GENLIN: The Hessian Matrix is singular, some convergence criteria are not satisfied

[dave-2]

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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[Bruce Weaver]

Dave wrote

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

If you want to test your idea that the problem is sparseness in the 6-10 range, recode the outcome variable like this:

recode DV (6 thru 10 = 6) (else=copy) into DV2.
value labels DV2 6 "6 or more".

...and try your model with DV2 instead of DV1.

[Maguin, Eugene]

Dave,

In addition to what Bruce said, you could look at the crosstabs of day(x)
with day(x+1). You don't say anything about sample size but since there's a
hundred cells in each of those crosstabs, I'll bet you have a lot of low
frequency cells. My understanding is that they can cause problems and a
small number is sometimes used to replace the count value of 0. I seem to
recall that some spss categorical rountines (genlog, for one) can replace
0's with a fractional value; however, I don't know whether that is a
possibility with genlin but I don't think it is as I read the documentation.

Although you have decided that an ordinal model is best, would treating the
response scale as continuous and using mixed be an adequate alternative?

Gene Maguin



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Dave
Sent: Thursday, September 23, 2010 8:36 AM
To: [hidden email]
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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[Ornelas, Fermin-2]

This is a comment in regard to the singularity of the Hessian. If your data is in the range of 0-5 mostly. It is very likely that the some of the columns in the Hessian are not independent. That is why you are getting the message. Obviously that problem will render your parameter estimates unstable.

Fermin Ornelas, Ph.D.

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Dave
Sent: Thursday, September 23, 2010 5:36 AM
To: [hidden email]
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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