2 species model psiBa parametrization

[gurutzeta]

Hi,

Could anyone tell me what are the parameters used in the PRESENCE "psiBa parametrization" of the 2species model? In the output file PRESENCE indicates that the parameters are:

"alternate parameterization requested: psiA,psiB1,psiB2,pA,pB,rA,rB1,rB2"

and it also refers to them as:

"psiA,psiB,psiBa,pA,pB,rA,rB,rBa"

I am not sure what psiB1, psiB2, rB1 and rB2 are and could not find any reference to this in the manual so I would be grateful if someone could give me a hint,

Thanks!
G

[jhines]

The alternate parameterization is a little different that the parameterization described in the book. Instead of estimating PsiA (Pr(occupancy by species A)), PsiB (Pr(occupancy by species B)), and PsiAB (Pr(occupancy by both species)), PRESENCE estimates PsiA, PsiB1(Pr(occupancy by species B, but not A)), and PsiB2(Pr(occupancy by species B and A)). The disadvantage of the original parameterization (PsiA,PsiB,PsiAB) is that it's possible to have combinations of those parameters which are impossible (eg.,PsiA=0.1, PsiB=0.1, and psiAB=0.9). The alternate parameterization does not have this problem. The alternate parameterization estimates the detection probabilities when both species are present (rA,rB1,rB2) the same way.

Take home message: If you have convergence problems with the orig parameterization, try alternate parameterization. If you need estimates from orig parameterization, convert estimates from alternate parameterization and use as starting values for orig parameterization.

Code: Select all

                                      Occ by B(psiB2)                   
                                     /
               Occ by A (psiA)
              /                      \
             /                         Not Occ by B(1-psiB2)
            /                     
N sites                                   
           \ 
            \                                 Occ by B(psiB1)
             \                              /
              Not occ by A (1-psiA)
                                           \
                                             Not occ by B(1-PsiB1)



[gurutzeta]

Hi Jim,

I was reading once again your previous message and I was wondering why you suggest to use the estimates from alternate parameterization as starting values for the original one. Isn't it enough to work with the alternate one? Can't we stop there?

In general, given that the alternate one is easier from the optimization point of view (i.e. less convergence problems in principle)... can't we just work with that one (and convert the parameters to SIF if needed)? Is there any benefit in using the original one?

Thanks!
Guru

[jhines]

If you are interested in the parameters in the alt parameterization, then there is no need for the orig parameterization. Or, if you only need the parameters from the orig parameterization, you can calculate them in a spreadsheet and compute variances using the delta method,(although lazy people like me might run the orig parameterization so I don't have to compute variances).

The situation where you have to use the orig parameterization is one where your hypothesis says that one of the parameters from the orig parameterization is a function of one of your covariates.