# eive

An R package for Errors-in-variables estimation in linear
regression

## Installation

### Install stable version from
CRAN

### Install development version

Please install `devtools`

package before installing
`eive`

:

`install.packages("devtools")`

then install the package from the github repo using

`devtools::install_github(repo = "https://github.com/jbytecode/eive") `

# The Problem

Suppose the linear regression model is

\[
y = \beta_0 + \beta_1 x^* + \varepsilon
\]

where \(y\) is n-vector of the
response variable, \(\beta_0\) and
\(\beta_1\) are unknown regression
parameteres, \(\varepsilon\) is the
iid. error term, \(x^*\) is the unknown
n-vector of the independent variable, and \(n\) is the number of observations.

We call \(x^*\) unknown because in
some situations the true values of the variable cannot be visible or
directly observable, or observable with some measurement error. Now
suppose that \(x\) is the observable
version of the true values and it is defined as

\[
x = x^* + \delta
\]

where \(\delta\) is the measurement
error and \(x\) is the erroneous
version of the true \(x^*\). If the
estimated model is

\[
\hat{y} = \hat{\beta_0} + \hat{\beta_1}x
\]

then the ordinary least squares (OLS) estimates are no longer
unbiased and even consistent.

Eive-cga is an estimator devised for this problem. The aim is to
reduce the errors-in-variable bias with some cost of increasing the
variance. At the end, the estimator obtains lower Mean Square Error
(MSE) values defined as

\[
MSE(\hat{\beta_1}) = Var(\hat{\beta_1}) + Bias^2(\hat{\beta_1})
\]

for the Eive-cga estimator. For more detailed comparisons, see the
original paper given in the Citation part.

# Usage

For the single variable case

`> eive(dirtyx = dirtyx, y = y, otherx = nothing) `

and for the multiple regression

`> eive(dirtyx = dirtyx, y = y, otherx = matrixofotherx) `

and for the multiple regression with formula object

`> eive(formula = y ~ x1 + x2 + x3, dirtyx.varname = "x", data = mydata) `

Note that the method assumes there is only one erroneous variable in
the set of independent variables.

### Citation

```
@article{satman2015reducing,
title={Reducing errors-in-variables bias in linear regression using compact genetic algorithms},
author={Satman, M Hakan and Diyarbakirlioglu, Erkin},
journal={Journal of Statistical Computation and Simulation},
volume={85},
number={16},
pages={3216--3235},
year={2015},
doi={10.1080/00949655.2014.961157}
publisher={Taylor \& Francis}
}
```