"Hessian is not negative semidefinite" when using xtmixed

[Sue Park]

Hi,

I am analyzing several waves of longitudinal dataset to see whether there are significant interaction between genetic factor (pgsgeneral) and trauma experience(dichokid, 0=no, 1=yes) on cognitive measures (crystal), after controlling for covariates (variables listed after the syntax global control) using xtmixed.
Syntax that I am using is as below.

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global control "rfemale rage rage_sq rempl rret rsd rsingle rfair rgood rvgood rexcel rhibp rdiab rc
> ancr rlung rheart rstrok rcesd rpsych rarthr i.rsmokcat i.rbmicat i.rlight lnrdrink ihshwealth i.edu
> cat hnoppl chld rhins lnhinc PCA PCB PCC PCD PCE"

. xtmixed crystal c.pgsgeneral##i.dichokid $control || hhidpn:rage if sample_woedu_1==1, covariance(un
> structured) mle

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However, after running this syntax, I encountered the message that Hessian is not negative semidefinite. Please see below. However, when I used different outcome measures other than crystal, it does not show the error message. Crystal is such an important outcome measure, so I am trying to find a way to solve this error.
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Performing EM optimization:

Performing gradient-based optimization:

Iteration 0: log likelihood = -23195.549
Iteration 1: log likelihood = -22974.72 (not concave)
Iteration 2: log likelihood = -22951.83 (not concave)
Iteration 3: log likelihood = -22942.059 (not concave)
Iteration 4: log likelihood = -22937.871
Iteration 5: log likelihood = -22925.872
Iteration 6: log likelihood = -22921.494
Iteration 7: log likelihood = -22921.452
Iteration 8: log likelihood = -22921.452
Iteration 9: log likelihood = -22921.452
Hessian is not negative semidefinite
r(430);

end of do-file

r(430);
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In this case, what does this error message mean? I was trying to find the answer by googling this stata forum and several literature, but I have no clue yet.
I am wondering if there would be anyone who would have some clue how I can address this issue. Thank you very much in advance for any of your input or experience.

[Joseph Coveney]

I am wondering if there would be anyone who would have some clue how I can address this issue.

Two ways are conventional:

1. Simplify your model

2. Gather more data

If you're using mixed, then you can also play around with the maximization settings, e.g., difficult, technique() and matlog, but these are less likely to be gratifying.

[Carlo Lazzaro]

Sue:
following Joseph's helpful advice, see also https://www.stata.com/statalist/arch.../msg00113.html

[Sue Park]

Thank you very much for Joseph and Carlo for sharing their insight!