the second derivatives is close to singularity

[Andy]

Hello Professor Bierlaire,

Thank you so much in advance for developing Biogeme and making it available to use by many around the world. It helps a lot.

A logistic regression to model mode choice was calibrated, but it indicated a low minimum eigen values (-7.25243e-08) and "the second derivatives is close to singularity".
I wonder why did it happen?
Does it affect the validity and goodness of fit of the model? If so, what should we do to fix it?
Do you have any documentations/references regarding this matter? I could not find any on Biogeme website.

Thank you so much for your help.
Kindest regards,
Andy

[Bierlaire Michel]

On 5 Sep 2022, at 06:29, Andy <fadhlulla...@gmail.com> wrote:

Hello Professor Bierlaire,

Thank you so much in advance for developing Biogeme and making it available to use by many around the world. It helps a lot.

A logistic regression to model mode choice was calibrated, but it indicated a low minimum eigen values (-7.25243e-08) and "the second derivatives is close to singularity".
I wonder why did it happen?

You model is not identified, or there is not enough variability in the data. The maximum likelihood estimates are not unique. 

Does it affect the validity and goodness of fit of the model?

No. But it means that there is a specification issue that you want to investigate. The reported eigenvector should help you to identify parameters involved in the issue. 

If so, what should we do to fix it?
Do you have any documentations/references regarding this matter? I could not find any on Biogeme website.

Thank you so much for your help.
Kindest regards,
Andy

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