I'm applying growth curve modelling and am interested in modelling a three-way interaction between predictors A x B x C. From what I remember a condition for modelling three-way interactions in regression analyses is to model all underlying related interactions as well (so AxB, AxC, and BxC in order to be allowed to model AxBxC). Can anyone confirm this (preferably providing a source) or am I confusing things and I could happily model higher-order interactions without including those lower order interactions of less interest?
The short answer is yes there are very good reasons to include lower order interactions. This has been answered before:
You might find this article helpful as well.