Time consistency of interaction effect in GLM

I am thinking about how one should check for time consistency of in a GLM.

Model:

$$\eta_{ijk} = \beta_{0} + \beta_{i}Year+\beta_{j}Var1+\beta_{k}Var2+\beta_{jk}(Var1 \times Var2)$$

If I were to add a time-interaction for the interaction variable (i.e. without time interactions for main effects) $\beta_{ijk}(Var1\times Var2\times Year)$, and plot the predicted values for each year we would see how the modeled interaction variable varies with time. But would it be more suitable to control for the main effect time interactions as well?

Given that the main effects are fairly consistent with time my opinion would be that it sould not matter.

Any objections or suggestions?

• It is nearly always a bad idea to include an interaction without the lower order terms, and I don't this is an exception to the rule. Why force the 2 way interactions to be 0? – Peter Flom Nov 2 '12 at 11:11
• My thought was that if the main effects are independent of year it should not matter, if using the model above we are assuming that this is the case as well. You are correct, given this assumption including $(Var1\times Var2\times Year)$ would not be a pure interaction of time and interaction variable. We might also catch some of the time inconsistency of main effects as well. – Patrik Emanuelsson Nov 2 '12 at 11:29
• OK, but if you are right, then you lose very little - you estimate two parameters that will be close to 0. If you are wrong, you've got a real mess. There are some cases where the lower order terms can be left off, but they are rare. See this question and its comments for more. – Peter Flom Nov 2 '12 at 11:36