M ran via E. In testing for the significance of β e, the false positive rate was only significantly elevated if the correlation between T and M ran via E (7.50%), but not if the correlation ran via A or C (4.57 and 5.26%, respectively). The additional simulations summarized in Table 2 show that the false positive rate of the univariate moderation model is a) correct if M1 and M2 are unrelated, i.e., when the variance in M is completely due to nonshared environmental influences E, b) slightly too low if M1 and M2 are correlated 1, i.e., when the variance in M is completely due to shared environmental influences C, and c) correct if the covariance between M and T runs in equal proportions via A, C and E. This latter result shows that the extent to which the false positive rate of the univariate moderation model is elevated depends on the specific mix of, or ratio in which, A, C and E contribute to the covariance between M and T since the positive and negative semi-partial correlations as described in Table 1 can more or less cancel each other out.Table 2Results Simulation study 1: false positive rates under
