Interaction terms: significance and interpretation

[Marine Jouvin]

Hi,

I'm currently performing a conditional logit with FE with some interactions.

I, as an example, interact a dummy variable indicating a game session number (taking the value of 2 or 3) with a continuous variable (a "cheating observation rate"). I have the following results:

I'm not sure how should I interpret the results for the interaction term. Does this suggest that what I called "cheating observation rate" does indeed have a negative relationship with my dependent variable, but only during session 2?

[Luca Calianno]

Hi, with logit it is difficult to interpret the coefficients right away. You can only interpret the signs, and I would agree with your interpretation.
Nevertheless, I suggest you use the command margins (e.g. margins, dydx(cheating rate) over(sesstion) ) and then you can have an easier interpretation of your results.

[Marine Jouvin]

Hi Luca,

Thanks for your answer ! Indeed, I use margins rather than the coeffs. I have a related question.

Here are the results from a same xtlogit regression with FE as in my previous post, displaying coeffs :

Here are the margins for every variable in the model (except the interaction one), obtained with

margins, dydx(*) post

:

And here are margins for the interaction term, obtained with

margins, dydx(prev_cheat_rate) over(id_session)

:

I was wondering which margin should I report for the variable "prev_cheat_rate" ? Should I report the margin associated with "prev_cheat_rate" (-.281) or the one associated with prev_cheat_rate##session 1 (-.106) ?

[Luca Calianno]

It depends on what you want to argue/show. Both are valid measures to be reported.
The average marginal effect of prev_cheat_rate for all session is obtained from: margins, dydx(*) post. -0.106 is the effect of prev_cheat_rate in the first session.
I really don't know what you are estimating, I would very broadly suggest that if you want to show the effect of the cheat rate overall show the -0.28; if you want to show how it varies by session show the second table