One chain not moving: sampling for complex nonlinear mixed effects model

[martinmodrak]

@meghs

So, I finally have a working model. The parameter estimates also seem reasonable and PP checks look OK. However, I still have a few divergent transitions (~200). Do let me know if you have any thoughts on this.

Unfortunately, divergences usually cannot be safely ignored.

@meghs

It does seem like the model [mis]behavior is determined largely by the data in this case. When I used the model for another data set, I had no issues at all! I tried some prior predictive checks to understand what might be the problem.

This is actually quite frequently the case - not all datasets inform all the parameters of the model well (which can then result in divergences). For example, if BA.con.15m and BA.het.15m correlate well in one dataset, it may become impossible to distinguish how much does each of the exponentials contribute to the response - only their sum is identified.

Examining pairs plots for the population-level effects might help us diagnose this as it should show some weird correlations between the parameters as well if this is the case.

@meghs

As you suggested, I simplified the models sequentially, starting with no random effects on the exponents and no hierarchical predictors for the parameters. These models behaved well.

@meghs

I still had to run a few trials to tweak inidividual priors - it seemed like the model is very sensitive to prior specification for the group SDs.

This might be an important hint (at is definitely a sign that something is wrong). Maybe this dataset has too few observations per each sp and quadrat combination to inform the varying intercepts well… If you cannot fit the model without narrowing the priors more than you can justify from domain knowledge, it probably means you need more data or need to simplify the model.

A smaller note:

@meghs

I used the posteriors from simpler models to inform my priors for the full model.

I would not recommend that. Priors should generally be defensible by simply referring to domain knowledge, without any reference to the actual data you happened to collect. The process you describe makes the priors depend on the data and could thus introduce some bias into your inference (it could be small, but it is hard to say).

Hope this helps at least a little bit!