# datamix: datamix In saeME: Small Area Estimation with Measurement Error

## Description

This data generated by simulation based on Fay-Herriot with Measurement Error Model by following these steps:

1. Generate x1i from a UNIF(5, 10) distribution, x2i from a UNIF(9, 11) distribution, ψi = 3, c1i = c2i = 0.25, and σ2v = 2.

2. Generate u1i from a N(0, c1i) distribution, u2i from a N(0, c2i) distribution, ei from a N(0, ψi) distribution, and vi from a N(0, σ2v) distribution.

3. Generate x3i from a UNIF(1, 5) distribution and x4i from a UNIF(10, 14) distribution.

4. Generate x.hat1i = x1i + u1i and x.hat2i = x2i + u2i.

5. Then for each iteration, we generated Yi = 2 + 0.5*x.hat1i + 0.5*x.hat2 i + 2*x3i + 0.5*x4i + vi and yi = Yi + ei.

This data contain combination between auxiliary variable measured with error and without error. Direct estimator `y`, auxiliary variable x.hat1 x.hat2 x3 x4, sampling variance ψ, and c1 c2 are arranged in a dataframe called `datamix`.

## Usage

 `1` ```data(datamix) ```

## Format

A data frame with 100 observations on the following 8 variables.

`small_area`

areas of interest.

`y`

direct estimator for each domain.

`x.hat1`

auxiliary variable (measured with error) for each domain.

`x.hat2`

auxiliary variable (measured with error) for each domain.

`x3`

auxiliary variable (measured without error) for each domain.

`x4`

auxiliary variable (measured without error) for each domain.

`vardir`

sampling variances for each domain.

`var.x1`

mean squared error of auxiliary variable and sorted as `x.hat1`

`var.x2`

mean squared error of auxiliary variable and sorted as `x.hat2`

saeME documentation built on Jan. 13, 2021, 11:03 a.m.