Having issues with model fit to the lower bound of the RT distribution

[theonlydvr]

I'm trying to fit an RLDDM to my data using HSSM. In the past I used HDDM for a similar use case. My model fit is running well in HSSM, but I'm consistently having issues with the fit on the lower-bound of the RT distribution leading to poor estimation of model parameters and failed posterior predictive checks. I had these issues in the past in HDDM, but I was able to resolve them by including a lapse probability and enabling non-decision time variance in the full DDM. As far as I know, there isn't a robust LAN yet for the full DDM which I could use to fit my new models. I was wondering if anyone had alternative suggestions or guidance to get a working LAN for the full DDM (I've had some trouble getting the LANs I've fit for this model to accurately reflect simulated data)?

[krishnbera]

Hi, if the model is unable to capture the lower bound of the RT distribution, a good check would be to see if the parameters are hitting the bounds. If you are using a LAN, this could arise from the LAN parameter range cutoffs.
Re- lapse probability, if you are specifying a custom RLDDM model, you can also introduce and recover a lapse probability mixture distribution.
Re- full DDM, one approach could be utilizing the hddm_wfpt package to get the likelihoods of full DDM.

[krishnbera]

On that note, if you are using RLDDM, we just introduced the first version of RLSSM models in HSSM.
While we working on a full integration of such models into HSSM (so that you can also utilize p_outlier functionality, etc.), you can look at a sample implementation here. Also feel free to share feedback if any!

[theonlydvr]

Hi Krishn,

The parameter values I'm estimating don't appear to be hitting the LAN cutoffs. RTs are in a reasonable range (0-3s) but there are a number of very low RTs because this is rat data with some potential for very fast "pre-committing" trials.

I am including the lapse probability term and attempting to recover it. When I've included the term and allowed it to be a free parameter, I've seen the sampler estimate a lapse probability of around 15%. This is far higher than what I've seen in the past (~1% is typical for my data) and visually appears to be the sampler's attempt at blurring the distribution because it can't estimate the lower bound of the RT distribution well (the distribution it estimates rises too quickly rather than gradually). I've including an example below (the first is with the estimated p_outlier, the second is with forcing p_outlier to 0.01 which illustrates the issue, red line is real data, blue lines are simulations from model parameters):

I was looking at the full DDM in the hddm_wfpt package but as far as I could tell there was no way to include it in a differentiable callable. When I've tried using blackbox likelihoods in the past with this data, sampling has been far too slow to be viable.

As far as using the new RLDDM integration in HSSM, I'm still in the process of giving it a look. I have a custom RL model and some custom DDM terms which would require me to modify the default implementation (which appears to be very similar to the custom version I'm running at the moment without my added terms). I also am testing the DDM with a deadline option where failures to respond can either come from the DDM or from a distraction probability.

[AlexanderFengler]

@theonlydvr it looks like there are a few things going on here. Let me just leave a few thoughts:

1. Concerning the Lapse distribution. One issue is the following: The early RTs are likely creating trouble for the gradients, because the LAN (as well as the analytical DDM likelihood) have some trouble on the leading edge of the RT distribution. While the lapse distribution in principle helps to make the parameter estimation less affected by these outliers, the gradients can still get messed up if the original problem is outliers in the leading edge. Outliers in the tail are less of a problem. We have some save-guards for that, but I think it's still not bullet-proof. However don't have an immediate idea off the top of my head either on how to improve that situation once and for all.

2. From your graph it seems like RTs are spiking around 3s mark, which I assume comes from the deadline you mention. Are you taking that data out when estimating parameters? This is a bit of a rabbit hole, but leaving that data in as de-facto 3s observations is probably the worst of the options. Just making sure that that's not what you are doing.

Overall, if these extremely short observations are not crucial to stay, I would try to get rid of these from your dataset and see if that yields. From a parameter-estimation viewpoint, I consider these early outliers as less interesting than e.g. deadline induced omissions. Not suggesting it as a blanket-statement, but at the very least should be worth testing.

If this is an RL setting and you can't just have missing data at random, then consider exchanging the respective RT with the mean RT of that subject (or e.g. the lowest "reasonable" RT for your context).

[theonlydvr]

Thanks for the thoughts Alexander! I was aiming to avoid removing the trials since I was worried about the effect it would have on the RL process as a whole. As to the RT spike at 3s, those are the omissions/missed deadlines. I'm currently using a mixed model where omissions can either come from a LAN (I found a model shared on the Github a while back which seems to work well for that purpose) or with some fixed probability that is fit during sampling.
I was able to approximate variability in the non-decision time by performing pseudo-integration during sampling (taking 5 values over the uniform distribution for non-decision time and averaging the likelihood from the LAN for each value). This actually seemed to work quite well (but did take a long time to fit/converge):

I still need to do some work to validate the approach but it at least seems functional... Do you see any obvious issues with trying to fit the model this way?