I have a quite complex hierarchical model for which I'm estimating parameters and producing posterior predictive using STAN (rstan) for some psychophyiscal data.
I'm (sometimes) observing some strange behavior:
These are traceplots and diagnostics of two different variables (group means). As can be seen, three chains mix nicely, but the forth is getting stuck. It is not highly implausible that there is some local optimum (and by restricting parameter ranges I can avoid it) but I'm a bit surprised that it is always the same chain even on different variables. These variables are not connected by any model structure and the data is from independent experimental conditions.
The only connection could be that the real values in the participants are correlated. The parameter describes some rate of information processing. A person with a high rate in one condition will also have a high one in the other condition.
So my question is: (without considering any other details of the model) can such a relation in the data, or some other factor, lead to autocorrelated behavior in the same chain for different variables (which are not connected by any model structure and are estimated from non-overlapping data)?
Many thanks and best regards Jan
[P.S.: One alternative explanation that I have not looked at yet comes two mind: Maybe the trace plots decide the colors of the chain based on the average value and not on the chain id? That could be misleading ... ]