Common Error 14: Interpreting Moderation Based on the Moderated Model, Excluding X and M

Early methodological work addressing multicollinearity concerns in moderation analysis proposed omitting the components (X and M) and testing reduced models containing only the product term (Y = XM; Sharma et al., 1981). Some researchers adopted this approach when it appeared to enhance statistical significance, a practice that persists in approximately 26.64% of contemporary studies - an improvement from the 43.9% prevalence reported by Aguinis et al. (2017), yet still methodologically problematic. This specification suffers from fundamental limitations (Becker et al., 2023; Dawson, 2014). The Y-XM correlation inherently depends on the constituent variables' properties (Irwin & McClelland, 2001), potentially conflating main and interaction effects. This confounding becomes particularly acute when main and moderation effects share directional signs (Cohen, 1978), compromising the reliability of moderation tests. Consequently, scholars must include all constituent terms alongside their product in moderation analyses regardless of their statistical significance (Cronbach, 1987), as proper model specification supersedes collinearity concerns.

调节分析: 常见问题十四  错误地设定模型（遗漏X与M的主效应项）

这是一个更为根本且严重的模型设定错误。为应对多重共线性，部分研究（约26.64%）采用了早期文献中一种有缺陷的建议：在模型中完全省略自变量（X）和调节变量（M）的主效应项，仅保留其乘积项（X*M）进行检验。这种方法在方法论上是不成立的。乘积项与Y的相关性严重依赖于X和M自身的分布与特性，这会导致主效应与交互效应完全混淆，使得乘积项的系数无法被正确解释，调节检验的结果也因此不可靠。

问题实质：

调节分析模型必须遵循 “层次原则” 。交互项（X*M）是建立在X和M的效应基础之上的高阶项。省略底层的主效应项，相当于建立了错误的数学关系模型，其统计结果缺乏有效的理论解释基础。

解决建议：

严格遵守全模型规范：正确的、可解释的调节分析模型必须同时包含所有构成项：Y = b₀ + b₁X + b₂M + b₃(X*M) + e

• 无论主效应项（b₁, b₂）是否统计显著，都必须强制保留在模型中。

• 正确的模型设定是科学推断的前提，其重要性绝对高于对多重共线性的担忧。共线性问题应通过其他诊断（如VIF）和方法（如中心化）来管理，而非通过错误地省略必要变量来解决。

Reference

• Aguinis, H., Edwards, J. R., & Bradley, K. J. (2017).      Improving our understanding of moderation and mediation in strategic management research. Organizational Research Methods, 20(4),      665-685.

• 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.

• Cronbach, L. J. (1987). Statistical tests for moderator variables: Flaws in analyses recently proposed. Psychological Bulletin,      102(3), 414-417.

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

• Irwin, J. R., & McClelland, G. H. (2001). Misleading heuristics and moderated multiple regression models. Journal of      Marketing Research, 38(1), 100-109.

• 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.