Questions about numerical integration and normalization strategy in ICLV model

[可可]

Dear Biogeme-group,

I have two questions about ICLV model in Biogeme:

1. I'm using numerical integration in ICLV model by Biogeme, such as:

loglike = log(Integrate(condlike * density, 'omega'))

I want to know the specific algorithm about the numerical integration, because there are multiple ways to do numerical integration.

2. In the ICLV calibration program provided by Biogeme, both the sigma and coefficient of one indicator are fixed to 1 in the measurement model. However, our usual practice to fix only the coefficient of one indicator in the measurement model, and we do not try to constrain the sigma in the measurement model. May I ask if the practice in Biogeme leads to an over-constraint problem? If not, may I ask why?

Any help could be useful,

Thanks!!

[Michel Bierlaire]

> On 14 Oct 2024, at 14:45, 可可 <kek3...@gmail.com> wrote:
>
> Dear Biogeme-group,
>
> I have two questions about ICLV model in Biogeme:
>
> 1. I'm using numerical integration in ICLV model by Biogeme, such as:
> loglike = log(Integrate(condlike * density, 'omega'))
> I want to know the specific algorithm about the numerical integration, because there are multiple ways to do numerical integration.

Gauss-Hermite.
The implementation is here:https://github.com/michelbierlaire/cythonbiogeme/blob/main/src/cythonbiogeme/cpp/bioGaussHermite.h
https://github.com/michelbierlaire/cythonbiogeme/blob/main/src/cythonbiogeme/cpp/bioGaussHermite.cc
https://github.com/michelbierlaire/cythonbiogeme/blob/main/src/cythonbiogeme/cpp/bioGhFunction.cc

>
> 2. In the ICLV calibration program provided by Biogeme, both the sigma and coefficient of one indicator are fixed to 1 in the measurement model. However, our usual practice to fix only the coefficient of one indicator in the measurement model, and we do not try to constrain the sigma in the measurement model.

Indeed.

> May I ask if the practice in Biogeme leads to an over-constraint problem? If not, may I ask why?

I don't remember why I had to constrain the sigma as well. It may also be a mistake. I'd need to investigate it again.

>
> Any help could be useful,
>
> Thanks!!
>

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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