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=β0+β1x+ε

where y is n-vector of the response variable, β0 and β1 are unknown regression parameteres, ε 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+δ

where δ is the measurement error and x is the erroneous version of the true x. If the estimated model is

y^=β0^+β1^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(β1^)=Var(β1^)+Bias2(β1^)

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}
}