Interactions in statistical models: Three things to know

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 (Formula presented.), where x₁x₂ is an interaction term that measures departure from additivity of effects. 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. 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. 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.