In Asymmetric Fixed-effects Models for Panel Data (available here open access: https://journals.sagepub.com/doi/10....78023119826441) Paul D. Allison indicates the following:

For the two-period case, there are several equivalent ways to estimate the fixed-effects model, all producing identical estimates.

Here are the three most common methods:
1. Least squares dummy variables (LSDV).
2. Mean deviation.
3. First difference.
I have also seen mean deviation referred to as mean difference. My question is, which method does xtlogit use and which does clogit use, and is this the same method regardless of number of time periods?

I have read the manuals (xtlogit: https://www.stata.com/manuals/xtxtlogit.pdf) and (clogit: https://www.stata.com/manuals/rclogit.pdf) but find myself lost in some of the more technical terms...

Any help would be appreciated!

John