In summary, we demonstrate that modeling gene-environment interaction using a cross-product term when the genotype is coded using three categories is problematic and should be abandoned. We present a reparameterization of the regression equation that accurately captures the shape of potential interactions that may exist in the data. We suggest that researchers interested in the study of gene-environment interaction effects (as well as any researchers testing for interaction with polytomous variables) use a six-parameter model equation (or more, depending upon the number of levels within the categorical variable) in future tests of interaction effects. Moreover, existing reports of interaction effects in the literature that applied the cross-product regression approach (the four-parameter model) tothree-category genotype variables must be re-evaluated to assess their accuracy.
