accommodate the varying association between M and T. As a result, the remaining moderation, which is actually located on the cross paths, is now picked up in the extended univariate moderation model as if it were located on the unique paths of T. Additional simulations (not shown), in which either β ac , β cc or β ec equaled .10 while the other two cross path moderation parameters equaled .05, showed even higher hit rates for the extended univariate model (up to 65%), while the hit rate of the full bivariate moderation model remained .05 or lower.Table 4Results Simulation study 3: false positive rates under the extended univariate moderation model and the full bivariate moderation model when the covariance between T and M is moderatedDrop β a Drop β c Drop β e % hitsnsim% hitsnsim% hitsnsimBaseline: β ac = β cc = β ec = 0 Ext univariate.051999.052000.051999 Full bivariate.022000.012000.052000 p < .001 p < .001 p = .42 β ac = .10; β cc = β ec = 0 Ext univariate.181998.181999.081996 Full bivariate.032000.022000.062000 p < .001 p < .001 p < .01 β cc = .10; β ac = β ec = 0 Ext univariate.132000.131999.071999 Full bivariate.022000.022000.052000 p
