Site-specific probability of detection

questions concerning analysis/theory using program PRESENCE

Site-specific probability of detection

Postby saldanh » Sun Jul 11, 2021 9:06 pm

I have a monitoring dataset that consists of three visits to each site per year for several years. The data recorded are presence/absence data. I am trying to quantify detection probabilities specific to one site based solely on the monitoring data associated with that site. This would either be per year, or across years, but still only for one site .

From what I understand, PRESENCE produces an estimate of detectability for all sites, but can account for variation as it pertains to a set of a covariates. This is not what I am trying to do.

Is there a way to calculate what I am interested in within PRESENCE? If not, are there other resources I should use?


Thanks!!
Dan
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Re: Site-specific probability of detection

Postby jhines » Mon Jul 12, 2021 9:00 am

If you have data for only 1 site, estimating p is either impossible or trivial. If you have at least one detection, then you know the site is occupied and p=n/k (simple binomial), where n=number of surveys with detections and k=number of surveys (in each year). If you have no detections in a year, then it is impossible to distinguish between occupied with no detections and not occupied. So, you can't estimate p or psi, but you know their product is zero.

If you can use information from other sites to gain information about occupancy for the site you're interested in, then you would be able to estimate p.

You can use Presence to do the analysis by adding an indicator site covariate which has the value, '1' for the site in question and '0' for all other sites. Then run a model using that covariate for detection. In this case, the variation in detection as it pertains to that covariate IS what you want.
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Re: Site-specific probability of detection

Postby saldanh » Tue Jul 13, 2021 4:18 pm

Thanks for the quick and helpful response!

I am wondering whether instead of using information from other sites, you can use the the detection history from previous years from the same site to say something about probability of detection independent of other sites. For instance, if the detection history looked like;

110 001 111 000

Would there be a way of calculating an average P that applies across years while still using the data from the last year (ie. the 000 year)?

I am trying to keep my estimates of P for each site independent of what is occurring at other sites. If that is not possible, then the method you outlined in the previous reply is also useful.


Thank you!
Dan
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Re: Site-specific probability of detection

Postby jhines » Wed Jul 14, 2021 11:17 am

Am I correct in thinking that you want to estimate site-specific detection probabilities? With enough data, it might be possible, but I don't see any value in it. I don't think anyone expects detection probabilities to be exactly the same every site, but the reason to build models is to simplify what happens in the real world in order to try to understand it. The accuracy of the estimates depends on the quantity of repeated data going into them. It boils down to the accuracy vs precision trade-off. A single estimate of detection probability for all sites will be the most precise, but may be inaccurate for sites which are different from the average. Site-specific estimates might be the most accurate, but will be the least precise (and probably inestimable for many sites due to sparse data). You might find that you have estimates for each site, but the 95% confidence intervals span the entire zero to one interval for each one. A good compromise is to build a model where sites are grouped into a limited number of groups, where you assign each site to a group based on other information (covariates) which might affect detection probabilities.
If you only wanted to single out that one site from the rest, then my previous post would do the trick. You would create a site covariate (eg., “siteX”) where siteX=1 for the site you want separate detection estimates for, and siteX=0 for all others. Then, the design matrix for p would be:
p(1) 1 siteX
p(2) 1 siteX
:
p(k) 1 siteX
Since all p’s have the same design-matrix structure, they will all be the same (p(1)=p(2)=…p(k)), just as you wanted. The detection estimate for siteX will probably be way less precise than the estimate of detection for the other sites.
You can create as many different indicator groups as you need, but each additional group will decrease precision as each group will consist of fewer sites of data.
In the extreme, you have each site in its own group. The design matrix for p would be:

p(1) site1 site2 ... siteN
p(2) site1 site2 ... siteN
:
p(k) site1 site2 ... siteN

site1 is a site covariate which =1 for site 1 and =0 for all other sites.
site2 is a site covariate which =1 for site 2 and =0 for all other sites.
etc.
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