Need help with xtmlogit

[Erda RH]

Hi everyone,
I would like to ask if someone can help me please with the problem I got when I tried to run xtmlogit.
So, I did xtset followed by xtmlogit, and the analysis came out as "cannot compute an improvement -- discontinuous region encounteredr(430);' at the end of the analysis (as I copy pasted below).
May I have an idea of what could be the reasons and how to solve this? I am sorry if my question is very technical, I am a very beginner in STATA.
Thank you so much, I really appreciate your help.

. xtset districtcode

Panel variable: districtcode (unbalanced)

. xtmlogit abres4cat nmilking

Fitting comparison model ...

Refining starting values:

Grid node 0: log likelihood = -186.34118
Grid node 1: log likelihood = -184.06224

Fitting full model:

Iteration 0: log likelihood = -184.06224 (not concave)
Iteration 1: log likelihood = -183.56712 (not concave)
Iteration 2: log likelihood = -183.32706 (not concave)
Iteration 3: log likelihood = -183.22912 (not concave)
Iteration 4: log likelihood = -183.22422 (not concave)
Iteration 5: log likelihood = -183.22324 (not concave)
Iteration 6: log likelihood = -183.22285 (not concave)
Iteration 7: log likelihood = -183.22284 (not concave)
Iteration 8: log likelihood = -183.22284 (not concave)
Iteration 9: log likelihood = -183.22284 (not concave)
Iteration 10: log likelihood = -183.22284 (not concave)
Iteration 11: log likelihood = -183.22284 (not concave)
Iteration 12: log likelihood = -183.22284 (not concave)
Iteration 13: log likelihood = -183.22284 (not concave)
Iteration 14: log likelihood = -183.22284 (not concave)
Iteration 15: log likelihood = -183.22284 (not concave)
Iteration 16: log likelihood = -183.22284 (not concave)
Iteration 17: log likelihood = -183.22283 (not concave)
Iteration 18: log likelihood = -183.22283 (not concave)
Iteration 19: log likelihood = -183.22283 (not concave)
Iteration 20: log likelihood = -183.22283 (not concave)
Iteration 21: log likelihood = -183.22283 (not concave)
Iteration 22: log likelihood = -183.22283 (not concave)
Iteration 23: log likelihood = -183.22283 (not concave)
Iteration 24: log likelihood = -183.22283 (not concave)
Iteration 25: log likelihood = -183.22283 (not concave)
Iteration 26: log likelihood = -183.22283 (not concave)
Iteration 27: log likelihood = -183.22282 (not concave)
Iteration 28: log likelihood = -183.22282 (not concave)
Iteration 29: log likelihood = -183.22282 (not concave)
Iteration 30: log likelihood = -183.22276 (not concave)
Iteration 31: log likelihood = -183.22276 (not concave)
Iteration 32: log likelihood = -183.22276 (not concave)
Iteration 33: log likelihood = -183.22275 (not concave)
Iteration 34: log likelihood = -183.22228 (not concave)
Iteration 35: log likelihood = -183.21928 (not concave)
Iteration 36: log likelihood = -183.21913 (not concave)
Iteration 37: log likelihood = -183.2172 (not concave)
cannot compute an improvement -- discontinuous region encountered
r(430);

[Maxence Morlet]

It seems like the log-likelihood function is not concave: the second derivative of the log likelihood is not negative, meaning that any estimate that's generated will not be a global maximum - quite problematic for maximum likelihood estimation...

Stata proceeds using the Newton-Raphson algorithm, where x_t+1 = x_t - f'(x)/f(x) (someone please correct if I'm wrong) and in your case, I presume that at some point, the first derivative was undefined, so Stata had to stop its iterations.