Add McFadden's choice model

[tyleransom]

I have written code to estimate McFadden's choice model (asclogit in Stata). I am not sure how to incorporate it into your package, though.

What I had in mind was to add it as another method in solvers.jl. However, I don't quite follow the custom types you've created. Also, in McFadden's choice model, Z is the array that stores alternative-specific variables, so one would need to clarify that that's not referring to an instrumental variable for that method.

If you're interested in seeing the code I have so far, here's a gist that includes it. It exactly replicates the example from the Stata help entry for asclogit.

Finally, I think your ordered logit code can be improved by making use of the fg! method in Optim. However, I'm still trying to figure this out myself (see here), so I can't help you just yet.

[Nosferican]

I saw the code from the Discourse post and had planned to go over it in the next couple days. Thanks! I have a few improvements I haven't push just yet and will check if I it covers fg! methods (it might require a Hessian which I could not analytically code after many attempts or maybe be included automatically through the use of Twicedifferentiable). I will try to look at it and see how best to incorporate McFadden's choice as a dispatch.

[tyleransom]

it might require a Hessian which I could not analytically code after many attempts

Definitely not worth it to hand-code the Hessian!

[Nosferican]

From my understanding the steps to implement McFadden would be the following,

1. Implement the conditional logistic regression clogit
2. McFadden's is a special case of it with structure given by asclogit

or

1. Implement Cox (or use Survival.jl implementation)
2. Adapt the data to à la survival

I think either approach should eventually yield the same functionality. I took a look at the code and got some of it, but not all. Could you post some references that might help me understand the code/implementation or any edits to comment the code for make it more transparent would help.

If you are attending JuliaCon we could also meet then to further this development.

[tyleransom]

will check if I it covers fg! methods

The functionality we need currently has a bug, but the Optim.jl contributors have been made aware. So for now what you've got is the best we can do.

The route I've taken is "clogit --> asclogit" but you're correct that I need to add some more annotations. I will do that soon and point you to the right place.

[Nosferican]

@matthieugomez, could FixedEffects.jl support GLM features absorption? Stammann (2018) has the algorithm and there is an implementation in CRAN's alpaca.

[matthieugomez]

No, sorry, I don’t have the time to do it.

[Nosferican]

No worries, if I end up implementing it or if/when it happens I will let you know in case you want to port it there.

[Gkreindler]

This conversation is above my level, but does https://github.com/jmboehm/GLFixedEffectModels.jl now implement GLM features absorption? Could that help with clogit here?

[Nosferican]

I would have to take a look at it. Potentially.

[Gkreindler]

Thank you for this entire package and no worries!

The context on my side is that I am looking for a way to include fixed effects (not too large, but too much to type by hand) in a discrete choice model. I've looked at DiscreteChoiceModels.jl but I don't know how to do that there. This is why I found this thread interesting.