Costs and Benefits of Including or Omitting Interaction Terms: A Monte Carlo Simulation.

What costs or benefits might accrue from including or omitting interaction terms? Failing to account for theoretically important interaction creates the risk of omitted variable bias. Yet, introducing many interaction terms whose effects are small may unnecessarily complicate the model and its interpretation. This analysis uses a Monte Carlo simulation to investigate how wrongly omitting or including an interaction term affects the predictive power of models and the bias of coefficients. Wrongly including an interaction term has little effect on the bias of estimates or on the loss of predictive power. Wrongly omitting an interaction term creates larger biases and a loss of adjusted R2. The bias of estimates is largest in the case of data with dichotomous variables and depends on the size of the interaction effect, whereas the loss of predictive power is largest in the case of the interaction of two strongly correlated continuous variables, and in data-sets with small error variance.