There are at least two related potential objections to the recommendation to include all relevant covariate-by-gene and covariate-by-environment interactions to models estimating a G×E term. The first has to do with overfitting: with so many terms, it may be unrealistically hopeful to obtain precise estimates of all the covariate interaction terms, especially if sample sizes are small. However, the purpose of including covariate interaction terms is not to estimate their effects per se, but rather to control for their effects on the G×E term of interest. The second potential objection is that, with a large number of interaction terms included in the model, multicolinearity may degrade evidence for the G×E term. However, this is entirely the point. To the degree interaction terms containing covariates are correlated with the G×E term, alternative explanations for the observed G×E interaction are possible. Moreover, inclusion of covariate interaction terms in a model tested on the full dataset is a much more statistically powerful approach for controlling potential confounders than is splitting the data by covariates and testing the G×E term in each subset of
