by **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.