To investigate the effect of partialling out M on T within each individual twin on the significance of parameters β a, β c, and β e, we simulated data according to the models shown in Figs. 2a–c, i.e., with correlations between T and M running either exclusively via A, exclusively via C, or exclusively via E. In these simulated data, T and M were both standard normally distributed. Also, T and M were correlated, but moderation effects of M on the cross paths and on the variance components of the residual of T were absent. For each scenario, we simulated 2000 datasets each comprising Nmz = Ndz = 500 pairs. We then fitted to these datasets the standard univariate moderation model with moderator M modeled on the means (Fig. 1b), and then constrained either β a, β c, or β e to zero to test for the significance of each parameter individually, i.e., a 1-df test. The difference between the −2 log-likelihood of the full model (the specific moderation parameter estimated freely) and the −2 log-likelihood of the restricted model
