sigma.sq convergence issue

[Giada Brunod]

Hello,

I am working on fishing cat occupancy for my master’s thesis. I am fitting a single-species, single-season spatial occupancy model using spPGOcc(). My dataset is relatively small: I have 245 locations, and the species was detected at 24 locations across 41 independent events.

Most model parameters converge well with n.batch = 1000 and batch.length = 25, except for sigma.sq. I tried increasing n.batch up to 5000 and still does not fully resolve the issue. I also tried increasing the burn-in (to 20% of the total iterations), as suggested in another comment.

I am not sure whether continuing to increase n.batch is a good approach, or if there are more efficient strategies you would recommend, or whether my data are simply insufficient to support estimation of a spatial covariance term.

Below is an example of one of the models I fitted.

I used the default priors (including phi.unif = c(3 / max.dist, 3 / min.dist), as recommended in the documentation) and the default initial values, as I do not have prior information to inform them.

thanks in advance,

Giada

[Jeffrey Doser]

Hi Giada, 

I would consider your model sufficiently converged based on the summary output you shared. While it does appear that the MCMC chain for sigma.sq mixes more slowly than the other parameters, you have a sufficiently large ESS (over 2000) and the Rhat value is about 1.01. Oftentimes 1.1 used as the cutoff for when a parameter can be converged (or more stringent cutoffs can be 1.05). I would feel comfortable moving forward with your current model and interpreting the results. 

Jeff