Convergence issues of occurrence random effect variance

[Jacob Twersky]

Hi there,

I am using PGOcc to create single species single season occupancy models of stream breeding salamanders across 180 stream reaches distributed evenly among 30 streams. I'm using an occurrence random effect to account for clustering of reaches within streams instead of running spatially explicit models because I only have one set of coordinates for each site. I've been successful achieving convergence for the occurrence random effect for most of my species by increasing n.samples and n.burn. I have one species that is only distributed among 21 of my drainages which drops the number of reaches to 126, and I have not been able to achieve convergence of the occurrence random effect in this case. The stream-to-stream variation of occupancy for this species does appear high in addition to the small sample size. Is tightening the priors of sigma.sq.psi my best option or should I just acknowledge that the random effect variance is high and challenging to estimate with such a small sample size? Here is an example of a model run:

It should be noted that this is my global exploratory model. When use only covariates that have CIs excluding zero, I do get convergence of my occurrence random effect. 

Any suggestions would be much appreciated.

Thanks!

Jacob Twersky

[Jeffrey Doser]

Hi Jacob, 

Thanks for the question. This problem could arise for a variety of reasons. First off, it certainly seems like the random effect variance is unidentifiable in this case given the massive credible interval. This could be a result of the data for this species not being able to estimate all parameters in this model (e.g., if there are a small number of detections, the detections are highly clustered in a small set of the sites). I would not recommend simply trying to set a stricter prior on sigma.sq.psi, as this suggests to me there is not enough data to identify the problem. I would encourage you to take a look at the traceplots of the random effect estimates (i.e., both the variance in "sigma.sq.psi.samples" as well as the actual estimated random effect intercepts stored in beta.star.samples). Looking at those values may help reveal the root cause of what's causing the problems with estimating the random effect. In your simpler models that you say converge, I would also look at the magnitude of the credible intervals for the variance. Is it similarly large, or are the values more reasonable? If they are more reasonable, this likely indicates the full model is too complex and the data for the species can't estimate the parameters. If it is similarly large, the model still may just not have much information to estimate the random effect. Regardless, I'd encourage you to dig into the actual locations of where the detections for this species are and how that might be contributing to the challenge in estimating the RE variances. 

Hope that helps, 

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