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https://github.com/jbytecode/eive
An R package for Errors-in-variables estimation in linear regression
https://github.com/jbytecode/eive
compact-genetic-algorithm errors-in-variables linear-regression r
Last synced: 22 days ago
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An R package for Errors-in-variables estimation in linear regression
- Host: GitHub
- URL: https://github.com/jbytecode/eive
- Owner: jbytecode
- Created: 2019-04-17T18:05:08.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2023-08-21T09:09:33.000Z (over 1 year ago)
- Last Synced: 2024-10-15T16:56:54.235Z (2 months ago)
- Topics: compact-genetic-algorithm, errors-in-variables, linear-regression, r
- Language: R
- Homepage:
- Size: 372 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
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README
# eive
An R package for Errors-in-variables estimation in linear regression
## Installation
### Install stable version from CRAN
```R
install.packages("eive")
```
### Install development version
Please install ```devtools``` package before installing ```eive```:
```R
install.packages("devtools")
```
then install the package from the github repo using
```R
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
```R
> eive(dirtyx = dirtyx, y = y, otherx = nothing)
```
and for the multiple regression
```R
> eive(dirtyx = dirtyx, y = y, otherx = matrixofotherx)
```
and for the multiple regression with formula object
```R
> 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
```bibtex
@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}
}
```