Is it possible to calculate AMEs for non-linear interactions

[Sarah Thea Smith]

My logistic regression model includes the following interaction:

x1*x2*time*time^2

Where x1 and x2 are both dummy variables, and time is a variable ranging from 0 to 25.

In a previous model that only contains a x1*x2 interaction, I was able to calculate the AME of the interaction term using the following code (I am using mi imputed data):

mimrgns x1, dydx(x2) predict(pr) pwcompare

Is it also possible for me to calculate individual AME values to be presented in a regression table for the interaction terms that arise from my more complex model, namely:

x1*x2

x1*time
x2*time

x1*time^2
x2*time^2

x1*time*time^2
x2*time*time^2

If so, how should I go about doing it? (I'm using StataSE v16.01)

At present, I am presenting log-odds in the regression table to give an initial idea of the relationships, and then plotting the AMEs over time, but I have received feedback asking me to already present AMEs in the regression table as well, which is why I am asking.

Thank you!

[Andrew Musau]

The conventional thinking is that there is no marginal effect for an interaction term. You cannot change the interaction term independently, holding constant its constituent terms. I would refer you to Richard Williams's SJ article and slides which have an extensive discussion on marginal effects, including the point I make. So if I were you, I would not follow some of these old literature - but it is no criticism on the literature itself. See https://www3.nd.edu/~rwilliam/stats/Margins01.pdf and https://www.stata-journal.com/articl...article=st0260.

[Sarah Thea Smith]

Thank you, that is very helpful.

Would you argue the same in the case of the cross-sectional example with two dummies? In that case being able to calculate a single AME value for a table did make sense to me given that both variables are either 0 or 1, so the AME of the interaction term is essentially the difference between x1 when x2=0, and x1 when x2=1 (and vice versa), but I don't know whether presenting an AME table goes against convention no matter what.

[Andrew Musau]

With the -contrast- option of margins, you can compute the discrete interaction effects as I illustrated in your earlier thread. The approach is not incorrect, but I don't see people doing that these days. And probably readers would have a hard time interpreting what these results are. Usually, they report the logit/ probit coefficients and if also reporting AMEs, these do not include interaction terms (as the -dydx()- option of margins will drop these). Outside economics, odds ratios are popular and few researchers report AMEs. Have you looked at recent publications in your field? What do they do?

[Sarah Thea Smith]

Thank you, that makes sense. Odds ratios do seem the most common in my field, but my supervisor is adamant that I should present AMEs, and he does know the field better than me. I will discuss this with him again!