Graphing interactions with margins after melogit with random intercepts

[Amanda Smith]

I have an interaction term between season and temperature in my final model (both 4-level categorical), and I want to graph this to show the probability of my outcome variable (a dog testing positive for a disease - dichotomous Y/N) for each category of temperature during each season.

I used melogit for the model with random intercepts for state and county. I then used the margins command and marginsplot to graph the interaction:

melogit Positive i.AgeC GenderCC i.RegionCC i.Year i.DogDensC i.UICC i.PDSIC i.PrecipC i.SeasonC##i.TempC || CustState: || FIPS:

margins TempC, at(Season=(0(1)3))

marginsplot, by(SeasonC)

This produced graphs with the marginal predicted means on the y-axes (see below). I had read in another topic thread within this forum that these marginal predicted means are in fact the probabilities? Is that true? If so, then why are these y-axes starting at -0.05? Is that just because of the large confidence interval on the season=3 graph? (note: my dataset has 40,118 observations, but there are 0 observations when temp=0 and season=3 and only 32 when temp=1 and season=3. That is why the graph for season=3 looks the way it does.)

If the marginal predicted means are not the probabilities, then is it possible to estimate probabilities to graph the interaction given this model?

[Clyde Schechter]

Yes, those are the predicted probabilities. And, yes, the negative values on the vertical axis are there because the graph is trying to accommodate the lower confidence limit that goes below 0. It seems paradoxical that a confidence interval for a probability could extend outside the 0 to 1 interval, but that happens because -margins- uses the delta method to calculate the standard errors, and then uses normal theory approximation to calculate the confidence interval from those. This sometimes works out to implausible limits on confidence intervals when the predicted probability itself is close to 0 or 1 and the prediction itself is not very precise.