For our primary analyses, we evaluated whether parent–child conflict moderated the etiology of CP using the ‘extended univariate G × E’ model (Purcell, 2002; van der Sluis et al. 2012). In this model (see Fig. 1a), the variance decomposition of CP was modeled as a function of parent–child conflict. To circumvent possible gene–environment correlational confounds (in which genetic effects overlap across the moderator and the outcome), the moderator values of both twins were entered in a means model of each twin’s CP. Moderation was then modeled on the residual CP variance (i.e. that which does not overlap with parent–child conflict). The first and least restrictive of these models allows for linear and non-linear moderation. We then fitted a series of more restrictive moderator models, constraining the moderators to be zero and evaluating the reduction in model fit.
