The results of these simulations are presented in Table 6. In all scenarios, the extended univariate moderation model picks up moderation more often than the full bivariate moderation model. However, these results can, except for the Baseline model, not be interpreted as the extended univariate moderation model having more power than the full bivariate moderation model. Given the results of Simulation study 3, which showed that the extended moderation model picks up the moderation on the cross paths as if it is moderation on the unique paths, we conclude that the power of the extended univariate moderation model is too high, or at least that the location of the moderation that is detected, is uncertain. That is, β a, β c, and β e are biased in the extended univariate moderation model because the moderation on the cross paths (β ac, β cc, and β ec) is not adequately accommodated by the regression coefficients in the means part of the model.
