Common Error 11: Lack Attention of Lower-Order Interactions in the Three-Way Interaction Model

In analyses involving multiple moderators, researchers frequently misinterpret three-way interactions (Becker et al., 2023). Although only 14 of 274 (5.11%) reviewed articles exhibited this specific issue, its significance remains substantial—particularly given the relatively limited number of studies testing three-way interactions. A critical methodological error occurs when researchers test three-way interactions (XMW) without first including all constituent lower-order interaction terms (XM and XW) in the model. This omission is problematic because the three-way interaction effect is conditional upon these lower-order terms (Dawson, 2014). Failing to incorporate these necessary components can yield erroneous conclusions about both the three-way interaction and the overall model interpretation. As Becker et al. (2022) emphasize, researchers must rigorously specify models to include all relevant interaction terms. Utilizing appropriate statistical software (e.g., SmartPLS) that supports complex interaction estimation is equally essential. Adherence to these principles prevents common analytical pitfalls and ensures both validity and interpretability of findings in multi-moderator models.

调节分析:常见问题十一  在三向交互模型中忽略低阶交互项

在检验包含三个变量（如X， M， W）的复杂调节模型（三向交互：X * M * W）时，一个关键错误是未将全部必要的低阶交互项（X * M 和 X * W）纳入模型。三向交互效应的检验是有条件的，它建立在包含了这些低阶交互项的模型基础之上。遗漏它们会导致对三向交互效应乃至整个模型的错误解释（Dawson, 2014）。

问题实质：

这就像建造一座三层楼房（三向交互），你不能跳过第二层（低阶交互）直接去盖第三层。模型必须包含所有构成性的、低一阶的交互项，其检验才具有正确的统计和理论根基。

解决建议：

严格遵守层级原则：在模型中包含三向交互项（XMW）时，必须同时包含：

• 所有构成它的主效应项（X, M, W）

• 所有可能的二阶（两两）交互项（XM, XW, MW）

只有在这个完整的模型框架下，对三向交互项的系数估计和显著性检验才是有效的。使用支持复杂模型设定的统计软件（如SmartPLS, Mplus）有助于规范操作。

Reference

• Becker, J. M., Cheah, J. H., Gholamzade, R., Ringle, C. M.,  & Sarstedt, M. (2023). PLS-SEM's most wanted guidance. International  Journal of Contemporary Hospitality Management, 35(1), 321-346.

• Becker, J. M., Ringle, C. M., & Sarstedt, M. (2018).      Estimating moderating effects in PLS-SEM and PLSc-SEM: Interaction term generation*data treatment. Journal of Applied Structural Equation  Modeling, 2(2), 1-21.

• Dawson, J. F. (2014). Moderation in management research: What, why, when, and how. Journal of Business and Psychology, 29(1), 1-19.

• Xu, Y., & Shiau, W. L. (2026). Moderation analysis in business and management research: Common issues, solutions, and guidelines for future research. International Journal of Information Management, 86,  102995.