Measurement, sampling, and scaling issues

Common Error 4: Lack of Attention to Measurement Errors of the Interaction Term

Measurement error is a primary source of low statistical power in moderation analysis, biasing estimates and attenuating effects (Aguinis, 2017; Carte & Russell, 2003; Dawson, 2014; Memon et al., 2019). While neglect of this issue has decreased in top journals (~10.95% in our review), a major problem persists: over half of studies using latent variables still neglect the specific measurement error inherent in interaction terms. To avoid misattributing non-significance to a weak true effect rather than methodological limitations, researchers must use reliable measures, report reliability estimates (Aguinis & Edwards, 2014; Aguinis & Vandenberg, 2014), and refer to methods for assessing product term reliability (Busemeyer & Jones, 1983). An effective solution is to use CB-SEM or PLS-SEM, as SEM offers key advantages over methods that ignore measurement error (Aguinis et al., 2017).

常见问题四：忽视交互项的测量误差

测量误差是导致调节分析统计功效不足、结果产生偏差的主要根源（Aguinis, 2017; Carte & Russell, 2003）。具体而言，当预测变量（X, M）存在测量误差时，会导致非标准化系数估计值有偏，直接影响ΔR²的显著性；而当结果变量（Y）存在测量误差时，则会衰减对解释方差的估计（Memon等, 2019）。尽管顶级期刊对此问题的关注度有所提升（我们的综述中估计其忽视率已降至10.95%），但一个严峻的问题依然存在：超过一半使用潜变量的研究，仍然忽视了交互项本身固有的、特定的测量误差。若不严谨处理，研究者可能会错误地将不显著的调节效应归因于真实关系微弱，而忽略了方法本身的局限。

问题实质：

在调节分析中，交互项（X*M）的测量信度通常低于其构成变量。若忽略此误差，就如同用一把刻度不准的尺子去测量细微的变化，极易得出“没有效应”的假阴性结论，严重损害分析效度。

解决建议：

Ÿ  报告并评估信度：必须使用信度良好的测量工具，并报告其信度系数（如Cronbach‘s α、组合信度），以证明测量质量，排除因巨大测量误差导致的结论失效（Aguinis & Edwards, 2014）。对于乘积项的信度计算，可参考Busemeyer和Jones（1983）的方法。

Ÿ  采用能处理测量误差的建模技术：最有效的解决方案之一是使用基于协方差的结构方程模型（CB-SEM）或偏最小二乘结构方程模型（PLS-SEM）来构建包含潜变量的交互项。正如Aguinis等人（2017）指出，SEM相比那些完全忽略测量误差的方法“具有重要优势”。

Reference

• Aguinis, H., & Edwards, J. R. (2014). Methodological      wishes for the next decade and how to make wishes come true. Journal of      Management Studies, 51(1), 143-174.

• 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.

• Carte, T. A., & Russell, C. J. (2003). In pursuit of      moderation: Nine common errors and their solutions. MIS Quarterly,      27(3), 479-501.

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

• Memon, M. A., Cheah, J. H., Ramayah, T., Ting, H., Chuah, F.,      & Cham, T. H. (2019). Moderation analysis: Issues and guidelines. Journal      of Applied Structural Equation Modeling, 3(1), i-xi.

• 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.