dataHBMEbeta {saeHB.ME.beta}

Sample Data for Small Area Estimation with Measurement Error using Hierarchical Bayesian Method under Beta Distribution

Description

This data generated by simulation based on Hierarchical Bayesian Method under Normal Distribution with Measurement Error by following these steps:

1. Generate x_{1} ~ UNIF(0, 1), x_{2} ~ UNIF(0, 1), x_{3} ~ UNIF(0, 1), and x_{4} ~ UNIF(0, 1)

2. Generate v.x_{1} ~ Gamma(2,1) and v.x_{2} ~ Gamma(2,5)

3. Generate x_{1h} ~ N(x_{1}, sqrt(v.x_{1})) and x_{2h} ~ N(x_{2}, sqrt(v.x_{2}))

4. Set Coefficient \beta_{0} = \beta_{1} = \beta_{2} = \beta_{3} = \beta_{4} = {0,5}

5. Generate u ~ N(0,1) and \pi ~ Gamma(1,0.5)

6. Calculate

   {\mu} =\frac{\beta_{0} + \beta_{1}*x_{1h} + \beta_{2}*x_{2h} + \beta_{3}*x_{3} + \beta_{4}*x_{4} + u}{\beta0 + \beta1*x1h + \beta2*x2h + \beta3*x3 + \beta4*x4 + u}

7. Calculate A = \mu\pi and B = (1-\mu)\pi

8. Generate Y ~ UNIF(A,B)

9. Calculate Mean of Variable Y with

   {E(Y)}=\frac{A}{A+B}

10. Calculate Variance of Variable Y with

    {Var(Y)} = \frac{AB}{ (A+B+1)(A+B)^2}

Direct estimation Y, auxiliary variables x1 x2 x3 x4, sampling variance v, and mean squared error of auxiliary variables v.x1 v.x2 are arranged in a dataframe called dataHBMEbeta.

Usage

data(dataHBMEbeta)

Format

A data frame with 30 rows and 8 variables:

Y

direct estimation of Y.

x1

auxiliary variable of x1.

x2

auxiliary variable of x2.

x3

auxiliary variable of x3.

x4

auxiliary variable of x4.

vardir

sampling variances of Y.

v.x1

mean squared error of x1.

v.x2

mean squared error of x2.