Beta {saeHB}

Small Area Estimation using Hierarchical Bayesian under Beta Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Beta Distribution. The range of data must be 0<y<1. The data proportion is supposed to be implemented with this function.

Usage

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

Arguments

formula

Formula that describe the fitted model

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

refVar

Estimated random effect variances

coefficient

A dataframe with the estimated model coefficient

plot

Trace, Dencity, Autocorrelation Function Plot of MCMC samples

Examples

#Data Generation
set.seed(123)
m=30
x1=runif(m,0,1)
x2=runif(m,0,1)
x3=runif(m,0,1)
x4=runif(m,0,1)
b0=b1=b2=b3=b4=0.5
u=rnorm(m,0,1)
pi=rgamma(1,1,0.5)
Mu <- exp(b0+b1*x1+b2*x2+b3*x3+b4*x4+u)/(1+exp(b0+b1*x1+b2*x2+b3*x3+b4*x4+u))
A=Mu*pi
B=(1-Mu) * pi
y=rbeta(m,A,B)
y <- ifelse(y<1,y,0.99999999)
y <- ifelse(y>0,y,0.00000001)
MU=A/(A+B)
vardir=A*B/((A+B)^2*(A+B+1))
dataBeta = as.data.frame(cbind(y,x1,x2,x3,x4,vardir))
dataBetaNs=dataBeta
dataBetaNs$y[c(3,14,22,29,30)] <- NA
dataBetaNs$vardir[c(3,14,22,29,30)] <- NA


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


## For data without any nonsampled area

vc = c(1,1,1)
c = c(0,0,0)
formula = y~x1+x2
dat = dataBeta[1:10,]


##Using parameter coef and var.coef
saeHBbeta<-Beta(formula,var.coef=vc,iter.update=10,coef=c,data=dat)

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

##Do not use parameter coef and var.coef
saeHBbeta <- Beta(formula,data=dataBeta)