

Prior initial value of inverse of Variance of area random effect 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, if there is non sampled area, then the result of estimation of mu in nonsampled areas are the probabilites

refVar

Estimated random effect variances

coefficient

A dataframe with the estimated model coefficient

plot

Trace, Dencity, Autocorrelation Function Plot of MCMC samples

Author(s)

Azka Ubaidillah [aut], Ika Yuni Wulansari [aut], Zaza Yuda Perwira [aut, cre], Jayanti Wulansari [aut, cre], Fauzan Rais Arfizain [aut,cre]

Examples

#Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,0,1)
b0=b1=b2=0.5
u=rnorm(m,0,1)
n.samp1=round(runif(m,10,30))
mu= exp(b0 + b1*x1+b2*x2+u)/(1+exp(b0 + b1*x1+b2*x2+u))
y=rbinom(m,n.samp1,mu)
vardir=n.samp1*mu*(1-mu)
dataBinomial=as.data.frame(cbind(y,x1,x2,n.samp=n.samp1,vardir))
dataBinomialNs = dataBinomial
dataBinomialNs$y[c(3,14,22,29,30)] <- NA
dataBinomialNs$vardir[c(3,14,22,29,30)] <- NA
dataBinomialNs$n.samp[c(3,14,22,29,30)] <- NA


##Compute Fitted Model
##y~x1+x2


## For data without any nonsampled area
formula = y~x1+x2
n.s = "n.samp"
vc = c(1,1,1)
c = c(0,0,0)
dat = dataBinomial


## Using parameter coef and var.coef
saeHBBinomial<-Binomial(formula,n.samp=n.s,iter.update=10,coef=c,var.coef=vc,data =dat)

saeHBBinomial$Est                                 #Small Area mean Estimates
saeHBBinomial$refVar                              #Random effect variance
saeHBBinomial$coefficient                         #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHBBinomial$plot[[3]]) is used to generate ACF Plot
#plot(saeHBBinomial$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBBinomial <- Binomial(formula,n.samp ="n.samp",data=dataBinomial)



## For data with nonsampled area use dataBinomialNs