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Uri Simonsohn, 'Interacting With Curves: How to Validly Test and Probe Interactions in the Real (Non-linear) World
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Uri Simonsohn (email@example.com) ABSTRACT
Hypotheses involving interactions, where one variable modifies the association between another two, are very common. They are typically tested relying on models that assume effects are linear, e.g., with a regression like y=a+bx+cz+dx·z. In the real world, however, few effects are linear, invalidating inferences about interactions. For instance, in realistic situations, the false-positive rate can be 100% for detecting an interaction, and a probed interaction can reliably produce estimated effects of the wrong sign. This paper proposes a revised toolbox for studying interactions in a curvilinear-robust manner, giving correct answers 'even' when effects aren't linear. It's applicable to most study designs, and produces results that are analogous to those of current -often invalid- practices. The presentation combines statistical intuition, demonstrations with published results, and simulations.