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