Assessing the Impact of Measurement Error on Regression Model Accuracy and Parameter Estimation Efficiency

Posted: Dec 12, 2016

• Emily Davis
• Emily Hill
• Emily Taylor

Abstract

Measurement error represents a fundamental challenge in statistical modeling and data analysis, affecting virtually all empirical research across scientific disciplines. While the presence of measurement inaccuracies is widely acknowledged, the systematic quantification of their impact on regression model performance remains inadequately explored, particularly in the context of modern high-dimensional datasets and complex modeling frameworks. Traditional statistical theory has primarily addressed measurement error through classical error models that assume simple additive structures and independence between errors and true values. However, these assumptions rarely hold in practical applications where measurement errors may exhibit complex correlation patterns, heteroscedasticity, and systematic biases that interact with model structure in non-trivial ways. The consequences of ignoring measurement error extend beyond simple attenuation of coefficient estimates, potentially leading to distorted inference, invalid hypothesis tests, and compromised predictive performance. Despite extensive literature on measurement error correction methods, including instrumental variables, regression calibration, and simulation-extraction approaches, there remains a significant gap in understanding how different error structures propagate through various regression frameworks and how this propagation affects both parameter estimation efficiency and overall model accuracy. This research addresses this gap by developing a comprehensive analytical framework that systematically evaluates measurement error impacts across diverse regression contexts.