The results for both the extended univariate moderation model and the full bivariate moderation model are described in Table 3, and depicted as PP-plots in Fig. 4 for the extended univariate moderation model.
\\ \end{aligned} $$\end{document} With 12 parameters (6 to describe the variance part of the model: 3 related, and 3 unrelated to the moderator; and 6 parameters to describe the means models: 3 for MZ twins, and 3 for DZ twins), this extended univariate moderation model is still more parsimonious than the bivariate moderation model (17 parameters of which 15 concern the variance decomposition).
In a fourth and fifth simulation study, we investigate whether the false negative rate of the extended univariate moderation model is comparable to the false negative rate of the bivariate moderation model when the covariance between M and T is not subject to moderation (Simulation study 4) or when this covariance is subject to moderation as well (Simulation study 5).
The p-values concern p-values of the binomial test for comparing two proportions, used to test whether the number of hits under the extended univariate moderation model is significantly different from the number of hits under the full bivariate moderation model The results of these simulations are presented in Table 6.
Overall, we conclude that researchers should use the full bivariate moderation model to study the presence of moderation on the covariance between M and T. If such moderation can be ruled out, subsequent use of the extended univariate moderation model is recommended as this model is more powerful than the full bivariate moderation model.
The p-values concern p-values of the binomial test for comparing two proportions, used to test whether the number of hits under the extended univariate moderation model is significantly different from the number of hits under the full bivariate moderation model.
We conducted Simulation study 2 to investigate whether the false positive rate of this extended univariate moderation model is correct, and comparable to the false positive rate of 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.
In 5 out of 9 scenarios, the power of the extended univariate moderation model was significantly higher than the power of the full bivariate moderation model.
Since all conditions were met, we concluded that the proposed mediated moderation model was supported.
