Three-way interactions examine the joint impact of multiple variables relying statistically on the multiplicative combination of three predictors in a product term. While effective, this approach is inherently sensitive to data quality, because the multiplicative nature of product terms amplifies even small deviations in the predictors. This sensitivity makes three-way interaction models particularly vulnerable to issues that compromise data integrity. Our study focuses on measurement error and multivariate outliers, which are commonly encountered in empirical research. While two-way interactions may still yield meaningful results under such conditions, that is likely not the case for three-way interactions. Building on these challenges, this study systematically explores the effects of measurement error and multivariate outliers on critical parameters such as statistical power, regression coefficients, and effect sizes through Monte Carlo simulations. Additionally, we examine common research practices, such as scale shortening, and evaluate the effectiveness of various outlier detection methods. Based on these analyses, we propose practical strategies to mitigate the adverse effects of measurement error and outliers in three-way interactions.
