Summarizing the results of Simulation study 2, we conclude that the extension of the univariate moderation model avoids the inflated false positive scores that were observed for the standard univariate moderation model, while the full bivariate moderation model actually proved too conservative. However, Simulation studies 1 and 2 concerned scenarios in which the covariance between M and T was itself not subject to moderation, i.e., β ac, β cc, and β ec on the cross paths between M and T in Fig. 1a were fixed to 0. That is, the covariance between M and T did not dependent on the level of M. In practice, however, it is possible that the covariance between M and T fluctuates as a function of M. Simulation study 3 was conducted to investigate the false positive rate of the extended univariate and the full bivariate moderation models in the context of data in which the covariance between M and T is moderated. These simulations are of specific interest since moderator-dependent variation in the strength of the covariance between M and T is not well
