2026/07/01 by Aljoscha Rimpler, Henk A. L. Kiers, Don van Ravenzwaaij · 1 voice
Psychology · Decision Sciences · Neuroscience · #Mental Health Research Topics #Psychometric Methodologies and Testing #Neural and Behavioral Psychology Studies
paper · doi:10.31234/osf.io/s47xz_v1
openalex publication_date 2026/07/01 · openalex created_date 2026/07/02 · openalex updated_date 2026/07/15
Measurement error in predictors and unmodelled interaction effects pose recurring challenges in psychological research, yet their joint consequences for regression analysis have not been analytically characterized. We show that classical measurement error and the omission of a true interaction effect are not independent sources of bias, but become entangled such that their combined effects cannot be recovered by applying standard corrections for either problem alone. Specifically, we derive closed-form expressions for the probability limits of OLS regression weights under joint measurement error and interaction omission, characterize the implied asymptotic residual structure, and establish expressions for model fit and prediction error for infinite samples. A key finding is that the residual contributions from measurement error and interaction omission can partially cancel each other out, so that prediction error reduces marginally while leaving coefficient bias large. As a consequence, qualitatively different models can become difficult to distinguish by standard fit metrics, even in large samples. Furthermore, we demonstrate via Monte Carlo simulation that models with more biased estimates can exhibit lower estimator variance, meaning misspecified models may dominate in both inferential and model selection procedures. These results have direct implications for the replicability and interpretability of linear regression models in psychological research.