Effect of measurement error size in linear heteroscedastic measurement error models

Abstract

Measurement errors affect the properties of obtained optimal estimators. Further, they affect the accuracy of estimation, although the size of the measurement error required to invalidate an estimation method remains unknown. In this study, we described the effects of measurement errors on estimation and the derived asymptotic covariance matrix by using the properties of unbiased estimating equations. We evaluated different estimation methodologies using various combinations of sample sizes and average reliability ratios. Simulation studies have compared estimators in terms of simulated bias, mean squared error, and coverage probability for the slope parameter. By comparing estimation approaches in terms of bias, mean squared error, and coverage probability, we found that the average reliability ratio of 0.65 and a sample size of 20 yielded estimator stability, with only slight differences in these three attributes. If the sample size was increased, the cutoff point for the average reliability ratio could be relaxed. This process has been in this study illustrated using real datasets.

Keywords:

• Average reliability ratio
• bias
• coverage probability
• mean squared error
• heteroscedastic measurement errors

Acknowledgements

The authors are grateful to the referees for their comments to improve the exposition of the paper.