Interpretation of occupancy in a spatial vs. non-spatial model

[Marc Kéry]

Dear all

we have been fitting spatial occupancy models to some tiger data and for comparison also fitted non-spatial ones with the same set of covariates. The resulting distribution map is much more "pointed" under the spatial than under the non-spatial model. That is, the spatial model produces smaller islands of higher-occupancy predictions, while the high-occupancy islands in the maps under the non-spatial model are more 'smeared out': larger and with lesser maximum.

Now I have a question about the interpretation of the occupancy parameter in these models. Would the following make any sense ?

- A covariate-only model depicts the potential distribution (if the model is "right enough"). That is, it shows which sites look similar, in terms of their covariate values, to sites where tigers were detected (or were they are estimated to occur, by factoring in detection).

- In contrast, the spatial model depicts more of the actual distribution, i.e., it shows how likely there are any tigers in each quadrat right now. This is because the observed detections constrain the predictions of occupancy much more strongly than in the non-spatial model.

So, spatial predictions tell us where tigers are likely to occur now, while covariate-only predictions tell us where they could potentially occur, given the habitat and our model.

Thanks and best regards  --- Marc

[Jeffrey Doser]

Hi Marc,

Thanks for the interesting query. I think your interpretation seems reasonable for your analysis, although I don't think such an interpretation is fully applicable across all spatial vs. nonspatial models. Such an interpretation in large part depends on what patterns you think the residual spatial random effects are picking up, as well as how complete the set of covariates is in describing the species-habitat requirements. If the fine-scale patterns of the spatial random effects are potentially related to local-scale habitat variables not included in the covariate values, then the spatial model could very well also represent the sort of "potential distribution" you describe, it would just also be taking into effect smaller scale factors than what your covariate values are explaining. However, if you think the spatial patterns arising from the spatial REs is less so related to specific habitat requirements and more so reflective of locations within a home range that individuals just happened to be using over the course that sampling took place, then I think your interpretation makes good sense. So, I think the interpretation is logical, but likely context dependent on the specific scenario. Of course, it won't always be the case that the spatial model provides more "pointed" predictions than the non-spatial model, which all depends on the estimated spatial decay parameter (phi) and the spatial autocorrelation in the covariate values themselves.

Kind regards,

Jeff

[Singye Wangmo]

Dear Jeff and all,

I hope you're keeping well.

I’m writing to seek your guidance on a point from our spatial occupancy analysis. We’ve been comparing model selection results across different NNGP configurations (using neighbour sizes of 5, 15, 30, and 50). Interestingly, the model with NNGP-5 produced the lowest WAIC, suggesting the best predictive performance among those tested (PFA).

This outcome seems to imply that the spatial structure may already be adequately captured with just 5 neighbours, and that increasing the neighbour size beyond this does not offer substantial improvement in explaining spatial patterns.

Given that a larger number of neighbours is typically thought to better approximate a full Gaussian Process, I’d appreciate your insights on the following

-Would it be reasonable to conclude that NNGP-5 is sufficient for capturing the spatial variation in this case?

-Would this sort of stability across different neighbour sizes be expected when the underlying spatial signal is relatively smooth?

Any advice on interpreting neighbour-size sensitivity in this context would be greatly appreciated.

Warm regards,

Singye

--
You received this message because you are subscribed to the Google Groups "spOccupancy and spAbundance users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to spocc-spabund-u...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/spocc-spabund-users/2c41466c-b216-4975-822d-4be5743b3eb5n%40googlegroups.com.

--

---

This message and/or any associated files may contain confidential and/or privileged information intended solely for the use of the individual or entity to whom they are addressed. If you are not the intended or authorized recipient, you must not use, copy, disclose or take any action based on this message or any information contained therein. If you have received this message in error, please advise the sender immediately by sending a reply email and delete this message. The recipient should check this email and any attachments for the presence of viruses. The Royal Government of Bhutan accepts no liability for any damage caused by any virus transmitted by this email or any/or associated files.

---

[Marc Kéry]

Dear Jeff,

thanks, that is very helpful and makes much sense. Helps us not overinterpreting things.

Best regards  ---- Marc

--

You received this message because you are subscribed to the Google Groups "spOccupancy and spAbundance users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to spocc-spabund-u...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/spocc-spabund-users/2c41466c-b216-4975-822d-4be5743b3eb5n%40googlegroups.com.

--

______________________________________________________________
 
Marc Kéry
Tel. ++41 41 462 97 93
marc...@vogelwarte.ch
www.vogelwarte.ch
 
Swiss Ornithological Institute | Seerose 1 | CH-6204 Sempach | Switzerland
______________________________________________________________

*** Hierarchical modeling in ecology ***

https://www.mbr-pwrc.usgs.gov/pubanalysis/roylebook/

[Jeffrey Doser]

Hi Singye,

I'm very sorry for my delay. Yes, your conclusions here for this analysis that using NNGP = 5 seems very reasonable given the WAIC results you present. You are also correct in that a lower number of neighbors is likely to be more suitable for long-range spatial dependence as opposed to very fine-scale spatial dependence. Basically, fine-scale spatial dependence is a more complicated pattern than long-range spatial dependence, and so for a more complicated pattern you will likely need more information (i.e., more neighbors) to get a good approximation. The number of neighbors you need will also increase with the complexity of the distribution of point locations in space. In other words, the less evenly distributed the points are across a study area, the more likely it is you will need more neighbors to approximate the spatial process.

Kind regards,

Jeff

--

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