Because we are interested in the full explanatory power of the interaction model (Equation 3) as compared to the main-effect model (Equation 2), we compare each model to the non-genetic base mode (Equation 1). When the main effect model is compared to the base model using a likelihood ratio Chi-square test with one degree of freedom, the significance of the overall main effect (β4) is evaluated. To evaluate the joint significance of the main effect and interaction, the interaction model (Equation 3) is compared with the base model (Equation 1) using a two-degree of freedom likelihood ratio Chi-square test. This approach has been formally explicated by Kraft and colleagues, who showed it to be comparable in power to other approaches for detecting G x E, with little loss of power in detecting main effect association where G x E is non-significant (Kraft et al. 2007). To facilitate evaluation of the goodness-of-fit for both main effect and interaction models, we present Akaike’s information criterion (AIC) for all genetic analyses. AIC is a log-likelihood based measure of model fit that penalizes for
