can quite easily be accommodated by adjustment of the remaining parameters, resulting in a too low false positive rate. In addition, it is important to realize that the variance components unique to trait T under the bivariate model (Au, Cu and Eu in Fig. 1a) are not the same as the variance components of the residual T″ in the extended univariate parameterization. In Appendix 1, we show how the residual T″ is calculated when M and T are correlated via A, or C, or E. The fact that the variance decomposition of T″ is not the same under the bivariate and the univariate moderation model implies that either model can constitute a more or less erroneous approximation, depending on the real data generating process, which is generally unknown.Table 3Results Simulation study 2: false positive rates under the extended univariate moderation model and the full bivariate moderation model when the covariance between T and M is not moderatedDrop β a Drop β c Drop β e % hitsnsim% hitsnsim% hitsnsimrM,T .24 via A Ext univariate.042000.042000.041998 Full bivariate.012000.012000.042000 p < .001 p < .001 p = .88rM,T .24 via C Ext univariate.042000.042000.052000 Full bivariate.011999.011998.042000 p < .001 p < .001 p =
