Correction of estimator bias in linear regression with categorical covariates with classification error

TL;DR

This paper introduces an asymptotic correction method for linear regression estimators affected by classification errors in covariates, improving parameter estimation without needing true covariate data.

Contribution

The work develops a novel correction technique based on least squares estimators and error probabilities, enhancing estimation accuracy in models with misclassified categorical covariates.

Findings

Correcting the intercept significantly improves estimation accuracy.

The proposed correction method effectively reduces bias in parameter estimates.

Simulations demonstrate the method's robustness across different scenarios.

Abstract

The objective of this work is to propose an asymptotic correction method for the estimators of parameters from regression models with covariates subject to classification errors. A correction was developed based on the least squares estimators from regression with erroneous covariates, the marginal probability of the true covariates, and the conditional probability of the erroneous covariates given the true covariates. In this way, we can correct these estimators without the need to correct the erroneous covariates or observe the true covariates. We performed simulations to quantify the performance of the proposed corrections, identifying, that correcting the intercept is crucial for a significant improvement in estimation.