hessian matrix error in pasw/spss mixed model analysis

[Daand]

Dear all,

Who can help me out? I received the following error for fitting my Model 1 in PASW 18:

“The Final Hessian matrix is not positive definite although all convergence criteria are satisfied. The MIXED procedure continues despite the warning. Validity of subsequent cannot be ascertained.”

Led to intercept .0000a

Thanks is advance for your help!

Best regards, Danielle

[Kristian Karlson]

It can’t compute the variance component correctly (leading to wrong standard errors). I would go for another specification of the model–or look for possible errors in your specification. You may post your syntax code and your output–I can have a look at it.

Kristian

[Daand]

Dear Kristian,

Thanks for posting. This is my model 1 syntax. Earlier on I removed predictor that might have rendered errors. That worked. But now again the Hessian matrix warning occurs.

MIXED sDDEIndivLp WITH ICprofEMaj ICprofEMin1 ICprofEDec ICcompPre1 ICcompPre2 ICcplxInno ICtrialAS
ICtrailSCC ICtrailCLE ICtrail2005 ICtrail2006 OCCdiscCPX OCScentIP OCScplxFRAG OCSsizeINST
OCSleadSHIFT OCSleadATT OCSopenLAW OCSopenTRE OCPpowDIS CPCagenACT
/CRITERIA=CIN(95) MXITER(100) MXSTEP(5) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0,
ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=ICprofEMaj ICprofEMin1 ICprofEDec ICcompPre1 ICcompPre2 ICcplxInno ICtrialAS ICtrailSCC
ICtrailCLE ICtrail2005 ICtrail2006 OCCdiscCPX OCScentIP OCScplxFRAG OCSsizeINST OCSleadSHIFT
OCSleadATT OCSopenLAW OCSopenTRE OCPpowDIS CPCagenACT | SSTYPE(3)
/METHOD=ML
/PRINT=SOLUTION
/RANDOM=INTERCEPT | SUBJECT(InstituteNr) COVTYPE(UN).

Thanks for helping out!

Have a nice weekend,

Danielle

[Daand]

PS: is it possible that SPSS sees scores 1, 2 and 3 as categories? For these are not categories but numbers, thus scale.

[Kristian Karlson]

Good question. The syntax looks fine. How many level-2 predictors (=explanatory variables) do you have and how many level-2 units (= number of cases on second level)? There may be a mismatch.

Have you checked that the variance component (the random intercept) is significant? If not, you may have explained all level-2 variation and the model for level 2 is overparametrized (i.e., “over-fitted”).

You may want to try to fill in a couple of extra zeros in “SINGULAR(0.000000000001)”. You may also remove the COV(UN), because you only have a random intercept (thus only a single random parameter).

A final advice: If possible, standardize all variables (and thereby their interactions). This may help.

Kristian

PS: No, I do not think SPSS treats it as discrete variables (that would be visible in the output as well).

[Daand]

Thank you so much for posting, Kristian!
Will let you know if it works.

Two questions for clarification:
Variance component (random intercept):
Do you mean empty model, see pdf attached to this message.
Or do you mean the coefficient and standard error of the model 1.

What do you mean by standardizing all variables?
You mean: DESCRIPTIVES VARIABLES = …. /SAVE?
Or is there some other standardization possible?

Thank you for braining with me,
Danielle

[Kristian Karlson]

(1) Variance component: I think in the full model, not in the empty model.
(2): Yes, standardize with Descriptives. (Other standardizations are possible, but not convenient for your purpose).

Kristian

[Daand]

Dear Kristian,

I tried to remove the COV(UN) and changed it to COV(VC). This works for some errors!
But I’m not sure when to use COV(UN) or COV(VC).
What are the rule of thumb for this?

Now the variance component (the random intercept) is significant.
Thus fitted. However, I’m in still in doubt whether to use ML or REML.
Some errors persist when using ML and disappear when using REML.
I have no small groups (n for groups =26).
But I cannot use ML in model 1 and REML in model 2.
Any thoughts on this?

Thank you so much again for responding.

Danielle

[Kristian Karlson]

Sounds interesting. COV(UN) is for unstructured random effects, that is, you estimate both the variance of the intercept and coefficient, and the covariance between the two. COV(VC), as far as I remember, assumes the random effects to be uncorrelated, that is, the covariance is set to zero.

If you are to compare estimates from two or more models, you will have to use ML. REML-estimates is not directly comparable across models. I don’t know whether it will effect your results in any substantive way, but using ML would be the right thing to do.

Kristian

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