The Stata Journal (2010) Vol. 10 No. 2, pp. 305-308.
In non-linear models we can often present results on an additive scale, by presenting marginal effect, or on a multiplicative scale, by presenting odds ratios, or incidence-rate ratios, or hazard ratios. Interpreting interactions on an additive scale is relatively complex (see for example this article by Edward Norton, Hua Wang, and Chunrong Ai). In the current paper I illustrate how the interpretation of interactions is substantially easier when interpreting the effects on a multiplicative scale, but also shows that both types of effects answer subtly different questions, meaning that there is an added value in having both tools in ones toolbox.
There is also an active debate on whether interaction effects in non-linear models for binary dependent variables have any interpretation at all. This article does not deal with that debate. I am less pessimistic than others in this regard. The arguments for this optimism are set out in this working paper.