saeHB (version 0.2.3)

Beta: 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,
  seed = 1,
  quiet = TRUE,
  plot = TRUE
)

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

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

seed

number used to initialize a pseudorandom number generator (default seed = 1). The random number generator method used is "base::Wichmann-Hill".

quiet

if TRUE, then messages generated during compilation will be suppressed (default TRUE).

plot

if TRUE, the autocorrelation, trace, and density plots will be generated (default TRUE).

Examples

# \donttest{
# 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)
m <- exp(b0 + b1 * x1 + b2 * x2 + b3 * x3 + b4 * x4 + u)
Mu <- m / (1 + m)
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)
# }