Testing witthout interaction terms

[Claude Francoeur]

Hello,

Our OLS model is : Y = FBR + FBRsquared + AL + FBR X AL + FBRsquared X AL

Using this model, we get significant coefficients for all variables, but since the results are not easy to interpret, we calculate marginal effects (slopes) at different levels of FBR and predictive values at different levels of FBR for both values of the binary variable AL.
We also us graphs to depict the relationships between FBR and Y, with and without the interaction term AL.

But, our reviewer claims that we need to run our models without the interaction terms included. He also demands that our results hold without the interaction terms included.
Is this a fair demand, or can it be debated? Without the interaction terms, the p-values of the coefficients of FBR and FBRsquared go up to close to 10% or a little more.

Thanks for your help.

---

[Clyde Schechter]

Is this a fair demand, or can it be debated?

Well, it depends on what conclusion you are trying to draw from the results. An interaction model is usually best used to explore the differences in the effect of one variable conditional on another. If, however, your research question just asks about the overall effect of one variable, regardless of the other, then an interaction model is misleading.

So I think to answer your question, we would need to know exactly what your research question was and what answer to it you are claiming to make based on your results. It would also be a good idea for you to show the exact Stata commands you used for the regression and -margins-, as it is also possible that an interaction model was appropriate, but not correctly implemented in Stata. The results of those regressions and -margins-, would shed additional light on the dispute as well as it would facilitate interpretation of the results more specifically. (Just knowing that some terms were "significant", or even knowing the full p-values, really is not at all helpful in understanding what the results mean, especially in interaction models.)

[Claude Francoeur]

Thanks. Our first hypothesis is that the effect of FBR on Y is curvilinear. When running Y = FBR + FBRsquared + AL, we do not get significant coefficients of FBR and FBRsquared.
But, when we run a more complete model to test H1 and H2 together (H2 implies interactions) we do get significant coefficients for FBR and FBRsquared..The complete model is: Y = FBR + FBRsquared + AL + FBR X AL + FBRsquared X AL,

Same pattern for the marginal slopes at different levels of FBR.

We think our second model is more thorough. But how can we convince ourselves (and the reviewer, that is the case)?

Thanks for your help.

[Clyde Schechter]

In #3 you have basically just repeated what you said in #1. You have not really replied to my questions in the second paragraph of #2, so there is nothing more I can say to you at this point. And, reflecting further on what I said in #2, I left out something important specifically for this situation. It is critical to know what the variables Y, FBR, and AL are, and what the qualitative relationships among them are--in particular the nature and direction of any causal relationships among them.

[Claude Francoeur]

Thank you.