Caution with of Suggestions for Interpreting Regressions with Interactions

The central idea of an interaction is to model a conditional effect, i.e., the effect of one variable (x(i)) on the dependent variable (y(i)) depends on the values of another variable (z(i)). In their article, Mayerl and Urban discuss the properties of main and interaction effects and the pitfalls that can arise in their interpretation. Unfortunately, Mayerl and Urban give the impression that main and interaction effects can be meaningfully interpreted independently of one another. Although this may be true in exceptional cases, it is not generally recommendable. We show that an isolated or independent interpretation of main and interaction effects can be misleading, even if the specific problems discussed by Mayerl and Urban are not present. Because the effects of covariates that are part of the interaction are conditional effects, it is advisable to present and interpret them in a way that includes all covariates involved in the interaction. We recommend a (graphical) representation that gives information about how the effect of x(i) on y(i) varies over the range of z(i).