Positive latent variable

[Hafsoah Ahmad]

Dear Prof. Bierlaire,

I hope you're doing well. Kindly help me with the following problem.

I have to estimate an ICLV model. One of the latent variables (L1), which represents latent travel time, needs to have a restriction that its value should be positive. How should I enforce this ? 

All four of the socio-demographic variables in the structural equation are binary. For the measurement equations, the indicators are positive and continuous. Without enforcing any restrictions, their corresponding parameters are positive. 

I tried taking the exp value in the final utility function and/or the structural equation. In both cases, the gradient became infinite and the model was not estimated. I cannot use abs() because the function doesn't take an expression containing operators as its input.

Thank you in advance for your help.

Regards,

Hafsoah

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[Michel Bierlaire]

> On 2 May 2024, at 18:01, 'Hafsoah Ahmad' via Biogeme <bio...@googlegroups.com> wrote:
>
> Dear Prof. Bierlaire,
>
> I hope you're doing well. Kindly help me with the following problem.
> I have to estimate an ICLV model. One of the latent variables (L1), which represents latent travel time, needs to have a restriction that its value should be positive. How should I enforce this ?


> All four of the socio-demographic variables in the structural equation are binary. For the measurement equations, the indicators are positive and continuous. Without enforcing any restrictions, their corresponding parameters are positive.
> I tried taking the exp value in the final utility function and/or the structural equation. In both cases, the gradient became infinite and the model was not estimated. I cannot use abs() because the function doesn't take an expression containing operators as its input.

abs is not differentiable.

Using exponential should work, although it is indeed numerically challenging. Make sure that the initial value of the scale parameter is sufficiently large, but not too large. You may need to play a little bit with it.

Also, start performing a sequential estimation to make sure things are OK.
See https://transp-or.epfl.ch/documents/technicalReports/Bier18b.pdf

>
> Thank you in advance for your help.
>
> Regards,
> Hafsoah
>
>
> CONFIDENTIALITY NOTICE: The contents of this email message and any attachments are intended solely for the addressee(s) and may contain confidential and/or privileged information and may be legally protected from disclosure. If you are not the intended recipient of this message or their agent, or if this message has been addressed to you in error, please immediately alert the sender by reply email and then delete this message and any attachments. If you are not the intended recipient, you are hereby notified that any use, dissemination, copying, or storage of this message or its attachments is strictly prohibited.
>

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Michel Bierlaire
Transport and Mobility Laboratory
School of Architecture, Civil and Environmental Engineering
EPFL - Ecole Polytechnique Fédérale de Lausanne
http://transp-or.epfl.ch
http://people.epfl.ch/michel.bierlaire