Detection probabilities with covariates, multi-method

[KerryK]

Hello again

I am using PRESENCE to look at the detection probabilities of two different survey methods using the multi-method technique. I have four surveys and two different methods.

My basic model is Psi(.), theta(.), p(method) so the detection tab looks like this (I believe this is correct looking at previous posts):

B1 B2
p[1-1] 1 0
p[1-2] 0 1
p[2-1] 1 0
p[2-2] 0 1
etc etc....

I would like to see how detection is affected in surveys 2, 3 and 4 if previous detections have been made. So I set up a survey co-variate tab, I put 0's in column 1-1 and 1-2 because these were the first survey and obviously had no recaptures, then a 1 or 0 in the other survey columns depending on whether the species had been detected in prior surveys.

My question is, how should I then set up the detection tab, so that PRESENCE selects the right column of recaptures for each survey and each different method and ignores the first survey... is this correct, where "rec" is the name of the covariate?

B1 B2 B3 B4 B5 B6 B7 B8
p[1-1] 1 0 0 0 0 0 0 0
p[1-2] 0 1 0 0 0 0 0 0
p[2-1] 1 0 rec 0 0 0 0 0
p[2-2] 0 1 0 rec 0 0 0 0
p[3-1] 1 0 0 0 rec 0 0 0
p[3-2] 0 1 0 0 0 rec 0 0
p[4-1] 1 0 0 0 0 0 rec 0
p[4-2] 0 1 0 0 0 0 0 rec

Many thanks for your assistance!

Kerry

[jhines]

How to set up the design matrix depends on how you want to model detection probabilities. You'll have to be more specific about what model you're trying to build in order to determine if the design matrix is correct or not.

B1 B2 B3 B4 B5 B6 B7 B8
p[1-1] 1 0 0 0 0 0 0 0
p[1-2] 0 1 0 0 0 0 0 0
p[2-1] 1 0 rec 0 0 0 0 0
p[2-2] 0 1 0 rec 0 0 0 0
p[3-1] 1 0 0 0 rec 0 0 0
p[3-2] 0 1 0 0 0 rec 0 0
p[4-1] 1 0 0 0 0 0 rec 0
p[4-2] 0 1 0 0 0 0 0 rec

Since your covariate, rec, can be zero or one, this design matrix will estimate the same detection prob for method 1 for all 4 surveys, and another detection prob for method 2 for all 4 surveys, when there are no previous detections. When there are previous detections, it will estimate a different detection prob for each survey and method. If this is what you wanted, then it is correct.

If you wanted a model where detection probs are different for each method and whether there are previous detections or not (so, 4 paramaters - p(x-1-noPrevDet), p(x-2-noPrevDet), p(x-1-PrevDet), and p(x-2-PrevDet)), then the design matrix would be:

Code: Select all

B1 B2 B3 B4
p[1-1] 1 0 0 0
p[1-2] 0 1 0 0
p[2-1] 1 0 rec 0
p[2-2] 0 1 0 rec
p[3-1] 1 0 rec 0
p[3-2] 0 1 0 rec
p[4-1] 1 0 rec 0
p[4-2] 0 1 0 rec

[KerryK]

Dear Jim

Thanks very much for your swift reply. It looks like I set it up correctly for the question I was asking, so that's a huge relief!

Many thanks again

Best wishes

Kerry