Data were simulated as described in Simulation study 3 with covariance between M and T running via A, C and E, and moderation on the cross paths was introduced by setting either β ac, β cc, or β ec to .10 (see Table 6 for description of the scenarios). Moderation on the unique parts of T was now simulated to be present as well, with moderation parameters being either β a = .08, or β c = .10, or β e = .035 (as in Simulation study 4). For each scenario, we simulated 2000 datasets and analyzed these using both the full bivariate moderation model (estimating moderation parameters on the cross paths as well as on the paths unique to T) and the extended univariate moderation model (estimating moderation on the variance components of the residual T″). We then tested whether the moderation parameter of interest (either β a, or β c, or β e) was significant given α = .05.Table 6Results Simulation study 5: false negative rates under the extended univariate moderation model and the full bivariate moderation model
