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. The false positive rate of the extended univariate moderator model is in most cases not significantly different from 5%, and where it is (when variance in M is completely due to C, and thus rM1,M2 = 1), it is too low, i.e. the test is too conservative. In contrast, the false positive rate of the full bivariate model is always too low, and significantly lower than the false positive rate of the extended univariate model, when testing β a or β c, irrespective of the nature of the correlation between M and T. Apparently, slight misfit in the full bivariate moderation model resulting from dropping one parameter 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
