Request for Feedback on Detection Model Selection in spOccupancy

[arianna vicari]

Dear Jeff and spOccupancy group,

I firstly want to thank you for the availability and readiness with which you respond.

I am currently working on fitting single-season occupancy models using spOccupancy and would greatly appreciate your feedback on my approach and interpretation of results.

In the attached image, you will find a table summarizing several detection sub-models I tested. Each entry includes the detection formula, its ecological interpretation, and the associated goodness-of-fit metrics (Bayesian p-values) and WAIC scores.

For context:

• All models use the same occupancy formula, which includes all the covariates I plan to evaluate in the final analysis.

• The detection covariates include:

  • days: the number of camera trap deployment days (deployment effort),

  • site_id: a numeric identifier for each camera site (1 to X).

Based on the results, I have selected Formula 3 (~ (1 | site_id)) as the preferred detection model for both study sites. It yields consistently strong goodness-of-fit values and substantially lower WAIC scores compared to the naïve model. Additionally, for site B, I am concerned that using more complex models (Formulas 5 and 6) may risk overfitting, particularly at sites with few detections.  

I would be grateful for your insights on the following points:

1. Am I interpreting the ecological meaning of the detection formulas appropriately?

2. Is my procedure for selecting the best detection model methodologically correct?

3. Do you agree that Formula 3 is the most suitable for both sites? Or would you recommend a different model for site B?

Thank you very much for your time. I look forward to your feedback.

Warm regards,
Arianna Vicari

[Marc Kéry]

Dear Arianna,

I think your interpretations are correct. In terms of which model your inferences to base on I have two comments:

1. Adherence to the rule to take the best-predicting model, which is the one with the lowest value of the WAIC, should lead you to choose models 5 or 6. However, I think that these models are far too highly parameterized and I would rather not consider an occupancy model with fixed (as opposed to random) site effects in detection.

2. Based on GoF results the choice is between models 3 and 4. I would then base my choice on statistical commonsense and take model 4, assuming that detection probability per occasion must depend on the number of days during that occasion when a trap was deployed. ---- Having said that: what is your definition of an occasion ? Taking the number of trap days as a measure of effort within an occasion only makes sense if effort varies among sites and/or occasions.

Please note that it may be confusing to call both each of the two study sites a "site" and also the actual camera-trap locations.

Best regards  --- Marc

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______________________________________________________________
 
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/

[arianna vicari]

Dear Marc,

Thank you very much for the rapid response.

Regarding the first point, I agree with you a proceed with my modelling applying that.

For the second point, the camera traps sites (around 100 in both study areas) had different length in their deployment (from 40 to 100). This is why I wanted to include this covariate in the detection probability formula, as I am assuming that the longer a camera records, the higher the probability that the animal is captured. This covariate does not change through time, but it is an intrinsic characteristic of the camera trap station. 

Thank you also for the last comment, I am aware that site is not synonym of study area, it just slipped my mind while writing the email.

Again, thank you for the valuable feedback, and I wish you a nice day.

Kindly,

Arianna Vicari