The simplest version of the interface would just be one formula for survival part of the model and one for recapture part, ideally implementing all the bells and whistles you have for GLMM's. It's something I'll be looking at getting into in April.
Krzysztof
I see, thanks Daniel. The model I'm proposing incorporating differs because:
a) recapture/survival (or other event probabilities) can be specified by passing in a (sparse) model matrix, so we could borrow a lot of the other rstanarm parameterization machinery. In my case it made it easy to do efficient 3-D spline models.
b) individuals do not need to be recaptured at the same time for each occasion. In CJS it's often assumed that whenever there is a recapture occasion all the individuals are "at risk" for recapture for the same short period of time. Different datasets stretch this assumption to different extents and it's not really necessary.
The formulations that have this N (individuals) by K (occasions) parameterization are standard within the field but as far as I can tell they are a relic of the original estimators based on sufficient statistics. They're great if you really need to estimate a few survival parameters or test if parameters vary by occasion but there's no need to jam everything into that framework.
Krzysztof
It's a funny literature---or at least I think it's funny, some people take it very seriously, especially calling models by their right and true name. My touchstones for it are the original three papers (by Cormack, Jolly, and Seber, respectively) because they derive the sufficient statistics-based estimators that still have their mark on the current software implementations (e.g.-program MARK and a few others). They also state the problem pretty clearly. I just peeked at Jolly (1965) again and it gives a good sense of where this is all coming from. Then there was an extended "bells and whistles" period that's summarized nicely in Lebreton (1992), though I think a few features arrived afterwards. All that just deals with a two-state partially observed system. I think the next big touchstone is Kendall (2002) which (maybe?) is the original multi-state version of the model.
If you skim Jolly (1965), read Lebreton (1992), and assume you know what's in Kendall (2002) based on modern stats you end up with a decent sense of what the field is like. If you want the gory details of how all the intervening papers are related to each other and medical multi-state survival models I have a lit review in my dissertation... :)
Sorry, that's long. It's been a while since I had to think this through. If you want it to be easy I have the pdf's, just ask. I guess I'm not supposed to post them here...
It would be fun to talk about this at the next Stan meeting if the language issues don't take up the whole meeting.
Turns out I have it too. Just sent it. K
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