Recent research has shown that interaction effects may often be non-linear. As standard interaction effect specifications assume a linear interaction effect, i.e. the moderator conditions the effect at a constant rate, this can lead to bias. However, allowing non-linear interaction effects, without accounting for non-linear effects of other (control) variables, can also lead to biased estimates. Specifically, researchers can infer non-linear interaction effects, even though the true interaction effect is linear, when variables correlated with the moderator have a non-linear effect upon the outcome of interest. We illustrate this bias with Monte Carlo experiments and an empirical replication. We also provide guidance for researchers by assessing the performance of more fully specified models, estimated using regularised estimators to avoid overfitting, that can mitigate this bias. Doing so allows for more robust estimation of interaction effects, whether they be linear or non-linear in nature.