predicted probabilities using xtlogit, fe: The state of the art?

[Jonathan Horowitz]

Dear Statalisters:

There are a million threads on Statalist already for similar topics (e.g., https://www.statalist.org/forums/for...ter-xtlogit-fe), so many that I experienced decision paralysis about which one to bump and decided to start a new one.

The issues that have been raised in the past is that because xtlogit, fe doesn't estimate the fixed effects it's impossible to know what the actual marginal effect would be. Have there been any advances in figuring out how to calculate population-level predicted probabilities over a given categorical variable (e.g., by race/ethnicity, gender, etc) or over a continuous variable (e.g., year, age, height, etc)? I want to dig into this a little bit more but if someone has figured it out--or come up with new reasons why it doesn't work with the conditional logit estimator--I'd like to know.

Thank you for your time.

[Jonathan Horowitz]

FWIW: So far, the latest I've found is that you should use xtreg, fe instead and just deal with it.
https://pubmed.ncbi.nlm.nih.gov/33308684/

[Jeff Wooldridge]

What are your data dimensions? I think your best hope is to obtain betahat by xtlogit, fe. Then, for each i, use a logit with x(i,t)*betahat as an offset and an intercept as the only other regressors. This gives an alphahat(i) for each i. Then use alphahat(i) + x(i,t)*betahat inside the logit function as the prediction. But this will be very noisy unless T is pretty large. Moreover, there's no good way to obtain confidence intervals. Have you looked at the correlated random effects approach?

[Jonathan Horowitz]

Thanks for the reply! There are a lot of independent variables but we're talking about each respondent averaging well north of 100 data points in the sample. So it could very well work. I hadn't considered confidence intervals yet but that's something I should put on my to do list to look at for my linear probability models; I'm not sure if it would make sense with what I'm doing, logically, but I should at least look at it.

There's a chance that, per the Timoneda article I linked to above, what I'm really interested in is not the smaller sample of people who vary on Y but the full sample, in which case it's all irrelevant. But if I can use xtlogit, fe I can probably avoid an argument or two along the way so if it works I'd like to try it that way.

Regarding a correlated random effects approach, is this just specifying that the random effects are correlated with the independent variables? I know that in SEM you can turn a random effects model into a fixed effects model pretty easily just by correlating the errors. Is this like this? SEM is absolutely not an option due to the number of data points per respondent, but if the correlated random effects approach gets the same benefits as the fixed effects model (i.e., all time-invariant errors drop out of the model) then this could very well be a solution to a lot of my problems, especially if there's a logit link function.

[Jonathan Horowitz]

Update: It looks like there is no easy way to do postestimation after xthybrid (which seems to be the way to do it with a logit link) so I'd have to find a way to save the (correlated) random effects and calculate it manually.
https://www.statalist.org/forums/for...ybrid-vs-meglm