Measurement Error and Interaction Effects in Linear Regression: A Comparative Simulation Study

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Allahverdi S. N., Dağalp R.

7th International Congress of Applied Statistics, İstanbul, Türkiye, 11 - 13 Mayıs 2026, ss.1, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.1
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet



 Measurement Error and Interaction Effects in Linear Regression: A Comparative Simulation Study

Saide Nur Allahverdi1*, Rukiye Dağalp2,

 

¹Ankara University, Department of Statistics, Ankara, Türkiye

2Ankara University, Department of Statistics, Ankara, Türkiye

 

 

*Corresponding author e-mail: nur.allahverdi@bilecik.edu.tr

 

Abstract

 

Measurement error in explanatory variables (error in variables) is a common issue in many applications and is known to lead to seriously biased and inconsistent parameter estimates in regression models. While the impact of measurement error on main effects has been extensively studied in the literature, its effect on interaction terms has received relatively limited attention. In particular, in models that include interaction terms, measurement error not only reduces estimation accuracy but may also, in some cases, lead to a change in the sign of the interaction coefficient. In this study, the impact of measurement error on parameter estimation in linear regression models with interaction terms is investigated. Specifically, the effects of measurement error level, sample size, and the correlation between explanatory variables on the interaction coefficient are analyzed. A Monte Carlo simulation framework is employed under the classical additive measurement error model. The performance of the naive estimator, regression calibration (RC), and SIMEX methods is compared across different scenarios. The results show that the naive estimator produces substantial bias, particularly for the interaction coefficient. Although regression calibration significantly reduces this bias, it fails to fully eliminate it under high measurement error conditions. In contrast, the SIMEX method demonstrates the best performance, consistently yielding the lowest bias and mean squared error across all scenarios. Overall, the findings indicate that measurement error has more complex and pronounced effects on interaction terms compared to main effects, highlighting the necessity of using appropriate correction methods for reliable statistical inference in such models.

 

Keywords: MEASUREMENT ERROR, INTERACTION EFFECTS, REGRESSION CALIBRATION, SIMEX, MONTE CARLO SIMULATION