When considering multilevel mediation, centring is often applied to lower-level variables. One well-established approach for this separates the lower-level variables into a W(ithin)- and B(etween)-cluster component in linear settings, as to effectively eliminate additive upper level confounding of the mediator M and the outcome Y. When moderated mediation is considered, however, careful thought is needed about the method of centring; partitioning the interaction can be achieved in two ways: multiply the main effects that make up the interaction first, and apply centring within clusters next, or the other way around. Alternatively, M and Y can also be modelled jointly, hereby also allowing for unmeasured additive upper M-Y confounding, but at the same time avoiding any necessity for centring of both the main and the interaction effects. Employing simulations, we study the performance of these three approaches in the presence of interactions under varying data generating mechanisms, and discuss the relative merits of each approach
