As opposed to that, both the right plot in Figure 4 and the original plot in Figure 1 represent interactions, because the effect of alcohol_per_month is different in both branches created by friends_smoke. In the right plot in Figure 4 the same split in alcohol_per_month is conducted in every branch created by friends_smoke, but the effect on the relative frequencies of the response classes is different: for those subjects who have no friends that smoke, the relative frequency of a “yes” answer is higher if they drank alcohol in 2 or more occasions (node 4 as compared to node 3), while for those who have one or more friends that smoke, the frequency of a “yes” answer is lower if they drank alcohol in 2 or more occasions (node 7 as compared to node 6). This example represents a typical interaction effect as known from standard statistical models, where the effect of alcohol_per_month depends on the value of friends_smoke.
