Interactions are tested by multiplying two first-order (here, gene and environment) predictors together, creating a product term. All three variables (the two first-order variables and the product term) are entered into the model, and a significant product term is evidence for interaction effect. It is often argued (e.g., in Caspi et al. [1]) that the reduction in power to detect interaction effects is due to the correlation between the product term and the first-order predictors, but this is incorrect; the correlations between the product and the first-order terms plays no role in the power to detect interactions (8). This can be seen by centering (subtracting the mean from) symmetrically distributed first-order predictors, which reduces the correlation between product and first-order terms to ~0 but does not change the significance level of the product term. (The same effect occurs for nonsymmetrically distributed predictors, although the constant subtracted will not be the mean; see Smith and Saski [28]).
