Date:         Thu, 23 Sep 2010 08:36:03 -0400
Reply-To:     Dave <davidallsopster@GMAIL.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Dave <davidallsopster@GMAIL.COM>
Subject:      GENLIN: The Hessian Matrix is singular,
              some convergence criteria are not satisfied

Hi,

I'm doing a longitudinal analysis using the GEE in the GENLIN command.
However everytime I run it it tells me that "The Hessian Matrix is singular,
some convergence criteria are not satisfied". And then it goes on to say
that "The Genlin procedure continues despite the above warnings. Subsequent
results shown for last iteration. Validity of model fit is uncertain."

My data is daily responses to a 10 point likert scale questionnaire (I am
using an ordinal probit model with a multinomial probability distribution
and an autoregressive correlation structure specified). The parameter
estimates table lists each of the 10 likert scale choices under the heading
"Threshold" - and the last choice (choice 10) has a small "a" next to it
indicating that " Hessian Matrix Singularity is caused by this parameter.
The parameter estimate at the last iteration is displayed."

I can't find much information on this anywhere - but what I have found makes
me think this could be related to my data sparseness. As I said, my likert
scale runs from 0 - 10. Most people have responded in the 0 - 5 range, and
very few people are scoring the higher 5 - 10 range...I'm not fully sure how
an ordinal probit GEE works under the hood, but I suspect that any likert
scale choices with very few entries in them would cause problems..

Is there a better way to analyse this data to make the results more
reliable? The participants in my study fill out a "feelings and sensations"
questionnaire each day for 14 days of a smoking quit attempt, so I have to
use the GEE approach, but maybe the autoregressive correlation structure
could be a problem? Any ideas for a better structure? I know that in SAS you
can only use an independent correlation structure for an ordinal probit
multinomial GEE analysis...but this would seem to ignore the within person
temporal structure in the data wouldn't it?

Maybe an exchangeable correlation structure is better if it doesnt lead to
singularities in the hessian matrix??

Sorry for such a dense message - just want to outline the problem.

I'd appreciate any ideas,

Thanks

Dave

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