# Interpretation of average marginal effect for continuous variable in GLMM

I am trying to get a correct interpretation for the average marginal effect (AME) of a continuous variable in a logistic mixed effects model.

I know similar questions have been asked and answered (see here, here, and here), but I think there are subtleties here that justify asking this. (I am particularly asking about a logit link function but I think it is the same discussion with other link functions.)

My current understanding of the topic is (please correct me if I'm wrong) that the interpretation of the AME for a binary variable B in a GLMM is similar to its interpretation in a GLM.
Specifically, in logit models, if the AME is at the response scale (the default output in R's margins::margins or in Stata's margins, dydx), the interpretation of the AME is the average change in the predicted probability of the individuals in the sample to get Y=1 if B is changed for all of them from 0 to 1.

However, the marginal effect of a continuous variable X relates to the instantaneous rate of change for P(Y=1) with an infinitesimal change in X. And the AME is the average over all these changes.

First, please correct me if I am wrong here (e.g. is this indeed true also in GLMMs?). But even if it is true, could someone please help me figure out what this means in practice?

Specifically, my focal continuous variable is the serial position of an item within a sequence of items (there are many items), and I am modelling this as a continuous variable (there are also many other variables in the model that I control for). My computed AME for serial_position is 0.0032.
At the end of the day, I want to be able to write something like "on average, the probability of a yes response increases by 0.32% with each additional serial position", or, ideally, "the predicted probability of yes increases on average by 0.32*l percentage points from the first to the lth response in the sequence, which translates to 0.32*l*N additional yes responses merely as a result of the serial position of the item.

I am really not sure I can make such statements, but if I can't then it is unclear to me what use I can make of the AME here?

Thanks!