Andishe_ye Amari

Andishe_ye Amari

Linear regression in the presence of worse data

Document Type : Original Article

Authors
Statistics Department, Shahid Beheshti University
Abstract
This paper presents four approaches to the problem of fitting a linear regression model in the presence of spatially worse data. These approaches include the substitution method, simulation, nested regression, and maximum likelihood. In the first two approaches, by modeling the correlation in the explanatory variable, its prediction is determined at locations corresponding to the response variable. Then, by substituting the obtained predictors instead of the actual values ​​in the regression model, the model is fitted. It is shown that this causes a Braxen error, and this error also leads to a bias in the estimation of the slope of the regression model. To adjust for this bias, the nested regression approach is presented. In the maximum likelihood approach, the worst data are used directly and the parameters of the regression model are estimated. In fact, there is no need to predict the explanatory variable at locations corresponding to the response variable. Unfortunately, it is not possible to examine the properties of the maximum likelihood estimator in detail due to the lack of an analytical form. In a simulation study, the performance of all approaches is examined under several spatial models for the explanatory variable. It is observed that the regression model can significantly reduce the bias of the regression slope estimator compared to other methods. In addition, the nominal coverage of the confidence interval of the regression slope by this method is significant.
Keywords

Volume 18, Issue 1
September 2013
Pages 85-96

  • Receive Date 15 May 2025
  • First Publish Date 15 May 2025
  • Publish Date 23 August 2013