Spatially Varying Coefficients among multiple regions

[Miguel Silva]

Hello all,

I am currently interested in investigating occupancy patterns and relationships with predictors for multiple species that co-occur in multiple regions. Each region is comprised of a grid of camera sites, but although the biomes and several species are similar for all, these regions are fairly distant from each other. I don't want to assume that a species will have the same response among regions, and so was looking into the spatially varying coefficient models that spOccupancy offers. I also have looked into the work from the Bajcz et al. 2024 paper for a multiregion approach with spOccupancy and was interested in knowing if a similar approach would be sensible to use in an SVC model? In essence my research question aims at seeing how responses to the same predictors may vary within each region and among the regions as well. Say the response of a species to "distance to the forest edge" may be different in a highly fragmented region vs a more intact region, even if these distances per se are the same at a given camera. I had initially thought about a similar multi-region approach like the Bajcz paper but my understanding is that although each region is accounted for with a random intercept, it would assume that each species' responses are the same among regions. Is this the case? Is there a way that incorporating SVCs can amend these assumptions? I think I saw a response for a different question that mentioned including dummy variables for region and code those as SVCs. I'm not sure if this would apply for my specific question though. Currently, my occupancy predictors would be something like ~ (site level distance to forest edge) + (regional fragmentation) + (site level distance to nearest human population) + (regional human density) + (1|region). I also considered using interactions between the site and region level predictors but also wasn't sure how adequate it is.

I'm open to all kinds of feedback on all this! Thank you!

Miguel Silva

[Jeffrey Doser]

Hi Miguel, 

Apologies for the delay. You could try a model where you include a region-specific effect of your variable of interest (e.g., allow the variable to interact with region), and then also include an SVC. This sort of idea is talked about in our paper on SVCs in GEB here. This would allow you to quantify variation in the effect that occurs as a result of differences across regions, and then the SVC would allow you to account for any other variation in the effect. However, I will mention that an SVC model can be difficult to fit with data that are highly clustered, so you may find it difficult to estimate depending on how far apart your clusters are. If you choose to do such an approach, you may want to consider using an informative prior like the one used in Bajcz et al. 

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

Pronouns: he/him/his