non-converging parameters

[Esin Turkakin]

Hi everyone,

We have a within-subjects model where drift rate and threshold settings are allowed to vary with the difficulty level of a task. We have a convergence problem with the drift rate only on the difficult level. The convergence is fine for the other (easy and moderate) levels, as well as for other factors (as main effects as well as interactions), and for other parameters (namely a and t, and also z when included). 

When we excluded all difficult trials, the parameters were estimated at the same values for the remaining levels as they were for the model with full data. 

Is it safe to conclude that we can trust the estimates for the parameters and levels that did converge and simply report that drift rate did not converge for the difficult level? 

Any ideas why that level would be problematic are also welcome. We suspect high error rate (~42%) to be the culprit but cannot be sure).

Thanks in advance for your help,

Esin

[Thomas Wiecki]

Hi Esin,

It's hard to say whether that is a problem for the other parameters or not. But your check would certainly lend credibility to that. How terrible is the convergence? Sometimes it can look bad in the chain but with enough samples you should still get a reasonable / correct estimate of your posterior (the histogram is sometimes more informative in these cases).

Best,

Thomas

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[Esin Turkakin]

Thanks for the quick reply Thomas. I'm attaching the traces, histograms and autocorrelations for the mean and std nodes for the drift rate at the problematic level. The histogram for the mean node looks acceptable to me, but the std node histogram is very skewed and very close to 0. I don't know why std would be that low. Is that what's causing convergence issues?

Thanks,

Esin

[Esin Turkakin]

Sorry forgot to attach the graphs, here they are:

[Thomas Wiecki]

Yeah, that's very typical in hierarchical models. Intuitively, the the sampler gets stuck as the std goes to zero and all subject parameters get pushed to their mean. This is also known as the funnel (check around 1:16:00 https://www.youtube.com/watch?v=pHsuIaPbNbY). For a Gibbs sampler it's very hard to escape once in that funnel. It could mean that there is just not enough information to confidently estimate individual subject parameters. You could also try and turn it into a group-only regressor.