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Conditional effects, or interaction effects, do not imply multiplicative effects. However, product terms are the default method for modeling such conditional effects in psychological research. As a result, theoretically plausible conditional effects may go undetected when the functional form is misspecified. Our study had two objectives: (1) evaluate the extent to which non-linear phenomena can be identified as spurious multiplicative (i.e., standard) interaction terms in linear models, (2) assess how well linear models capture stepwise conditional effects. In Study 1, we examined spurious interactions from non-linear main effects. We found that traditional interaction terms were associated with increased Type-I error rates and small effect sizes. Importantly, this was also the case when the predictors were uncorrelated, indicating a mechanism beyond collinearity. Additionally, we found that, if captured, the spurious interaction effects did reduce prediction error on the population level. In Study 2, we simulated genuine conditional effects, following a stepwise pattern. When effects were monotonic, product terms performed adequately, however if the conditional effect is non-monotonic a traditional interaction term in a linear model does not sufficiently capture such an effect. We conclude that relying solely on traditional interaction terms in linear models can be misleading and the failure to replicate interaction effects may partly reflect a specification crisis: Researchers default to one functional form (multiplication) while the underlying theory may dictate a different form, creating a systematic mismatch between theory and model. To validly investigate conditional effects, researchers should specify and justify the expected functional form a priori.