# Multilevel Logit with Few Observations per Individual

**URL:** <https://discourse.mc-stan.org/t/multilevel-logit-with-few-observations-per-individual/20152>\
**Category:** Modeling\
**Tags:** economics, fitting-issues, specification\
**Created:** [January 11, 2021, 7:17pm UTC](https://discourse.mc-stan.org/t/multilevel-logit-with-few-observations-per-individual/20152 "2021-01-11T19:17:37Z")\
**Posts on this page:** 1\
**Showing post:** 2

<div class="post-metadata">

**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [January 25, 2021, 9:36am UTC](https://discourse.mc-stan.org/t/multilevel-logit-with-few-observations-per-individual/20152/2 "2021-01-25T09:36:13Z")

</div>

Sorry for once again missing your question. A few things to note:

- You seem to require large `adapt_delta` and `max_treedepth` - presumably to avoid divergencies. You then - if I understand you correctly - get rid of divergencies but get BFMI warnings. This is likely just a different manifestation of the same problem - for diagnostic purposes, it is usually better to run with default settings as it shows you _more_ of the problems.

> [@alexkellogg](#):
>
> Is it appropriate to use multilevel models to recover the latent λ\lambda population distribution?

I don’t think this is fundamentally problematic, but can definitely be a problem in practice for some specific settings.

> [@alexkellogg](#):
>
> Empirically, the posterior on ¯λ\bar{\lambda} is quite good even when D=1D=1 – so that I only observe one choice per individual. Is this a lucky coincidence, or can I actually hope to recover the population distribution even with 1 choice per individual (where I can’t hope to recover the individual λi\lambda\_i )?

Once again - this is not something that is IMHO problematic _in principle_ but might be a problem _in practice_.

> [@alexkellogg](#):
>
> I am running into a “BFMI Low” warning when I _increase_ the sample size from N=100 to N=1000 (particularly at D = 1, 2, and 3). The E-FMI is around 0.15 according to “[check\_energy()](https://mc-stan.org/rstan/reference/check_hmc_diagnostics.html)”. Why would that be?

As I said above, I believe the actual problem is not BFMI, so I would not fixate too much on this. (I admit I do not understand BFMI much, so I don’t want to speculate)

> [@alexkellogg](#):
>
> I’m also not entirely sure how to compute the pairs() plot, which I think are a suggested diagnostic for the BFMI warning, since there are so many λi\lambda\_i in the model.

I would just look at the `pairs` plot for a bunch of different subsets of the variables. Note also additional debugging strategies at [Divergent transitions - a primer](https://discourse.mc-stan.org/t/divergent-transitions-a-primer/17099). I would start by making sure you can fit a simpler version (e.g. non-hierarchical) of the model without ramping up `adapt_delta` or `max_treedepath`

Additionally:  
The hard lower and upper bounds are suspicious - why do you believe such hard bounds are sensible a priori?

Best of luck with the model!

---

_[View the full topic](https://discourse.mc-stan.org/t/multilevel-logit-with-few-observations-per-individual/20152)._