1. In ecological studies, the magnitude and direction of interactions among two continuous explanatory variables x₁ and x₂ are commonly evaluated by fitting a statistical model of the form , where x₁x₂ is an interaction term that measures departure from additivity of effects.
2. Here, we highlight three issues associated with evaluating interactions in statistical models of this form that appear underappreciated in the ecological literature, but which have important implications for how we fit models and correctly identify interactions.
3. First, the scale (additive or multiplicative) on which the outcome variable y is modelled matters. Transformations that change the scale of analysis alter the interpretation of interaction terms and can hide interactions of ecological importance. Second, spurious interactions can arise when explanatory variables are correlated and there are unmodeled nonlinear relationships, a situation likely to arise when fitting statistical models to non-experimental data. Third, interactions can be nonlinear such that the interaction term x₁x₂ will not capture all interactions of ecological interest.
4. We illustrate how each of these issues can result in potentially misleading outcomes using examples linked to the impacts of multiple stressors on biodiversity. We provide recommendations aimed at correctly identifying interaction effects from statistical models.

中文翻译：

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统计模型中的相互作用：需要了解的三件事

1. 在生态学研究中，两个连续解释变量x ₁和x ₂之间相互作用的大小和方向通常通过拟合形式为 的统计模型来评估，其中x ₁ x ₂是衡量偏离效应可加性的相互作用项。
2. 在这里，我们强调与评估这种形式的统计模型中的相互作用相关的三个问题，这些问题在生态文献中似乎没有得到充分重视，但它们对我们如何拟合模型和正确识别相互作用具有重要意义。
3. 首先，对结果变量y建模的尺度（加法或乘法）很重要。改变分析规模的转换会改变相互作用术语的解释，并可能隐藏具有生态重要性的相互作用。其次，当解释变量相关并且存在未建模的非线性关系时，可能会出现虚假交互作用，在将统计模型拟合到非实验数据时可能会出现这种情况。第三，相互作用可能是非线性的，以至于相互作用项x ₁ x ₂不会包含所有生态利益的相互作用。
4. 我们使用与多种压力因素对生物多样性的影响相关的例子来说明这些问题中的每一个如何导致潜在的误导性结果。我们提供旨在从统计模型中正确识别交互效应的建议。