I am currently fitting a negative binomial model (using brms) on the occurrence of an event by each month, across a number of areas - essentially a latent growth curve model. This model specification works fine on two other dependent variables, but on this third one, I am having some problems. In brms syntax, this looks like:

fit_3 <- y ~ x1 * time + I(time^2) + x2 + x3 +

(x1 * time + I(time^2)| area) +

(1|region)

My problem is: each time I fit the model, three of the chains finish sampling and converge relatively quickly, while the 4th chain often doesn’t even begin warmup until the other chains are done. If I let it go until it finishes sampling, the resulting model has huge Rhats. When I plot it, it looks like the three chains converge and mix relatively well, but the problematic one never does.

I have tried a number of things (increasing adapt_delta to .99, maximum treedepth to 15) to no avail. I’ve centered my variables and set normal(0,1) priors on most of the variables. The dependent variable I am measuring here is relatively rare, which might be causing havoc with the random effects? Any suggestions are quite welcome.