cmclogit + margins + interactions

[Irene Prix]

Hello!

I'm trying to use a McFadden's choice model using cmclogit with case- and alternative-specific variables. I'm interested in examining how the average marginal effect of an alternative-specific variable varies across alternatives.

Here's an example for the basic main effects model (with time being the alternative-specific variable, and mode the alternative-id)

use https://www.stata-press.com/data/r16/travel, clear

cmset id mode // setup case-id and alternative-id

gen time=traveltime+termtime

* main effects cmclogit-model
cmclogit choice time , casevars(income partysize)

It looks like this model could tell me how the (direct/indirect) average marginal effect of time varies across alternatives, e.g.

margins, dydx(time)
marginsplot

But I'm a bit unsure at this point: if I wanted to know how the effect of the alternative-specific variable varies across alternatives, wouldn't I need to interact it with the alternative-ID? Wouldn't the variation of the time effects across alternatives in the main effects model be partly due to the inbuilt interactions of the logit model, rather than necessarily indicating a "real" interaction (or am I completely on the wrong track in my thinking here)?

In other words, wouldn't I need the following model instead of the main effects model:

cmclogit choice time c.time#i.mode, casevars(income partysize)

If the latter model would be correct (it runs fine), I still wonder how I would use the margins command in this case: if this was an ordinary logit, I'd use margins dydx(time), over(alternatives) -- but that doesn't work after cmclogit.

Any help in getting me out of my confusion is greatly appreciated!

Best,
Irene