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You started this thread, by proxy, with a question about bcoeff (SSC).
bcoeff is by default just a wrapper for plain regress. When I said it was redundant, I was just referring to the facts advertised already in 2004 in the documentation on SSC that, depending on what you are doing, it is better to think about using regress (or some other model-fitting command) within a framework provided by foreach or statsby. You somehow take that as possibly explaining why the results from bcoeff are puzzling you. My challenge remains totally unanswered: if you regard the results from bcoeff as puzzling, then you need to show that bcoeff is somehow mangling your results. In principle, this is easy: run the results from regress separately and show that they are not as reported by bcoeff. If you can't do that, then the conclusion is just that you have puzzling regress results and whatever the reason for that it is nothing to do with bcoeff. If you don't understand what bcoeff is doing, then I see no point to your using it.
The failure to understand what you are doing is not just mine. Joseph explained at length that he cannot see how you got the results you report, but you don't address that point at all. Showing us different code for xtmixed and different graphs is not addressing that.
I suggest that you seek advice locally from someone with statistical and Stata expertise.
Thank you very much for the patience of letting me learn and know here. I feel so happy that I finally found the problem. It is you and Joseph who helped me a lot in the process of seeking the true answer. It's not easy for the beginners, but I really learned something.
You're right. It's not the problem with bcoeff, but my dataset. I debugged a few things in my dataset and reran the do file again and got what I expected at last.
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