When should I add interaction terms to my regression in practice?

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AcadiFi · Accepted Answer

Add interactions when theory or domain knowledge predicts that the effect of one variable depends on another. Do not add them mechanically as a data-mining exercise.

Clear cases for interactions:

1. Theoretical prediction. If Grimshaw Capital expects the effect of leverage on equity risk to depend on industry (utilities should be less affected than tech), an interaction between leverage and industry-dummy is warranted.

2. Policy or regime changes. Does marketing spend work differently before and after a brand refresh? Interact marketing with a post-refresh dummy.

3. Nonlinearity in a moderator. If two strategies combine multiplicatively rather than additively — e.g., return = skill × leverage — you need the interaction term to capture the product.

Signs an interaction helps statistically: the interaction t-stat is significant, AIC/BIC drops meaningfully, and out-of-sample prediction improves. If the interaction is insignificant and the main effects tell the same story without it, drop it.

Pitfalls to avoid: interactions invite overfitting, especially with small samples — a rule of thumb is you need at least 10-15 observations per estimated parameter. Always center continuous variables before forming the interaction so main-effect coefficients remain interpretable and multicollinearity with the product term is minimized. Include lower-order terms (both main effects) whenever the interaction is included, otherwise the model is misspecified and coefficient estimates are uninterpretable. Document WHY you included each interaction so reviewers don't mistake intentional theory for fishing.

When should I add interaction terms to my regression in practice?

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