two species design matrix where pA = rA and pB = rB

[micah]

I am having trouble setting up the design matrix for a two species model where only pA and pB are estimated for detectability. Given our study species we think it is reasonable to assume that rA = pA and rB = pB and that species are detected independently (i.e., delta = 1), thus I cam up with the following design matrix.
pA(1) 1 0
pA(2) 1 0
pA(3) 1 0
pB(1) 0 1
pB(2) 0 1
pB(3) 0 1
rA(1) 1 0
rA(2) 1 0
rA(3) 1 0
rB(1) 0 1
rB(2) 0 1
rB(3) 0 1
Delta(1) 0 0
Delta(2) 0 0
Delta(3) 0 0
We then fixed delta equal to '1'. Is this correct? Is there a way to set rA and rB = to pA and pB in the fix parameters tab?
Thanks!

[darryl]

You have to do it through the design matrix as you've done here. The fix parameters tab is only for fixing them to specific numerical values.
Darryl

[micah]

Thanks Darryl,
One more question on design matrices. To account for the fact that species co-occurrence may result from two species reacting independently to the same environmental variables I have included several different habitat covariates in my models.
For the design matrix in two-species models I have been coding habitat covariates as '0' for phi and leaving them in the same column for psi A and B.

......b1...b2...b3...b4
psiA..1...0.....0....Ponderosa
psiB..0...1.....0....Ponderosa
phi...0...0 .....1....0

However, PRESENCE only gives an estimate for the psiA covariate in the output which makes me wonder whether it is actually being taken into consideration in calculating psiB. Should I be adding two columns for each covariate and estimating them separately for each species as shown below or is the above approach the more appropriate way to include habitat covariates into two-species models? What about including a habitat covariate only in psiA's row?

......b1...b2...b3...b4............b5
psiA..1...0.....0....Ponderosa...0
psiB..0...1.....0....0..............Ponderosa
phi...0...0.....1....0..............0



Thanks for the online webinars this week, they have been very helpful as well!
Best,
Micah

[darryl]

Yes, the latter. The first design matrix say that the effect of Ponderosa is the same for both species.