Multi-level nested logit model

[Zeyu Sun]

Dear developer,

I am curious about whether biogeme package is able to deal with the multi-level nested logit model (more than 2 levels).

Best,

Zeyu

[Bierlaire Michel]

Yes. Any model such that you are able to write the log likelihood function can be estimated. 

However, this model is not part of the list of models that is already pre-packaged (see the list here http://biogeme.epfl.ch/sphinx/models.html ). 

You will have to code the log likelihood function. It should not be too difficult, using the existing models as examples.

The reason is that this model can always be replaced by a cross-nested logit model, where several nesting structures can be combined. And the cross-nested logit is pre-packaged in Biogeme.

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[Zeyu Sun]

Thank you for the answer.

I was not aware of that a d-level nested model can be replaced by a cross-nested model, may I ask for the reference in which I can study?

Best,

Zeyu

[Bierlaire Michel]

Well, there are plenty of papers using a cross-nested logit would do.

Here is a recent model that we have developed: 

https://transp-or.epfl.ch/documents/technicalReports/BeinBierDocq21.pdf

The intuition is simple. The reason why you need a two-level nested logit is because there is no partition of the choice set that captures the correlation structure that you have in mind. Some of the alternatives (or all of them) potentially belong to more than one nest. And the nested logit model is therefore not applicable. But this is exactly the purpose of the cross-nested logit model. It does not rely on a partition. Alternatives can belong to more than one nest. In addition, the cross-nested logit is more flexible than the two-level nested logit model. 

Actually, we have proved that any additive random utility model can be approximated by a cross-nested logit model. See https://dx.doi.org/10.1016/j.jocm.2013.05.002

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