The majority of these previous GxE studies used the univariate and bivariate models to study moderation as delineated in Purcell (2002). The univariate model allows for both linear and nonlinear moderation of either the mean or the variance (conditional on the moderator) of the behavioral outcome. The bivariate model explicitly models the covariance between the behavioral outcome and the moderator, and allows for moderation of both the common and unique variance components. In a more recent examination of these models, van der Sluis et al. (2012) demonstrated that under certain conditions, the bivariate model has an increased false negative rate (Type II error) and the univariate model can result in false positives (Type I error). To address this problem, van der Sluis et al. (2012) extended Purcell’s univariate model so that the behavioral outcome of each twin is corrected for the potential correlation with their own and their cotwin’s value of the environmental moderator. Simulation studies showed that this extended univariate model accurately detected moderation and is more powerful than the bivariate model. However, if the covariance between the moderator
