Paired Sites

[Rory Macklin]

Hi all,

Thanks for the help on a previous post. I have a question about the best way to approach a paired count study design. The aim of the analysis is to ask whether there greater bird abundances at points in protected areas compared to nearby points outside of protected areas. I see two ways of testing this question with unmarked.

1. Put all counts into one model (currently using gpcount) with a categorical covariate on abundance desginating a site as protected/unprotected. Examine the coefficient of this covariate and draw a conclusion from there on the effect of protection. Issue: doesn't account for the likely spatial autocorrelation between paired points and essentially abandons the paired nature of the design (unless there is a method for this that I am unaware of).

2. Put all protected area counts into one model, and all unprotected area counts into another. Predict abundances at each point from each model, and use some method of comparing the predicted abundances between paired points to assess whether there is a consistent difference between protected/unprotected area abundances. This reduces the concern of spatial autocorrelation as points within each model then become quite far away from one another.

Does either stand out as a particularly superior approach? Any concerns or points that I am missing?

Thanks,

Rory

[Jeffrey Royle]

hi Rory,

 I would do the first thing simply because it should produce more efficient parameter estimates due to sharing information between the two samples.  It's unclear to me from your description whether the sites are meaningfully paired rather then just being "control" and "treatment" sites.  If the pairing really is meaningful you might consider using a random effect in the model. In this case, I believe, you can now fit those in unmarked using the TMB engine with pcount thanks to Ken Kellner. Also his package ubms using Stan will accommodate that type of model and of course you can always use JAGS or Nimble to fit such a model.

regards

andy

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[Rory Macklin]

Hey Andy,

Thanks for the input. The sites are certainly spatially clustered through the pairing, so I think its worth it to include some random effect for site. Is there any implementation of this through gpcount? You mention that the TMB engine solution is implemented for pcount, but as far as I can see this doesn't extend to pcount. I suppose stacking my data and using pcount might be the best solution?

Thanks,

Rory

[Ken Kellner]

Hi Rory,

That's correct, gpcount does not support random effects. You could stack and use pcount. The drawback there is that adds yet another grouping component to consider (i.e., the same sites across time in addition to the paired sites).

Ken

[Rory Macklin]

Hi Ken,

Would you then suggest fitting a random effect for each paired site grouping-year combination? For instance, site X contains paired counts and was surveyed twice in each of 2022 and 2023, so the "site identifier" that the random effect is fit to would then be siteX-2022 and siteX-2023. That makes the most sense to me, as within-year spatial autocorrelation is likely more salient than between year spatial autocorrelation.

Thanks for the input,

Rory

[Ken Kellner]

Thinking about it more I guess maybe you still just want one grouping level for each pair, and that gets repeated across years. So the two paired counts both have grouping level "siteX" in year 2022, and then "siteX" again in year 2023. I think that captures the structure?

Ken

[Rory Macklin]

That makes sense. To me, we want to capture spatial structure (that may be consistent between years, hence keeping the same site identifier) and temporal structure which differs between years. So having separate random effects on abundance for site and year would best capture this structure as I see it.

Do you agree?

Thanks,

Rory

[Ken Kellner]

Yes, that makes sense to me.

Ken

[Rory Macklin]

Great, thank you for your help!

Best,

Rory

[aw...@scenichudson.org]

Let me first acknowledge that Andy and Ken are light-years ahead of me in all things stats, and my stats training is more out of date each day.  But, I'm going to float an idea for the sake of discussion, knowing full well there may be excellent reasons not to use the below approach, which perhaps folks on this forum will chime in with: 

The initial goal is to determine whether abundances differ inside and outside conserved areas using paired sites (with the pairing design to account for spatial differences among site-pairs).  This sounds like a paired t-test to me: testing the null hypothesis that the mean of the differences between each pair doesn't differ from zero.  Could one run separate models for the conserved and non-conserved sites in Unmarked, then use predicted abundances, which account for detection, for each site as the inputs for a paired t-test or other "old school" test, or some Bayesian analog?  (Apologies for my ignorance of hypothesis testing in Bayesian frameworks).

-Alex