When Do Interaction/Moderation Effects Stabilize in Linear Regression?

Andrew J Castillo

doi:10.1177/25152459251407860

2026-02-19

PRE

DOI：10.1177/25152459251407860

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在线性回归中，双向交互效应是指两个变量之间的关系会根据第三个变量的水平而发生变化。尽管交互效应被频繁使用，但由于效应量小且可靠性低，它们在估计准确性和统计显著性检验方面都极其困难。本研究采用蒙特卡洛模拟，确定了连续变量间双向交互效应的稳定性阈值，涵盖了可靠性（0.7–1.0）、主效应量（0.1–0.5）、共线性（0.1–0.5）和交互效应量（0.05–0.2）的组合。稳定性被定义为从同一总体中重复抽取相同样本量时估计效应量的一致性，并采用Schönbrodt和Perugini修正后的稳定性区间（corridor of stability）和稳定性点（point of stability）的定义进行操作化。结果显示，交互效应估计的稳定性主要由样本量和预测变量可靠性决定。在代表心理学领域现实研究的案例中，研究者对变量控制有限，稳定性出现在n=3,800时，需要72%的统计效力。在n≤100时，11%至45%的估计值符号错误（即真效应为正时估计为负）。大多数心理学研究参与人数远少于500人，而我们的结果表明许多已发表的交互效应可能不稳定。涉及高度可靠预测变量的分析（如实验设计中的分组分配），可能因对预期效应量的削弱小于测量误差较多的变量，而在更小的样本量下达到稳定。研究者应避免常规的双向交互效应检验，除非样本量和可靠性充足，且假设已预先明确。

Keyword:

interaction effects

linear regression

sample size

reliability

stability

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Advances in Methods and Practices in Psychological Science

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13.4

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purdue university

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