An Algorithm for Reducing Errors-in-Variable Bias in Simple and Multiple Linear Regressions.

eive

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

Installation

Install stable version from CRAN

install.packages("eive")

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}
}