When Interaction Models Go Wrong: Simple Checks to Avoid Misleading Results

🔍 What This Paper Tests

Multiplicative interaction models are commonly used to ask whether the relationship between an outcome and an independent variable changes with a moderator. Two routine assumptions are often overlooked: that the interaction is linear (changing at a constant rate with the moderator) and that there is adequate common support of the moderator to estimate conditional effects reliably.

📊 How Evidence Was Collected

• Replicated 46 interaction effects reported in 22 recent publications across five top political science journals.
• Focused on whether the core assumptions behind multiplicative interaction models hold in applied work.

⚠️ What Was Found

• The assumed linear interaction form frequently fails in practice.
• Lack of common support for the moderator often makes estimates of conditional effects misleading.
• Because of these two problems, a large portion of published interaction findings across political science subfields are fragile and heavily model dependent.

🛠️ Practical Tools and Recommendations

• Checklist of simple diagnostics to assess whether:
• the linear interaction assumption is plausible, and
• there is sufficient common support to avoid excessive extrapolation.
• Flexible estimation strategies that allow nonlinear interaction effects and that limit inference outside the supported range of the data.
• Statistical routines implementing these diagnostics and estimators are available in both R and STATA.

📥 Why It Matters

These diagnostics and flexible estimators provide straightforward safeguards for applied researchers. Using them reduces the risk that interaction-based conclusions are artifacts of model choice or unsupported extrapolation, improving the credibility of moderation claims in political science.