It was suggested to me recently that the significance of an interaction term in a glm has to be higher than a main effect. For example, p<0.05 is commonly thought of as significant for a main effect but a two-way interaction has to be higher (p<0.025 or something) and a three-way even higher. However, I can't find any literature on this so I am unsure. Are they getting confused with multiple comparisons I wonder? Or am I confused and the two things are linked?
I've never heard that and, to me, it makes little sense.
First there are all the usual problems with p values and cutoffs. But, if anything, I think the p value cutoff for interactions ought to be more lenient than that for main effects, since they can be harder to find if either or both main effects are measured less than perfectly reliably.