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

[Giada Brunod]

Thank you. 

I am fitting the same models on a subset of my dataset (53 locations, with fishing cats recorded at 10 locations across 24 independent events), including additional variables, and this model emerges as the best-performing one based on k.fold.deviance:

Is the convergence of sigma.sq still acceptable in this case, or should I exclude the model (given that Rhat is around 1.1)? Increasing n.batch does not seem to improve convergence substantially, so I suspect that the data may simply not be strong enough to support reliable estimation of spatial covariance.

In addition, after reading several discussions and references online, I am still somewhat confused about how to interpret phi and sigma.sq biologically.

thank you in advance,

Giada

[Jeffrey Doser]

Hi Giada, 

Fitting a spatial occupancy model with only 53 sites is a challenging task, as these models typically require more spatial locations than that. Doing cross-validation in particular would be very challenging with such a model, since that would involve fitting a model with an even smaller number of locations. Given the quite large uncertainty in your model parameter estimates and only having 53 sites, I think you are asking too much from your data. So, I would recommend trying a non-spatial occupancy model instead. 

As far as the interpretation of phi and sigma.sq goes. sigma.sq is just like any random effect variance parameter. The larger sigma.sq is, the larger the variance of the random effect, and the more variability there is from one site to another in terms of the size of the spatial random effects. phi is the spatial decay, which corresponds to how far across space two sites are correlated (after accounting for covariates). When using the exponential spatial covariance model, 3/phi is the effective spatial range, which is the distance at which two sites have a residual correlation of 0.05. I would not put too much weight in terms of trying to interpret what these parameters mean from a biological perspective. They are notoriously challenging parameters to estimate, and while they could have some biological meaning in theory (e.g., phi could relate to dispersal ranges), that would be very hard to assess in practice. Instead, estimating these parameters is usually just a way to account for spatial autocorrelation in the model and generate better inference/prediction on occupancy probability itself. 

Jeff

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Jeffrey W. Doser, Ph.D.

Assistant Professor

Department of Forestry and Environmental Resources

North Carolina State University

Statistical Ecology and Forest Science Lab

Pronouns: he/him/his