xtmelogit vs. melogit I have already asked some related questions, but I am still unsure about the following Stata commands. 
Could anyone tell me how these commands/models are different from each other? 
xtset subject decisionnumber
xtmelogit depvar iv1##iv2 || study:

melogit depvar iv1##iv2 || study: || subject:

 A: In Stata, xtset is used when you want to use the xt suite of commands and the purpose of xtset is to tell Stata what your panel ID and time variables are. Note that xtset is to be used in conjunction with a host of xt models, including xtreg, xtlogit, and xtpoisson but not xtmelogit. See the very clear documentation in Stata's xt manual.
xtmelogit depvar iv1##iv2 || study:

In this case, you are using xtmelogit, which is not the most up-to-date version of this command in Stata, and also, confusingly, does not connect with xtset. Thus, the xtmelogit command you are using assumes that there is only 1 random intercept of interest - study. That is not what you want. 
Instead, you should use 
melogit depvar iv1##iv2 || study: || subject:

which appropriately indicates your random effects structure as being 3-level, observations nested within subjects nested within study. As I mentioned in a previous response to you, with only 4 studies, it is questionable whether you want to study include this as a random intercept. You could easily include it as a fixed intercept and would not have to make the same distributional assumptions as you do by including it as a random effect:
melogit depvar iv1##iv2 i.study || subject:

Ultimately, it is  up to you which way you want to go with study. 
