Issue with interaction of random slopes

[sallidina]

Hi, I’m running into some issues with my hierarchical model that I’m hoping to get some advice on. I’m using hssm v 0.3.0 and my task setup is as follows: each participant completes two tasks (coded here as -1 and 1), and within each task there are two block types (coded here as -1 and 1). I am trying to model drift rate as a function of these two variables, at both the group and individual level. There are 600 participants, and each person completes 256 trials total.

This is my model:
model = hssm.HSSM(
data=dat,
include=[
{
"name": "v",
"formula": "v ~ 1 + blocktype2_num*task_num + (1 + blocktype2_num * task_num|participant_id)",
"link": "identity",
}
],
prior_settings="safe",
z=0.5,
link_settings='log_logit'
)

When I run this model without the interaction between the random slopes (i.e. the formula for drift rate is v ~ 1 + blocktype2_num*task_num + (1 + blocktype2_num + task_num|participant_id)), the model converges well with no apparent issues. However, with the interaction of random slopes included, the chains seem to get stuck and the final samples have chains with all very similar (or even the exact same) values.

I have also tried using the approx_differentiable likelihood since I saw this recommended in other threads, but this leads to samples with a very high number of divergences (almost all the draws) regardless of the random effects setup.

With both the analytical and approx_differentiable likelihood, I have also tried the following with no improvement:

• setting noncentered=False
• setting link_settings=‘log_logit’
• setting target_accept=0.95
• running for more iterations

I’ve also tried using the default blackbox likelihood on a subset of 50 participants, and this improved things quite a bit, though some parameters still failed to converge. However, this is prohibitively slow on my full sample of 600+ participants (after over a day, only 70 draws have completed).

I've previously run a similar model with an older version of hssm (0.2.3) that I am unable to install again, and it worked fine then. So hoping for any advice on how I can get it running in the newest version. Thanks in advance for any help!

[AlexanderFengler]

Hi @sallidina ,

I will look into this more closely, but as a short reaction I think it's quite likely that the full model you use is over-parameterized in the end and the resulting non-identifiability actually get the chains stuck.

Could you try running also with C(task_num), to make sure the tasks are treated as categorical?

If you send me (or @krishnbera / @AndrewZhang599 ) some subset of your data e.g. and maybe any relevant pre-processing you did, that could be helpful.

If you have some trace-plots or any other results you could share that might also help with the diagnosis here.

[sallidina]

Hi @AlexanderFengler ,

Thanks for your response! I've also tried running the models with C(blocktype2) and C(task) to make sure they're treated as categorical. When I run this on a subset of 50 participants, it seems to work fine (trace plots with 2 chains below):

However, when I run it on the full sample of ~600, it looks a lot worse. I played around with the sampler options a bit and setting init=’jitter+adapt_full’ and step_scale=0.5 makes the divergence warning disappear, but the chains are completely non-overlapping:

I also thought that perhaps the model was just too complicated and non-identifiable, and tried running a version on only the data from a single task with v ~ 1 + C(blocktype2) + (1 + C(blocktype2)|participant_id). However, the chains are also completely non-overlapping in this model.

I'll send you my data privately as well - would appreciate any help you're able to provide.

Thanks!

[AlexanderFengler]

@sallidina ,

did we ever help you with this? Apologies if this fell by the wayside.